General Physics and Mechanics (Unit 1)

excellent [Music] now in unit one we discuss General Physics and mechanics so things like measurements motion forces energy pressure moments and power stations and so on in this part this part one we&#39;re only going to talk about measurements in density mass and weight and gravity motion forces and momentum so that&#39;s what we&#39;re discussing today in this session so let&#39;s get started by looking at quantities and measurements first and at the beginning of every section in the revision sheet you&#39;re going to find this very small list this is a checklist that we use for revision like every sentence is exactly from the syllabus and the syllabus asks you to make sure you understand these points if you understand these points you have covered that portion of the syllabus some chapters sentences some chapters will have a lot more details they&#39;re just details but they&#39;re just Minor Details that you need to focus on so one of the best things to do on your own kand after we&#39;re done with the session that you read each sentence and make sure you understand what the sentence is trying to say if you understand it and you feel confident with it put a tick next to it okay okay if you&#39;re not very okay with a certain part of it you just go like uh maybe maybe you&#39;re not okay which means you need to either revise this or ask ask me about this and finally if you&#39;re not okay with something you say it&#39;s not okay which means you need to revise this study this again because it&#39;s going to give you trouble when it comes to problem solving what I&#39;ll do is I&#39;ll read the checklist with you and then I&#39;m going to start explaining things in the sheet so as we read through the checklist we&#39;re going to explain things through the sheet to make sure you understand and maybe go through a question if I found the suitable question for something let&#39;s start with quantities and making measurements this is a very short chapter it&#39;s not very relevant to it doesn&#39;t have its own set of questions it usually shows up as parts of other questions details in you need to be able to describe the use of rulers measuring cylinders to find length and volume so we need to know how to use rulers or we&#39;ll add a few other instruments to measure length and to measure volume how to measure a variety of time intervals using clocks and timers so you know how to measure time but we also need to know how to convert units of time finally determine an average value for the small for a small distance and for a short interval of time like the thickness of a sheet of paper small distance and the short interval of time the time of one oscillation of a pendulum we&#39;re going to apply in other chapters sometimes it&#39;ll be in unit two sometimes it&#39;ll be in unit four came in and we&#39;ll see that soon not very soon unit four but before we start every quantity in physics has a unit of measurement SI unit standard units answ in SI units unless the question changes that requiring the length is measured in what in meters time is me measured in what time is measured in what seconds Mass is measured in what kilograms temperatur is in kelvin how to change Kelvin to Celsius and back and current is in ampere we&#39;ve talked about electric current before and it&#39;s an a what about centimeters or millimeters and so on these are what we call prefixes from any unit to its prefix or from the prefix back to the unit the a for example you need to be able to convert from kilometers to meters or back so 1 kilometer for example is 1,000 M times a thand and from the meter back to kilometer you do the opposite action which is divide by 1,000 so we have three prefixes that are very important with two prefixes they&#39;re very rare we usually with variant and that&#39;s what you need to a focus on rarely but they do show up kilo means what times a th CTI means what divide by 100 Millie means what divide by th000 so I&#39;m going to give you a few examples of each Let&#39;s uh let&#39;s delete this and give an example of each one quickly if I have 3 kilomet convert that to meters if you have 36 CM convert that to meters if you have 28 mm convert that to meters so to convert from kilm to metimes 1,000 that&#39;s what the multip for 00 3,000 M from 36 cm to meters let divide by 100 that literally means divide by 100 so 36 over 100 is 0.36 M 28 mm to me remove M and divide by 1,000 so that&#39;s 0.028 m okay mister I want to convert them the opposite way met to kilm do the opposite thing which is divide by a th from meters to CM you divide sorry uh from meters to centimeters you multiply by or sorry oh multiply by 100 because when C divide so you do the opposite uh operation from millimeters to meter it&#39;s divide by th000 you from meter to MIM micro and what&#39;s Mega you almost never see them and we will only see them two maybe three times total the P papers variance but Mega is just a thousand thousand like it&#39;s a thousand kilometers and it&#39;s usually used with jewels or Watts suff for energy so Mega means times a million and micro right means divide by a million so keep them in mind when we start solving past papers in the Futures you will almost never see these two but you will see the rest let&#39;s move on to a few easier things how do you measure length uh with a ruler if it&#39;s up to a meter for very long distances use use a measuring tape the stuff that you spread out and a micrometer is what we use for very thin objects like coins and wires and thick cards right then what if you want to and this is up part three determine the average value of a small distance what if I want to measure the thickness oops of a sheet of paper the problem is that one sheet of paper is very thin so we measure more than one sheet we put several sheets on on top of each other you measure the thickness of all of the sheets so let&#39;s say it&#39;s 9 mm for example 100 sheets is 9 mm and then you get the thickness of one sheet how 9 mm / by 100 this gives you 0.09 millim for one sheet of paper which is very thin so this technique of measuring lots of a small thing than dividing by the number is very comp you almost always have to repeat and average your readings why because you can&#39;t really rely on the readings from one exact spot what if can air gap what if the paper is not perfectly uniform in thickness if I get a thin sheet of paper K it&#39;s not going to be equally a thick if you actually get a microscope and you check the thickness it&#39;s not going to be perfectly or equally a next he did ask us to talk about volume so what is volume volume is defined as the space occupied by an object how big an object is or how small it is and measuring volume depends on the substance you&#39;re measuring it&#39;s a liquid use a measuring cylinder just I have a cup of water here and I&#39;m going to use the hydrate all the time my nutritionist nutritionist was like at least drink two 2 lit of water a day like God help me I know I should but still but use a measuring cylinder for a liquid just pour it in this is what a measuring cylinder looks like for a regular solid a cube a square a cuboid a cylinder these have geometrical equations the most common is just length time width time height to get the volume of a regular cuboid or such but if I have a general uniform shaped object like a cylinder all right or a prism that&#39;s a triangle and then it&#39;s got a certain height the general area for volume is the area of the base times height the area of this base times height this is something you should have studied in geometry and we don&#39;t really use it often but keep it in mind because certain questions in electricity revolving around wires and the resistance of a wire crosssection area and the height it depends on those anyway finally how do you get the volume of an irregular solid like if I have a key for example I have a couple of keys here how do I get their volume we get it&#39;s called displacement we get a measuring cylinder pour some water inside and record this volume let&#39;s say it&#39;s 75 then you take your keys and you gently put it into the water the water level will rise in this case it&#39;s 125 so what&#39;s the volume of this rock or the keys that I put in it&#39;s 125 minus 75 which gives us 50 Okay so it&#39;s just three steps okay good next what about time well time is easy it&#39;s not a problem I just need you to remember how to convert hours to minutes that&#39;s time 60 and minutes to seconds that&#39;s times 60 and if I want to convert it backwards from six from seconds to minutes it&#39;s divide by 60 from minutes to hours you divide by another 60 so you can use stopwatches clocks timers it doesn&#39;t matter I&#39;m sure you know how to read a clock or to read a stopwatch that&#39;s not a particularly challenging thing to do but the challenging thing is how do I measure the time of one oscillation of a pendulum this doesn&#39;t just apply to pendulums though this applies to waves as well so what you learn here waves a pendulum it&#39;s just a thread and a mass that&#39;s allowed to swing I mean honestly a swing and like push you on the swing you are literally a pendulum you&#39;re just a living pendulum how do I find the time taken for a pendulum to finish one oscillation meaning starts here goes to the other end and comes back how do I do that okay I do that by measuring the time of 20 oscillations I do that by measuring time of 20 or 10 like at least 10 oscillations with 10 20 15 several oscillations and you divide the reading by their number sheets of paper so the technique to measure thickness oh sorry the thickness of a sheet of paper is the same Technique we use to find the time of one oscillation of a swing or pendulum which is measure the time then divide by the number it&#39;s always the time over the number of things or the value over the number of things it&#39;s like taking an average but it&#39;s not really an average after you do that it&#39;s always best to repeat your readings and take an average it&#39;s always best to repeat your readings and take can average okay why because it improves reliability makes your readings more reliable finally sometimes questions like these ask you to describe the entire process one of the precautions we use to ensure that our reading is accurate is to reset the stopwatch before we start making measurements I know it&#39;s very obvious I know it&#39;s very basic to you like it really shouldn&#39;t even be a point of question but it is that&#39;s the first part easy write measurements together let&#39;s talk about Mass because Mass affects what we call weight which is the force of gravity state that mass is a measure of the quantity of matter in an object at rest relative to Observer meaning this is the definition that he wants you to memorize if asks you in the new syllabus to Define mass okay we&#39;re not going to see a lot of definitions in our questions we don&#39;t actually ask you to define a lot but it&#39;s still there next state the weight sorry state that weight is a gravitational force on an object that has mass so it&#39;s the force of gravity essentially Define gravitational field strength as the force per unit mass and use the equation gal w m andise as in how do I calculate weight and what does g even mean and know that it&#39;s equivalent to the acceleration of Free Fall remember revision I&#39;ll send you this document and I want you to you know check these things as you understand them know that weights and masses can be compared using a balance so I can measure mass and I can compare language I can compare weights you don&#39;t measure weight with a balance you compare weights with a balance but you can measure mass with a balance describe and use the concept of weight as the effect of a gravitational field on mass gravitation field but first let&#39;s Define mass what is mass we know that mass is the amount of matter in an object how much stuff is in an object but if you&#39;ve studed studied chemistry at any level have you studied the mole before you can answer in chat yeah and if you remember the definition of mole it&#39;s the amount of it&#39;s a unit that measures the amount of a substance which is matter so Mass isn&#39;t just the amount of matter it&#39;s okay like even if you haven&#39;t studied it the mole is just a unit that measures the amount of a substance which is very similar to Kit amount of matter oh okay so what is mass mass is something that is one affected by gravity and two affects the [Music] what the motion of an object this is why we said it&#39;s a measure of the quantity of matter in an object at rest relative to an observer because when an object moves the mass affects that motion with the reason he says relative to The Observer and honestly it&#39;s not for o LEL it&#39;s because for higher level physics unless theory of relativity maybe if you&#39;ve watched Interstellar Mass actually is affected by motion it&#39;s not our thing but this is why he wants that kilit relative to observe he&#39;s keeping himself safe The Examiner is keeping themselves they&#39;re keeping themselves safe what do we use to measure mass a balance whatever the type of balance is the only technique you need to remember when measuring mass is how to get the mass of a liquid why because a liquid has no fixed shape you can&#39;t put it on a balance we put an empty container on a balance it gives us a reading we pour a liquid into the Container it gives us a second reading all right the difference between these two readings is the mass of the liquid that&#39;s inside okay very good so what do we do measure the mass of the empty container or the liquid inside and measure the mass of the container with the liquid calculate the difference between the two so that&#39;s Mass what&#39;s weight now we&#39;ve gone into the territory of forces a force is a push or a pull that has many different effects and the most common force that we experience every single moment of Our Lives unless our lives are like in outer space far away from planet Earth very far away from planet Earth is weight what is weight weight is defined as the force of gravity the gravitational force on an object planet Earth like any other planet or Celestial body like body in space has a lot of mass and attracts objects towards it that General force of attraction caused by a planet or a star on other masses that pulls other masses towards it is called gravity so the gravitational force is called weight like the the action itself is called weight the phenomena is called gravity why there&#39;s a difference in the phrasing oh this is my gravity it&#39;s not your gravity it&#39;s the gravity of the planet it&#39;s the phenomena of Attraction of the planet the amount of pull like the force of the pull that&#39;s what we call weight how do we calculate Weight here&#39;s your equation equation wal mg weight is equal to M so that&#39;s mass that depends on mass The more mass the more weight n g which is the gravitational field strength as in how strong the planet&#39;s gravity is the value of G on Earth that we have to memorize is 9.8 Newtons per kilogram the value of G is 99.8 Newtons per kilogram it also is equal to the acceleration of freeall which is what if you hold an object and you drop it like here&#39;s my pen and I drop it and it falls it will fall with an acceleration of 9.8 m/s squared it just so happens to be equal to weight uh sorry uh the gravitation field strength which is .8 discuss falling the concept of falling we&#39;ll discuss in a bit for now I want your only focus to be what weight what is it it&#39;s the pull of gravity on an object the gravitational force on an object and it&#39;s calculated using mass times G on Earth it&#39;s 9.8 other planets have different values of G we don&#39;t care we don&#39;t care about other planets we only care about Earth and field strength is the strength of Earth&#39;s field and it&#39;s defined as the force per unit Mass if you make G the subject W over m w over a m which is why it&#39;s defined as Force per unit Mass force over Mass that&#39;s if you make it the subject Newton per kilogram a unit that Force newon Mass kilogram now weight as a concept does not show up on its own a lot calculating weight shows up as parts of other questions it almost never shows up as its own idea it&#39;s part of other questions so when it comes to multiple choice questions I mean we can give you questions that are just about weight because questions are small on enough so these are two questions from the multiple choice paper paper two an object in space uh sorry an object in a space probe above Earth weighs 3.5 Newtons the gravitational field strength at the height of the space probe is 7 Newtons per kilogram here&#39;s a planet here&#39;s our planet and we have a probe I can say satellite think of a satellite and it&#39;s orbiting our planet As you move farther and farther away from a planet the gravity gets weaker so the G here is 7 Newtons per kilogram the gravitational field strength on Earth is 9.8 like the G on Earth is 9.8 what are the mass this is one question and the weight of the object on earth mass does not change I actually wanted to put that X on the change the mass of any object does not change okay so if I calculate the mass of this object when it&#39;s far away from Earth in space it&#39;s the same mass on Earth and when it&#39;s in space w g when it&#39;s in space g seven he has to give you the value of G if it&#39;s not on Earth Earth somewhere else you have to begin the value of G wal mg what&#39;s m w over g w 3.5 will G 7 3.5 over 7 which is half a kilogram if this is the mass in space in space probe it&#39;s also the mass on Earth so the answer is 0.5 that&#39;s either A or B then he asked me a second question what is the weight of the object on earth and I equation weight is mg we know the mass is 0.5 and we know that g is 9.8 on Earth not in space on Earth so 0.5 * 9.8 calculator I&#39;m working it out 4.9 so the answer here is B Mass W mg in space and then weight on Earth next which statement about mass or weight is not correct let&#39;s read masses can be compared using a balance this is a correct statement literally checklist mass is a force absolutely not mass is the quantity of matter of an object that rest relative to Ober weights can be compared using a balance yes they can balance weight is a force absolutely correct but what&#39;s the correct answer here B it&#39;s the only one that&#39;s wrong very good talk about something else that&#39;s also easy density yeah density and my favorite one of my favorite density jokes or questions is which is heavier a kilogram of steel or a kilogram of [Music] feathers and the trick is and they&#39;re the same they&#39;re both a kilogram exactly they&#39;re both a kilogram they&#39;re both 1 kilog and 1 kilog so volume and therefore their densities define density before we go density is defined as mass per unit volume recall and use the equation density is mass over volume describe how to determine the density of a liquid oh of a regular shaped solid okay and the regular irregularly shaped solid which sinks in a liquid including a appropriate calculations determine whether an object floats based on density we know that objects float in a liquid if it&#39;s less dense determine whether one liquid will float on another based on density data given that the liquids do not mix like I can pour some oil on water and I know these liquids don&#39;t mix if I see that the oil floats on water the oil is more less dense if oil floats on water is it more or less dense exactly first what is density it&#39;s the mass per unit volume basically the more dense and this is the symbol for density the more dense an object is The more mass it has and the smaller its volume basically think like a coin a metal coin whereas the less dense something is the less Mass it has and the more volume it has think of a balloon balloons are very large but they have very low mass almost less than can a the coin even though they&#39;re larger so density is just the ratio mass and volume and the equation is density equals mass or volume you don&#39;t have to say row because most of the time you just write it down so the pronunciation is not very important it&#39;s just density equals mass over volume the unit of density is either kilogram per meter cubed or gram per ctim Cub type how do you measure density well measure the mass and measure the volume but the trick isn&#39;t density when it comes to measurement the trick is how do you measure mass and how do you measure volume so if it&#39;s a regular solid object like a box how do you measure mass with a balance how do you measure volume length and width and height and calculate the volume and then calculate density m one what if it&#39;s a liquid oh well first I need a measure measuring cylinder and keep an empty measuring cylinder mass then we fill that measuring cylinder with the liquid you give Mass two so the mass of the liquid is Mass 2 minus Mass one and the volume is obtained from the cylinder volume and we also got the volume so what&#39;s the density mass over volume finally an irregular solid just like my keys as long as it&#39;s a solid how do you measure mass balance and if you want volume what do you use a measuring cylinder or some water put your keys inside the water level rises at ULU V2 minus V1 gives you the volume of this of these keys and that allows you to calculate density using mass over volume okay now we already talked about floating and sinking but I&#39;ll remind you why do objects float because they are less dense their total density is less dense than liquid why do objects sink because their total density is more than the liquid it&#39;s in so if I throw a piece of wood like a plank of wood in some water why would it float because it&#39;s less dense Sal but that&#39;s wood density value like let&#39;s say water has a density of 1,000 kilogram per met cubed and this wood has a density of 800 it makes sense that it floats and if I have a of Steel it will sink because Steel m has a density of around 5,000 kilg per meter cubed it&#39;s very dense so it sinks but how does a ship float a boat float when I make a boat out of steel how can a boat float ah it&#39;s no longer longer about the density of the material it&#39;s about the density of the entire object a total object what we do with a boat and steel boats is like what we do with a balloon we take it and we get a very thin layer of Steel and we bend it so that we fill it up with air inside this means that it has a very large mass but sorry a very small Mass I meant volum very small mass in sheet of metal is very thin but it takes up a very large volume less dense the reason why ships can float like if you go on a cruise or if you ride a boat they float [Music] because and the air inside and the people inside they take up so much space and the density which explains why ships can sink like the Titanic for example Titanic I hope you do I hope I&#39;m not too old to reference Titanic do you know the Titanic please Titanic do you know the Titanic yes aldah ald I&#39;m not too old yet do you know the Titanic was like No And then I will kill all anyway why did the Titanic syn ah I&#39;m explaining it now again why did the Titanic sink because overall it&#39;s made of a very thin sheet of Steel that&#39;s full of air so the density of the ship is not 5,000 like the steel it&#39;s a lot less than 5,000 it&#39;s a lot less than 5,000 we take that piece of metal we spread it out we make it super thin as thin as we can and still maintain structural Integrity so the reason it floats it&#39;s because it&#39;s less dense than the liquid but the reason the Titanic sank was because when it was broken into by the iceberg you&#39;ve got water flowing in so that started filling in the ship with water M but the volume of the ship did not so what happens to the density it increases which makes it sink goodbye Titanic okay so why do things float if they&#39;re not like a block but they&#39;re actually like a balloon blown up they in size because the air space in size increases the volume without increasing the mass the mass of the air is negligible so this decreases the density do you understand that is that clear just like a balloon other details as long as objects have the same material they have the same density I don&#39;t care if you have a small coin made of wood or a large door made of wood if you put them in water they will both float why because they have the same density if you put them on water they will have the same density because they&#39;re made of the same material wood the only thing that can change the density of any substance is temperature for unit two and unit 2 we&#39;re going to study something called thermal expansion if you increase the temperature of an object its volume increases the volume increases and according to the equation of density density is mass over volume if if the volume increases and the mass does not change the density will decrease Le because density and volume are inversely proportional that&#39;s their relationship Max they inversely proportional so the less then something is the more space it takes up this can happen due to thermal expansion that&#39;s why heating something makes it less dense and hot stuff can float like hot air balloon when I heat up the air in a hot air balloon it fills up the balloon with very hot air Which is less dense than the surrounding air like it&#39;s even less dense than the surrounding cold air so the entire balloon starts to float okay let&#39;s solve a quick question a rectangular swimming pool is 50 m long 25 5 m wide and has a depth of 2 m so now I have the length and the width and the height depth is another way of saying height the density of the water is 1,000 kg per M cubed what is the mass of the water in the pole uh what yeah well let&#39;s write this down density is mass over volume he wants Mass so mass is density times volume what density oh it&#39;s 1,000 what&#39;s the volume you have length you have width you have height so it&#39;s going to be length time width times height 50 * 25 * 2 what does that give us 1,00 * 50 * 25 * 2 cuz it&#39;s a regular shape it&#39;s like like a rectangular swing pool 25 00 0 so D is your answer any questions before we move on to scalers and vectors and slightly harder things any questions very good next let&#39;s talk about scalers and vectors what&#39;s a scalar and what&#39;s a vector let&#39;s check the checklist first understand that a scalar quantity has magnitude only and a vector quantity has magnitude and Direction so whenever we describe an object like or State a value of a property or a quantity some quantities only need a value to be understood for example if I tell you uh because of my poor diet the past few months I&#39;ve gained some Mass I&#39;ve gained 5 kilograms do the 5 kilograms that I&#39;ve gained care about Direction 5 kg 5 kg towards the forward backward so they don&#39;t need a direction to be understood but if I tell you for example uh somebody pushed me forward with a force of 100 Newtons you now know in which direction I&#39;m going to move and if I omit the direction sh Direction somebody applied the force on me with 100 Newtons and in which direction will I move forward or backwards left or right or up down I don&#39;t know you need to know what the direction is to know what the effect of that quantity is vectors scalar quantities only have size or magnitude know that the following quantities are scalers distance speed and time and mass and energy and temperature makes a lot of sense because none of these things care about Direction know that the following quantities are vectors force and weight weight is a force so it&#39;s a vector velocity and acceleration and discuss them through motion momentum also something we&#39;ll discuss today electric field strength and gravitational field strength we will study this in electricity but it does have a direction like because we draw an electric field from positive to negative electric Fields have a direction a d Direction but the gravitational field strength also has a direction because gravity acts towards the center of the planet it pulls you in so there is a direction I know it&#39;s constant but it does have a direction finally determine by calculation or graphically the resultant of two vectors at a right angle limited to forces or velocities what does that mean we already understand scal vector scalers are quantities like Mass 75 Kg it&#39;s my mass it doesn&#39;t have a direction whereas Force for example could be 100 Newtons to the right right our moments could be 30 newon met clockwise or anticlockwise you need the direction determine by calculation or graphically the resultant of two vectors at right angles as the and if I have two vectors like a 10 Newton Force to the right and a 10 Newton Force pushing an object up top right or forward and to the right if this was a ball for example this ball would move to the right and to the top somewhere for no but what we want is to find out deep C this is called the resultant the result of these two forces and I want to know what the value of this force is and the exact Direction and when I say exact Direction I mean the angle between the horizontal line and the line of the result so I know exactly how many degrees above or below or to the left or to the right it is so how do we add them we have two methods you can either calculate them my preferred method is calculation or you can draw what we call a vector diagram to find the resultant and here&#39;s how you take these two forces the 10 and the 12 we&#39;ll call them fub1 and F2 and then you draw them it&#39;s just a sketch one after the other head to tail you take the head of one arrow and stick it to the tail of the other if you close off this line or draw a line from the starting point to the ending point this will look like a right angle triangle which means geometry is going to start working by now we have something called the Pythagoras Theorem which states what do you guys remember the Pythagoras Theorem that a that b and this is C Pythagoras states that c^2 is equal to a 2 + B ^2 that&#39;s what the Pythagoras Theorem States this also applies to the resultant result hypoten this is called the hypoten resultant hypoten C this means that if I want the resultant C I can use square root a s plus b s that&#39;s squ that squ under a under root the resultant so that&#39;s the rule that you use the resultant force or velocity whatever it is is F1 s+ F2 ^ 2 under root a Pythagoras but we also said vectors have magnitude and Direction magnitude and tell you what like let&#39;s find out 12 my calculator square root 10 2 + 20 s uh sorry 12 s 20 square otk 10 s + 12 s this gives us 15.6 Newtons so this Force this resultant force is 15.6 Newtons okay Mr I want the direction angle D how do I get this angle over here I want the angle trigonometry for trigonometry we have three functions called the S and the cosine and the tan if this is a triangle and this is your angle Theta the opposite divided by hypotenuse is called s the adjacent divided by the hypotenuse is called cosine which is the ratio of these lines and the opposite divided by the adjacent is what we call Tan I don&#39;t care which one you use just pick one and memorize it s or cosine or tan but wait you want Theta you want the angle s Theta you want the angle or tan you want the angle but for example opposite is 10 F2 10 and fub1 is 12 so if I say tan theta equals opposite 10 over adjacent 12 to get the angle Theta shift because what I want is formula on one side to the other shift tan answer 39.8 de which is about 40° please be careful guys if you ever lend your calculator to an as student like it could be a sibling it could be a friend at school make sure your calculator has the letter D written on top in dark you know black because that&#39;s the unit of angles degrees there are two other units called radians and gradients so R and G so if you ever see RNG G on top please change your mode like literally press shift mode and click degree three on your calculator press shift mode and you&#39;ll find a few options just click the option for degrees which is three on this calculator finally how do you get the resultant vector by drawing I don&#39;t really like the drawing method it&#39;s time consuming but here&#39;s how you do it step one you need a scale and 1 cm is 1 Newton so we draw a scale diagram but for the resultant of these two forces 12 or 10 12 to the right or 10 up top you measure a line that&#39;s 12 cm long to the right and from the end of it you draw a line that&#39;s 10 cm high but to scale then to connect a line from that starting point to the ending point this is your resultant it&#39;s length to scale 16 16 cm which is 16 newon roughly so you measure it and you get it to scale finally dire Pythor trigonometry get a protractor in order to get the angle put it here and then just measure what this angle is lot like 40° roughly 39 40 somewhere like that and that&#39;s how you can get any resultant V VOR if they&#39;re at 90° and let me interject H for a second the syllabus changed in 2023 before the syllabus changed students were required to know how to find the resultant Vector of two vectors not at 90° at different angles this has changed it is now only vectors at 90° so let&#39;s look at a question from March 23 a boat crosses a river I always like to sketch by the way and why do I like to draw because it helps me visualize the question don&#39;t have to do it just in my head a boat crosses a river the boat points at right angles to the river bank so if this is a river for example like the river is this way and here&#39;s a boat and the boat is going up top because it travels at right angles any perpendicular to the a to the river at a speed of 3.5 m per second so it&#39;s traveling at a speed of 3.5 Ms per second the river acts at right angles to the boat and the river has a speed of 2.5 m/s meaning two vectors to the right of 2.5 the up top 3.5 and the resultant will be somewhere here which makes sense this means that the boat is not going to travel upwards boat travel somewhere to the right and upwards by drawing a scale diagram or by calculation see he&#39;s giving you the option determine the speed and direction of the boat relative to the river bank and relative to the river bank R relative the River Bank horizontal it&#39;s almost always the horizontal measure this angle let&#39;s call it Theta how do we solve this well I want the resultant when I resultant Vector our resultant velocity is square root 1 squ + 2 squ 2.5 S + 3.5 s this gives us 2.5 S + 3.5 squ this gives us 4.3 okay so that&#39;s the speed me/ second what about the direction H use any trigonometrical function you want I like tan thet is equal to shift tan tan minus one opposite over adjacent 3.5 which is the opposite of the angle like it&#39;s facing the angle over 2.5 and we&#39;ll shift tan 3.5 over [Music] 2.5 and that&#39;s 54.5 de 54° next uh speed is a scalar Quant and velocity is a vector State the names of one other scalar and one other Vector what else is a scaler mass mass is a scaler what else is a vector you have acceleration you have Force you have momentum all of these are vectors that was a mouthful for it next see we have a lot to revise for the motion almost guaranteed p l motion or movement and motion is actually very simple like if you think about it it&#39;s very simple see if details okay Define speed what is speed we know what speed is it&#39;s distance over time and recall the equation speed is distance over time speed is distance over time how fast you travel you can measure speed in meters per second or kilometers per hour that&#39;s depends on the question Define velocity as the speed in a given Direction meaning velocity speed with a direction a vector speed is a scaler recall and use the equation average speed is total distance uh divided by I forgot to slash here divide by total time so average speed is total distance over total time it&#39;s speed But it includes the time when the object stops so it&#39;s just total distance travel divide by total time and you get the median or the average or the mean speed so for example somewhere somewhere like I don&#39;t know on school in the morning the only thing I can think of think I think of a school right now and I drive 50 kilometers right in 30 minutes if I drive a distance of 50 kilom in 30 minutes half an hour if you calculate my speed with 50 over 0.5 which is 100 kilm per hour this makes no sense why because realistically half hour day I didn&#39;t travel at 100 to I had to slow down a bit for Speed bumps or stop for traffic lights or speed up even faster when I&#39;m on like a nice big open road it&#39;s like nice and wide and super free so I can just drive at 120 so usually when you calculate speed you do you are getting the average speed next sketch and plot and interpret distance in speed time graphs distance with speed time graphs determine qualitatively from the given data or shape of a distance or speed time graph when an object is at rest moving at constant speed accelerating or decelerating being able to look at a graph and tell what type of motion this is calculate from the gradient of straight line section of distance time graph calculate speed from it calculate the area under a speed time graph I&#39;ll stop here for a second because now he&#39;s talking about speed time graphs distance time a distance time graph shows you how distance changes over time if the line is going up you&#39;re moving at constant speed if it&#39;s horizontal you&#39;re at rest because you&#39;re not changing your distance you are changing the distance the slope of the line shows you the speed the steeper the line is like the higher the line is the higher the speed and the lower the line is the lower the speed which means slope gradient Y2 - y1 / X2 - X1 and if you take two points and calculate the gradient that gradient gives you speed but what if the line is not straight what if the line is curved right what if the line is curved a if it&#39;s curving upwards this acceleration if it&#39;s curving downwards it&#39;s not going physically down that it&#39;s just curving and becoming more and more horizontal less steep it&#39;s called deceleration so you can&#39;t actually calculate acceleration which is speeding up or deceleration which is slowing down from a distance time graph before we talk about the speed time graph let&#39;s Define acceleration what is it it&#39;s defined as the change in velocity over time change in velocity over time and keep in mind that the word change in something has a symbol which we call Delta it&#39;s a triangle so if I tell you acceleration is Delta V / T I mean it&#39;s a difference in speed over time the speed increase the speed could decrease still works increase and decrease is all called acceleration however deceleration is just the special name given to when speed decreases and since the speed is decreasing like if a speed is decreasing it&#39;s decelerating we call it negative acceleration we call it negative acceleration because you&#39;re not really accelerating positively you&#39;re accelerating negatively and your speed is dropping we just call it deceleration what about speed time graph what can we learn from a speed time graph well first this doesn&#39;t have to be speed this could be velocity by the way this could be a VT graph and it&#39;s exactly the same thing for now when the goes up that&#39;s called acceleration when the line is horizontal that&#39;s called constant speed when the line goes down that&#39;s called deceleration line is horizontal is at rest zero speed that&#39;s at rest which means the steeper a line is the higher the acceleration and the less steep Aline is the lower the acceleration steeper means more change in speed over less time so what do we call this the slope that slant is the slope and the slope is the acceleration but I could use Y2 - y1 / X2 - X1 to get the acceleration of any line but there was another thing another very very important thing whenever you solve questions involving speed time graphs he would usually ask for distance you would usually ask for distance and we know that distance is speed times time this speed is not always constant for graphs instead rearrange distance speed times time when speed with time because the speed is not always constant we have to resort to another method calculating distance only from a speed time graph and that&#39;s by getting the area of the shape under the line so if I take this shape and I split it up and the triangle and and the square or rectangle okay if you calculate the area of the shape of this triangle using the numbers from the graph triang if I get the area under the graph here so as a friendly reminder triangles half Bas time height a rectangle is base time height a trapezium is half base 1 plus base 2 * height next finally if the line can curve any of these lines can curve this means that acceleration doesn&#39;t have to be constant if the line slopes upwards it&#39;s called increasing acceleration because the slope is increasing because it becomes steeper whereas this is called decreasing because it becomes less a steep I don&#39;t know why it&#39;s so thick just give me a second yeah finally a regularly shaped line when the slope is becoming steeper speed a increases left the acceleration increases and it&#39;s accelerating us it&#39;s already speeding up but the increase in speed is even higher with this decreasing acceleration speed Z with the decreasing amount you is it 0 10 20 30 the constant zero 20 and then 25 and then 26 this decreasing acceleration that change in speed is not increasing it&#39;s decreasing if the line is going down this means you&#39;re decelerating you&#39;re slowing down so if the slope is becoming steeper it deceleration with zed and slope less steep deceleration with a very good any questions so far acceleration before we head into forces and because it&#39;s got a lot of questions that we want to solve it&#39;s just forces and momentum but first let&#39;s solve this question a car accelerates uniformly in a straight line from rest at a time of zero I want to change the color to Red there we go at 3.2 seconds the speed of the car is 13 m/ second so you have the time you have the starting speed it&#39;s at rest and you have the final speed what what&#39;s the acceleration acceleration is change in velocity over time Delta V and change in velocity so the velocity was Zero it became 13 it&#39;s 13 minus 0 over how much time is this 3.2 seconds you pull out the calculator F 13 IDE 3.2 this gives us 4.0 625 huh how many significant figures should I write my final answer what do I like how many significant figures do I have to write three you must stay consistent and use three significant figures round up if you have to but D6 two two won&#39;t round up the six so it&#39;s 4.06 m/ second squared Why is it meters per second squared because acceleration units are m/s over second the m/ second per second m/ second squ okay explain in words what&#39;s meant by the term acceleration what is acceleration the change remember what&#39;s the definition of the change in velocity per unit time okay next the car travels at 13 m/ second from a time of 3.2 to a time of 12 seconds so it&#39;s giving me the time and the speed which is constant plot the speed time graph from 0 to 12 going back he said that it starts at rest time zero and at 3 2 it&#39;s 13 and it accelerates uniformly so from zero so from zero to how many seconds sorry oh there we go from 0 to 3.2 that&#39;s how many 20 seconds it accelerated to 13 which means from0 to 3.2 mister I can&#39;t see the 3.2 I can&#39;t read the scale it&#39;s getting blurry so what do I do every you need to find out every small square became like what&#39;s every small square if oh 10 small squares there four which means every small square is 0.4 0.4 0.8 1.2 1.6 2 so what does he want again why is from 0 seconds to 3.2 seconds in 3.2 okay that&#39;s two it&#39;s 2.4 yellow 2.8 3.2 for 3.2 a again DET distance traveled by the car from 0o to 3 oh sorry plot a gra from 0 to 12 3.2 speed of 13 so we go up to 13 and we Mark a point just for me because I know it&#39;s going to accelerate from 0 to 13 and then from 13 to 12 12 it travels at the speed of 13 which means constant speed but here&#39;s what I will draw straight line going up because he said it accelerates uniformly K it uniform wait k it uniform means at constant a rate so constantly uniformly and then it&#39;s constant speed until 12 so he wants this plot from 0 to 12 G plot Mister we&#39;ve drawn what does he want determine the distance traveled by the car between 0 and 3.2 seconds what how do you get distance in G area under speed time graph we get the area under the speed time graph when I want distance what I actually want is the area under the graph what shape is this the trapezium so I can use the trapezium rule I can say base 1 plus base 2 over 2 * height but does he want the entire graph thank you very much huh do you see do I want the entire graph I would use this that I wanted the whole graph he doesn&#39;t want the whole graph he only wants it until 3.2 so if I close this off till 3.2 what&#39;s the area of this shape ah he wants the triangle I would have used the trapezium if I wanted to get the whole thing but I don&#39;t I just want the triangle so it&#39;s halftimes base times height that&#39;s halftimes 3.2 * the height which is 13 how do I know it&#39;s 13 because again this was given to us earlier in the question5 * 3.2 * 13 this gives me 20.8 see how we get the area under the graph so you&#39;ve now seen how to use the equation for acceleration how to get the area under the graph how to plot a graph Define acceleration these are some of the very important things to keep in mind okay now before we move on to the last two sections which is forces and momentum we&#39;re going to take a short break let&#39;s continue let&#39;s talk about forces so what is a force we know that a force is a push or a pull it has many different effects like you know changing the motion of an object or the size size and shape of an object all of these are effects of forces so let&#39;s look at the checklist quickly know that that forces May produce changes in size and shape yeah Springs like that&#39;s the main thing sketch plot and interpret so you should be able to draw this or plot points if I&#39;ve given you a table and interpret as in understand and explain a load extension graph for an elastic solid and describe the associated experimental procedures like the steps that we take to do this and uh where is it Define the spring constant as a force per unit extension and recall the equation K = FX and Define and use the term limit of proportionality for a load extension graph and identify this point on a graph an understanding of the elastic limit is not required you&#39;re going to notice something in a bit regarding the term elastic limit and limit of proportionality but let&#39;s first explain this how does a force affect shape and size if you have a spring you apply a force on that spring that spring will will stretch as in it will get longer the greater the force the greater the stretching of that spring and that stretching is called the extension that increase in length is called the extension right so force and extension are proportional Force increases extension increases Force decreases extension decreases very good how do you get the extension you take the total length that you&#39;ve measured minus the original length of the spring and the difference is the extension but here&#39;s the thing every object like a spring has a limit if you stretch it too far and you let it go it will not go back to its original size or original length this means that it has exceeded what we call the limit of proportionality or what we can for now call the elastic limit the Mr Leo like why is it up here why up here sorry uh did he say an understanding elastic limit is not required because when you start studying as and A2 and college level physics you start realize that there are two different points like there&#39;s a point called the limit of proportionality and another called the elastic limit they&#39;re very close and they have very similar features but for now in O Lev we&#39;re going to assume they&#39;re the same thing right so elastic limit and limit of proportionality are the same thing for us if you plot a graph of force and extension it&#39;ll be a straight line why because it&#39;s proportional but after the limit of proportionality the line stops becoming straight and it starts to curve now keep in mind it will always curve towards where the extension is so if the extension is on the x-axis it curves to the right if I draw the same graph but the force and extension extensions on the Y y AIS it&#39;ll be straight and then it&#39;ll curve up extension okay this is called hooks law now what is the spring constant that he&#39;s talking about the spring constant is defined as the force per unit extension in engineering if you remember we said that this actually represents what we call the stiffness of the spring how tough a spring is the higher this value is the harder it is for you to stretch a spring it needs more Force per extension needs more Force per centimeter or per millimeter and the lower this is like if you have a very weak spring weak materials like plastic Springs they stretch very easily they have a low spring constant so how do you calculate it k equals FX but I prefer to remember this equation like this FAL KX and you can just rearrange it you can rearrange it to K = FX or calculate X which is the extension and so on now that&#39;s basically it when it comes to the effect of forces a on the shape and size of an object what about the effect of forces or sorry the resultant of forces in a straight line this is very straightforward compared to the previous thing if forces are in the same direction you add them if forces are in opposite direction you subtract them and the resultant direction is always in the direction of the larger Force so n is to the right you the resultant is to the right next what is friction a very important Force because the rest of our discussion here is about movement and motion so what is friction there are two different types of friction solid friction which is the friction between two two surfaces like if you put your hands on each other and you start rubbing them this is what we call solid friction when one surface moves relative to another but they&#39;re in contact with each other you experience a resisting Force meaning it tries to slow you down if you&#39;re the one moving that friction depends on the roughness of the surface if it&#39;s rough there&#39;s a lot of friction if it&#39;s smooth or if you put a lubricant on the surface like oil it&#39;ll slip and there will not be friction additionally friction is a force that produces heat the friction produces heat because it&#39;s a very common thing when we start discussing energy next time because when we press the brakes the brakes do what they slow down your car how do they slow it down by converting kinetic energy into heat energy or thermal energy but if you have friction with water or air we call this drag water or air resistance is called drag it&#39;s exactly like friction but it&#39;s not between two Solid Surfaces it&#39;s between a solid object and a liquid which again is basically friction but with a liquid or a gas water and air resistance or drag depends on two things your speed and your surface area the faster an object is moving like for example if you have an object that is fall through the air the faster it moves the more drag or air resistance act on and the larger it is the more a resistance or drag it experiences so it depends on your surface area and your speed finally let&#39;s get into motion what is Newton&#39;s first law now you don&#39;t have to memorize the law or the statement but you have to understand it and be able to describe the statement here&#39;s the statement an object either remains at rest or continues in a straight line at a constant speed unless acted on by a resultant Force what does that mean this means that if there is no resultant Force forward equals backwards and they cancel each other out an object either stays at rest or moves but at constant speed if the object is at rest already it stays at rest if an object is moving it continues to move thank you very much I know my art is fantastic so please don&#39;t feed this to an AI okay we&#39;re going to ruin AI art forever or maybe do if you don&#39;t like AI art that&#39;s another story but anyway the opposite of this statement is this if there&#39;s no resultant Force you&#39;re at rest or you move in a straight line but what if there is a force and this is very important what if there is a force if there is a resultant force acting on an object the object can change its speed you can change the velocity by either making it move faster or slower you can change speed or you can change direction to simplify this you have three cases if the resultant force is forward you speed up if the force is backwards air resistance driving force for example you slow down and if the force is sideways it&#39;s not forward and it&#39;s not backwards you change a direction this is like turning your steering wheel or turning your a uh steering wheel on a bike what what happens you turn your wheels to the side which creates a sideway force and that Force changes your direction that&#39;s the first law what&#39;s the second law it&#39;s an equation f equals m a force is equal to mass times acceleration that&#39;s literally it it&#39;s it&#39;s just a very important law because we use it a lot but keep in mind keep in mind in it must be the resultant backwards resultant so what does this mean this means that any resultant force acting on an object causes it to accelerate which makes sense because first resultant Force you speed up Force you slow down this is called acceleration resultant Force sideways and you change direction this is still considered acceleration because motion acceleration was defined as the change in velocity over time change in velocity includes change in Direction Change in speed it also includes change in a direction okay now the force and acceleration are always in the same direction acceleration is a vector which means it has a direction the direction of the acceleration is in the same direction of the force they are in the same direction next what about circular motion this is a special version of what we talked about here if a force is sideways not forward or backwards if a force is sideways this causes you to turn if you keep that sideway Force you continue to turn until you move in a circle we call the circular motion so what causes it it is caused by a force acting perpendicular to the direction of motion and you&#39;re moving to the right it&#39;s downwards or to the right and you&#39;re moving forwards but it always acts towards the center of the circle you&#39;re going in so if you&#39;re going in a circle the force is always towards the center of the circle this Force depends on three things your speed the radius of the circle and your mass the faster you move like at I&#39;m in a car I&#39;m driving I am pressing the gas pedal I&#39;ve turned my steering wheel a certain amount I move in a circle if I press the gas pedal and I start moving faster I need more Force to stay in my circle like if I&#39;m moving faster I have to turn my steering wheel harder and I need to apply more Force like the car has to apply a bigger sideway Force to stay in a circle or if I&#39;m moving at the same speed if I&#39;m moving slowly but then instead of going around a big circle urn which is a very short turn like very start hard turn you need to turn very hard I need to turn the steering wheel a lot to create a very big sideway Force so if the radius of the circle decreases you&#39;re going in a tighter Circle you need more Force and finally what if you&#39;re not driving a car what if you&#39;re driving a big truck truck Furniture bricks whatever it is your truck is very heavy because you have more mass you need more for which makes sense because mass as a property makes it harder for you to move again mass as a property makes it harder for you to move the more mass you have the more Force you need to make you turn so keep these in mind but can I say something really quick circular motion as a concept doesn&#39;t show up in questions a lot you look through M the past seven or eight questions variant in 2023 and 2022 and 2021 it doesn&#39;t show up on its own a lot usually it&#39;s a multiple choice question maybe it&#39;s like part of a little question but it doesn&#39;t appear a lot so it&#39;s not a very very important part of this chapter but it&#39;s there you need to revise it and let&#39;s move on to the last bit of motion this one is very easy falling objects if you drop an object and you allow it to fall and there is no air resistance as in vacuum it falls at a constant acceleration of 9.8 m/s squared which is the acceleration of Free Fall G this is just like the value of G because if there is no air resistance the only force acting on an object is weight and the weight causes it to accelerate at 9.8 m/s squ that&#39;s if the question says there&#39;s no air resistance air resistance is ignored you&#39;re falling in a vacuum it falls with a constant acceleration have a nice day there&#39;s nothing else to explain but if an object is falling through air like a sky diver for example and there&#39;s air resistance any object falling through air experiences three different stages of motion stage one when you just start to jump you like you&#39;ve just jumped there is only gravity acting on you so what do you do you fall with a constant acceleration so this is the sentence you say only weight acts on the object downwards so the object falls with a constant acceleration resistance depends on your speed So the faster you start to move the more air resistance starts to act on your body so as your speed increases the air resistance increases I&#39;ve mentioned the direction huh direction is very important so the downward resultant Force decreases wait 100 80 Newtons the resultant is now 20 when before it was 100 Newtons pulling me down now it&#39;s 20 now it&#39;s 10 now it&#39;s zero eventually your air resistance increases and becomes equal to the weight so they cancel out and what did we say happens resultant Force you a zero you move at a constant speed when the air resistance is equal to the weight the resultant force is zero acceleration is zero you move at constant speed this speed is called terminal velocity speed terminal velocity if I ask you to draw a speed time graph for this motion this is what it should look like it shouldn&#39;t be colored obviously you just draw it with your black or blue or pencil black or blue pen or a pencil but the first stage doesn&#39;t take a lot it&#39;s just a quick straight line Le because it&#39;s you know constant acceleration then this line starts to curve downwards my decreasing acceleration like we said earlier earlier and finally you move at constant speed constant speedly because air resistance is now equal to weight as an extra thing which sometimes shows up if we have a parachute like if I&#39;m skying with a parachute and I open the parachute the moment the parachute opens I slow down and I drop to a new constant speed why do I slow down like why would I slow down if I open a parachute because the air resistance is more than the weight the weight is less than the air resistance so you start to slow down you don&#39;t go upwards you just slow down suddenly then you move at a new constant speed let&#39;s solve a couple of questions some of these are super hard by the way like this this question is actually very hard like I chose a very hard question to solve on purpose this is from June 22 variant 2 figure 2.1 shows an object of Mass 2 kilograms on a bench so it&#39;s a 2 kilogram object the object is connected by a cord over pul to a 3 Kg object the 2 kilog object is released and then it accelerates at four accelerate why would it accelerate accelerate to the right with an acceleration of 4 m/s squ acceleration with an acceleration of 4 m/s squar to mister you just said in when an object falls and there&#39;s no air resistance be acceleration 9.8 that doesn&#39;t work here because there is a force resisting you it&#39;s not air resistance not yet at least it&#39;s what it&#39;s this object tension C we pull it up even though they&#39;re both falling it does apply you know a stretching upward Force so the 3 kilog object two forces the weight of the 3 kog object it&#39;s not friction or you could consider it friction me okay if there&#39;s any friction I&#39;m not sure because he didn&#39;t say if there&#39;s a rough force or not but I do know and there&#39;s tension here because this is a thread or a string that&#39;s is stretched but the thread itself is a pulling it up I don&#39;t have enough data to say if there&#39;s friction but it&#39;s a good thing to assume and I don&#39;t need that assumption upward Force F the resultant Force makes you accelerate with 4 m/s Square like I&#39;m just going to answer each question separ calculate the resultant force acting on the 2 kog object fals M Force 2 kg 4 eight came newton8 Newtons but it shed with resultant force of 8 Newtons that&#39;s all we&#39;re saying Cate the upward Force this is the hard question exerted by the chord on the 3 kog object you need to understand two things first this 3 kilog object exper expences two forces weight will upward Force F okay it&#39;s a very bad I don&#39;t know why called it and second and second in this object is moving with an acceleration of 4 m/ second because he said they&#39;re both connected and if they&#39;re both connected they&#39;re moving with the same acceleration and if they&#39;re moving with the same acceleration it&#39;s four but this mass is 3 kilog step one I&#39;ll do what I can which is force [Music] I which is mass time acceleration if I say 3 * 4 which is 12 Newtons would F this is weight minus F object it&#39;s falling downwards I can guarantee you up I can guarantee he&#39;s moving at constant speed he said it&#39;s accelerating 12 because remember fals M A give resultant Force give it a resultant force wus not directly directly weight weight questions don&#39;t show up on their own a lot but weight questions show up in the middle of other questions M which is 3 kilog times in 2022 G can new per kilogram 9.8 this is new syllabus starting 2023 9.8. weight 30 Newtons and W 30 Newtons minus FAL 12 fals a 30- 12 18 18 okay this is a hard question why you needed to use FAL ma to get the resultant of a weight will upward force and second you need to understand and if you weight we upward force and their difference is 12 Newtons then you need to get the weight of the block this is a separate question so you get the weight 30 - 12 the objects have a constant access acceleration show that the speed of the objects 0.08 seconds yeah that&#39;s time after release is 3.2 L speed the wait if they have a constant acceleration acceleration before rule just write down the rule acceleration equals change in velocity over time therefore change in velocity is equal to acceleration time time acceleration before will time of 0.8 4 * 0.8 3.2 m per second he wants to see the working show questions mean you need to show the working finally a card of width 2 cm the distance is fixed to the 2 kog object in Mass maybe I don&#39;t need it maybe I do as the 2 kog object moves to the left the card passes through a beam of light that is perpendicular to the card basically we got a laser pointer once we press the button creates a laser and then this object has a card sticking out of it this block has a card sticking out of it and as the block is being pulled forward this card cuts the laser like it touches the laser and it cuts the laser K use the speed given in CI which is 3.2 to calculate the time taken for the cart to pass through the beam of Light how long is the card I should pass through the beam of Light 2 cm how long is this card two cmers and how fast is it moving 3.2 what does he want time speed is distance over time equation speed therefore time is distance over speed the distance is 2 cm wait to change from C meter you divide by 100 okay over speed 3.2 0.02 3.2 0625 0.00625 seconds okay okay okay let&#39;s move on uh I&#39;ll answer that right after the session okay finish up momentum vectors Springs because we have to finish this and momentum and then when we&#39;re done I&#39;ll answer your question okay a force is a vector quantity state two features of a vector this is easy vectors have magnitude oh wow okay okay sorry uh that&#39;s huge have magnitude and Direction State the names of two other quantities that are vectors so he said Force so we could say velocity we can say acceleration they both work okay actually I want this question for this a student suspect a spring from a clamp stand and measures the length L the student then suspends loads of different weights from the spring and measures the length of the spring for each load this is the experimental procedure that we follow expansion extension length and so on he then plots a graph of the length of the spring against w weight figure 2.2 is the graph the students plot they ploted the graph if I look at the line it&#39;s curving upwards the limit we can easily tell that the limit is somewhere here because that&#39;s when it stopped being straight or maybe here but let&#39;s continue use figure 2.2 to determine the initial length of the spring to Y AIS is not extension it&#39;s length so the original length original length or initial length is the length of the spring at a force of zero oh uh well I don&#39;t know how to read the small square .02 this is after five squares this is 0.1 s012 0.2 since each one small square is 0.02 but the answer is 0.12 I need to I need the unit it&#39;s meters from the graph it&#39;s meters next state what is meant by the limit of proportionality and determine the weight of the load that causes the spring to just reach that limit here&#39;s how we Define it it is the a it is the maximum the maximum force or low after which the spring does not return to its original limit to only after which the spring no longer obeys Hook&#39;s law or does not extend proportionally the limit of proportionality what is the weight liity so like we said we&#39;ll look at the graph oops and we&#39;ll see when did it start it is the force not at which after which the load force is no longer proportional to extension you can okay after which they&#39;re not proportional now there it is uh this was straight and I want to show you a trick I do cuz sometimes you know what graphs are not very clear value what I do is I put my ruler on the line line and then value when the line started to curve away from the ruler this is good this is very obvious so I go down down down down down this is should use a ruler it&#39;s not 11 it&#39;s what it&#39;s 10.8 it&#39;s 10.8 this is what I like to do I put a ruler down when did the line start to deviate away from the ruler because it&#39;s sometimes hard to see with your eyes cuz Mister can&#39;t I just say 10 look it&#39;s nice and easy oh but it&#39;s still straight after 10 11 you mis it&#39;s easy you&#39;re right it&#39;s it&#39;s it&#39;s curved at 11 but when did it start to leave the line the the straightness of the line so 10.8 next determine the spring constant of the spring a to find the spring constant K is equal to F over X what is f f liit so choose any point on this graph and I would prefer to choose a point where the intersection is nice yeah like the line intersects at a really good point it&#39;s a very annoying graph s so let&#39;s say I like this one this is clear to an extent this is a nice intersection here this is also a nice intersection this is also a nice intersection like what I&#39;m looking for is an intersection where it&#39;s not like halfway through a square or a quarter way through a square or like kiding like this is an okay intersection board okay on looking at a graph that&#39;s printed in front of you is so much easier on the eyes compared to a screen or a monitor&#39;s let&#39;s pick this point let&#39;s pick this point pick any point force and extension force and 1 two 3 four five so this is 5.2 Han 1 2 3 4 5 this is 0.34 the mister is this the extension extension 0.34 like this is the force 5.2 Newtons extension length in order to get the extension extension is what original length minus it total oh total length minus original length so if I decided that this is my point to use you can use any other point but if this is my point to use the length extension sorry is not 0.34 it&#39;s 0.34 minus 0.12 and 5.2 by 0.34 minus 0.2 2 23.6 or so 23.6 what&#39;s the unit unit a table Newton for the force per divided by x x can be meters on the graph I said table accidentally earlier I meant Li a graph length is M and weight is n so it&#39;s n over M because it&#39;s Force overextension very good last bit this is a very small bit by the way like momentum is very simple because what is momentum momentum is just mass times velocity there&#39;s nothing special about it it&#39;s just masstimes velocity Newton velocity he multipli them and how do we calculate them how how do we calculate momentum it&#39;s Mass velocity so the definition is the equation or the equation is the definition the symbol for momentum is p but if you don&#39;t like it don&#39;t use it like M what is momentum Mass velocity the unit of mass is kilogram and the unit of velocity is meters per second so momentum is kilogram m per second what is impulse impulse is when you apply a force on an object in a very short time like you smack an object you hit it very fast that&#39;s called an impulse and it&#39;s calculated using force times time ft force times time both of these equations momentum have Force mass times velocity which is how much okay of course uh how much movement an object has and I have a truck at the same speed we say that the giant truck has more momentum more motion more movement simply because it has more mass it&#39;s harder to stop and that&#39;s what momentum is how hard it is to stop an object from moving depending on its mass and velocity impulse impulse is force time time momentum is mass time velocity these two are related because of a rule resultant Force Newton&#39;s Second Law or resultant Force defines resultant Force as change in momentum over time but this is the original Second Law in force is equal to the change in momentum over time if force is changing momentum over time Delta m t but ft equals change in momentum this means that impulse is also equal to the change in momentum impulse is equal to the change in momentum as a meaning because a lot of questions will ask you to calculate momentum and then ask you to State the impulse he or I can ask you to calculate the impulse but you only have mass and velocity so what do you do you calculate change in momentum they are the exact same thing in terms of calculation but in terms of definition impulse is force times time and momentum is mass times velocity and what is force change momentum over fine but you also need to know how to use this the principle of conservation of momentum and solve simple problems simple is uh in quotes because some questions are not simple as I&#39;ll show you in a bit in one dimension what is the principle of conservation momentum it states that the total momentum of a a closed system is always conserved or constant meaning the total momentum of the two objects before they Collide if you calculate the momentum of the objects before they Collide and you add them up so in this case it&#39;s m * UA like the velocity and mass of this object before the Collision Plus the mass times velocity of this object after before the Collision as well M Au UA plus MB U equals like when they bam Collide the sum of their momentums after the Collision total momentum is conserved is constant and before equals after but if I calculate the momentum of the objects of each object separately before and after the Collision before totally equal after so look at this formula m a UA plus MB U equals m a v a plus MB VB for example z z and we cancel it out and if a question gives you mass and U and mass and V and mass but not VB you try to find it and this is the LA this is the law and this is the law the exact same scenario an object called a that&#39;s going to hit an object called B okay truck a this is from June 2016 okay truck a of mass 6,000 kilg is moving at 5 m/s it is approaching a truck B of mass 5,000 kilog which is stationary calculate the momentum of truck a so this is a simple momentum question first like he was like hey here&#39;s truck a what&#39;s the momentum so mass time velocity which is 6,000 * 5 6,000 * 5 so that&#39;s 30,000 30,000 what unit mass time velocity so kilogram time met per second so kilogram met per second if you want to put a dot put a dot next the trucks Collide their buffers compress and they bounce off each other remaining undamaged after the Collision truck B has a momentum of 27,000 he kind of skipped a a few steps and he said hey after they collided and truck a a but I know [Music] Tru with a momentum of 27,000 kg M momentum a what was the momentum of truck B before the Collision like before it was hit uh zero if it&#39;s stationary and it&#39;s not moving it has no velocity momentum was Zero now the momentum is 27 determine the impulse we know that impulse is force times Time s but we also said that impulse is changing momentum I don&#39;t have force or time but I do have the momentum I even have the change in momentum okay I even have the change in momentum because the momentum before it was hit was Zero the momentum after it was hit is 27,000 so what&#39;s the change 27,000 minus 0 27,000 kilogram m per second it&#39;s 27,000 kilogram meters per second yeah it&#39;s two marks but it&#39;s the same answer all he needs to see is oh impulse is change in momentum and the change momentum is 27,000 I don&#39;t need even have to calculate next the trucks are in contact for 0.6 seconds it&#39;s giv me time the only formula momentum is force equals change in momentum over time this is the only formula with time okay this is the only formula with time what&#39;s the force change in momentum over time impulse impulse is force times Time Force is impulse over time I already have the impulse 27,000 I and I have the time 0.6 27,000 IDE by6 45 th000 45,000 Newtons how I use this like how did I work this out impulse divide by time listen you need to memorize the formulas you need to memorize so you can put them down and choose the correct one based based on what the previous value was calculate the final speed of truck a calculate the final speed of truck a this is the last thing I&#39;ll solve I know there&#39;s one more question left I&#39;ll let you solve it on your own and we can revise it next time but what&#39;s the final speed of truck a find speed of truck a and speed of truck a after the Collision which means we will use the law of conservation of momentum yeah total momentum before equals total momentum after then total momentum before equals total momentum after oh What&#39;s the total momentum before you don&#39;t need to calculate it you don&#39;t need to calculate it the total momentum before is shown we already have it it&#39;s 30,000 because that was the momentum of truck a before it collided and truck B was Zero now did he say he rebounded or did he just say they bounce off each other he said they bounce off each other I don&#39;t know in which direction did it go because he didn&#39;t say rebound and second look at the value of the momentum of B after the Collision if the total momentum was 30,000 kilogram m/s and this is zero to the left like the total momentum has to be 30,000 to the left after the corion what happened B went to the left 27,000 30,000 momentum I&#39;m not asking speed momentum the total has to be 30,000 that 27 3,000 he didn&#39;t say it went to the left it didn&#39;t say it went to the opposite direction he just said they bounc up as in they did not stick to each other like they bounced off as in did not stick to each other if he wanted rebound he would say rebound question rebound okay mister what does he want en total momentum before is 30,000 What&#39;s the total momentum after truck a plus b huh remember a plus b a mass times velocity plus b which is 27,000 mass time velocity Tru a is equal to 30,000 minus 27,000 3,000 remember I want the speed up speed subject VA is equal to 30,000 what was the mass of a forgot a there it is became 6,000 kilog 6,000 kilog velocity 0.5 m per second so again what was the concept total momentum is constant since the total momentum before the Collision was 30,000 after the Collision 30,000 literally the momentum was split B 27,000 a gets the rest which is 3,000 since we already have the momentum of a which is 3,000 we can get the velocity since momentum is mass times velocity and I want velocity but velocity equals momentum over Mass 3,000 over 6,000 but 0.5 m/s okay before I end the session I won&#39;t solve this I want you guys to try and solve this but keep in mind this is also a momentum question there are two tricks here units [Music] and look at this after hitting the object like a ball is going to hit the object the ball bounces back H did you notice back if a question changes the diction and you&#39;re solving momentum you don&#39;t add the total moment and if I said M here&#39;s ball that before the Collision the to the right and this is stationary after the Collision if this is moving to the left and this is stationary this is moving to the right M VA plus Z because it&#39;s stationary minus m a vaa plus MB VB minus so I&#39;ll just quickly show you the working mass times velocity is 0.19 because I changed this from grams to kilogram time 6.9 which gives me19 * 6.9 is 1.31 kilogram m/s but Mister did you need to do this GRS you would have left this as 190 you don&#39;t divide it by th and this answer would be uh what 2 three so 1,310 gram meters per second so going to keep it as kilog after hitting the object the ball bounces back with a speed of 1.5 the object has a mass of 1.8 what&#39;s the speed of the object after it&#39;s hit by the ball but basically momentum before which is this which we which we already calculated equals momentum after which is this minus because it&#39;s moving to the left relax but what was the velocity of this ball 1.5 mass time velocity 0.19 time 1.5 minus plus mass times velocity of this pin 1.8 time moment equals total momentum after before 1.31 after minus 0.19 * 1.5 it&#39;s moving to the left sign it&#39;s not added you don&#39;t add them subtract them minus this is 1.31 = 19 * 1.5 which is is 0.285 + 1.8 V but therefore V is equal to 1.31 + 0.285 over 1.8 this is just some algebra that I&#39;ve done I assume you can do the same divided by 1.8 this gives me 0.886 m per second and that&#39;s unit or half of unit one

excellent [Music] now in unit one we discuss General Physics and mechanics so things like measurements motion forces energy pressure moments and power stations and so on in this part this part one we&amp;#39;re only going to talk about measurements in density mass and weight and gravity motion forces and momentum so that&amp;#39;s what we&amp;#39;re discussing today in this session so let&amp;#39;s get started by looking at quantities and measurements first and at the beginning of every section in the revision sheet you&amp;#39;re going to find this very small list this is a checklist that we use for revision like every sentence is exactly from the syllabus and the syllabus asks you to make sure you understand these points if you understand these points you have covered that portion of the syllabus some chapters sentences some chapters will have a lot more details they&amp;#39;re just details but they&amp;#39;re just Minor Details that you need to focus on so one of the best things to do on your own kand after we&amp;#39;re done with the session that you read each sentence and make sure you understand what the sentence is trying to say if you understand it and you feel confident with it put a tick next to it okay okay if you&amp;#39;re not very okay with a certain part of it you just go like uh maybe maybe you&amp;#39;re not okay which means you need to either revise this or ask ask me about this and finally if you&amp;#39;re not okay with something you say it&amp;#39;s not okay which means you need to revise this study this again because it&amp;#39;s going to give you trouble when it comes to problem solving what I&amp;#39;ll do is I&amp;#39;ll read the checklist with you and then I&amp;#39;m going to start explaining things in the sheet so as we read through the checklist we&amp;#39;re going to explain things through the sheet to make sure you understand and maybe go through a question if I found the suitable question for something let&amp;#39;s start with quantities and making measurements this is a very short chapter it&amp;#39;s not very relevant to it doesn&amp;#39;t have its own set of questions it usually shows up as parts of other questions details in you need to be able to describe the use of rulers measuring cylinders to find length and volume so we need to know how to use rulers or we&amp;#39;ll add a few other instruments to measure length and to measure volume how to measure a variety of time intervals using clocks and timers so you know how to measure time but we also need to know how to convert units of time finally determine an average value for the small for a small distance and for a short interval of time like the thickness of a sheet of paper small distance and the short interval of time the time of one oscillation of a pendulum we&amp;#39;re going to apply in other chapters sometimes it&amp;#39;ll be in unit two sometimes it&amp;#39;ll be in unit four came in and we&amp;#39;ll see that soon not very soon unit four but before we start every quantity in physics has a unit of measurement SI unit standard units answ in SI units unless the question changes that requiring the length is measured in what in meters time is me measured in what time is measured in what seconds Mass is measured in what kilograms temperatur is in kelvin how to change Kelvin to Celsius and back and current is in ampere we&amp;#39;ve talked about electric current before and it&amp;#39;s an a what about centimeters or millimeters and so on these are what we call prefixes from any unit to its prefix or from the prefix back to the unit the a for example you need to be able to convert from kilometers to meters or back so 1 kilometer for example is 1,000 M times a thand and from the meter back to kilometer you do the opposite action which is divide by 1,000 so we have three prefixes that are very important with two prefixes they&amp;#39;re very rare we usually with variant and that&amp;#39;s what you need to a focus on rarely but they do show up kilo means what times a th CTI means what divide by 100 Millie means what divide by th000 so I&amp;#39;m going to give you a few examples of each Let&amp;#39;s uh let&amp;#39;s delete this and give an example of each one quickly if I have 3 kilomet convert that to meters if you have 36 CM convert that to meters if you have 28 mm convert that to meters so to convert from kilm to metimes 1,000 that&amp;#39;s what the multip for 00 3,000 M from 36 cm to meters let divide by 100 that literally means divide by 100 so 36 over 100 is 0.36 M 28 mm to me remove M and divide by 1,000 so that&amp;#39;s 0.028 m okay mister I want to convert them the opposite way met to kilm do the opposite thing which is divide by a th from meters to CM you divide sorry uh from meters to centimeters you multiply by or sorry oh multiply by 100 because when C divide so you do the opposite uh operation from millimeters to meter it&amp;#39;s divide by th000 you from meter to MIM micro and what&amp;#39;s Mega you almost never see them and we will only see them two maybe three times total the P papers variance but Mega is just a thousand thousand like it&amp;#39;s a thousand kilometers and it&amp;#39;s usually used with jewels or Watts suff for energy so Mega means times a million and micro right means divide by a million so keep them in mind when we start solving past papers in the Futures you will almost never see these two but you will see the rest let&amp;#39;s move on to a few easier things how do you measure length uh with a ruler if it&amp;#39;s up to a meter for very long distances use use a measuring tape the stuff that you spread out and a micrometer is what we use for very thin objects like coins and wires and thick cards right then what if you want to and this is up part three determine the average value of a small distance what if I want to measure the thickness oops of a sheet of paper the problem is that one sheet of paper is very thin so we measure more than one sheet we put several sheets on on top of each other you measure the thickness of all of the sheets so let&amp;#39;s say it&amp;#39;s 9 mm for example 100 sheets is 9 mm and then you get the thickness of one sheet how 9 mm / by 100 this gives you 0.09 millim for one sheet of paper which is very thin so this technique of measuring lots of a small thing than dividing by the number is very comp you almost always have to repeat and average your readings why because you can&amp;#39;t really rely on the readings from one exact spot what if can air gap what if the paper is not perfectly uniform in thickness if I get a thin sheet of paper K it&amp;#39;s not going to be equally a thick if you actually get a microscope and you check the thickness it&amp;#39;s not going to be perfectly or equally a next he did ask us to talk about volume so what is volume volume is defined as the space occupied by an object how big an object is or how small it is and measuring volume depends on the substance you&amp;#39;re measuring it&amp;#39;s a liquid use a measuring cylinder just I have a cup of water here and I&amp;#39;m going to use the hydrate all the time my nutritionist nutritionist was like at least drink two 2 lit of water a day like God help me I know I should but still but use a measuring cylinder for a liquid just pour it in this is what a measuring cylinder looks like for a regular solid a cube a square a cuboid a cylinder these have geometrical equations the most common is just length time width time height to get the volume of a regular cuboid or such but if I have a general uniform shaped object like a cylinder all right or a prism that&amp;#39;s a triangle and then it&amp;#39;s got a certain height the general area for volume is the area of the base times height the area of this base times height this is something you should have studied in geometry and we don&amp;#39;t really use it often but keep it in mind because certain questions in electricity revolving around wires and the resistance of a wire crosssection area and the height it depends on those anyway finally how do you get the volume of an irregular solid like if I have a key for example I have a couple of keys here how do I get their volume we get it&amp;#39;s called displacement we get a measuring cylinder pour some water inside and record this volume let&amp;#39;s say it&amp;#39;s 75 then you take your keys and you gently put it into the water the water level will rise in this case it&amp;#39;s 125 so what&amp;#39;s the volume of this rock or the keys that I put in it&amp;#39;s 125 minus 75 which gives us 50 Okay so it&amp;#39;s just three steps okay good next what about time well time is easy it&amp;#39;s not a problem I just need you to remember how to convert hours to minutes that&amp;#39;s time 60 and minutes to seconds that&amp;#39;s times 60 and if I want to convert it backwards from six from seconds to minutes it&amp;#39;s divide by 60 from minutes to hours you divide by another 60 so you can use stopwatches clocks timers it doesn&amp;#39;t matter I&amp;#39;m sure you know how to read a clock or to read a stopwatch that&amp;#39;s not a particularly challenging thing to do but the challenging thing is how do I measure the time of one oscillation of a pendulum this doesn&amp;#39;t just apply to pendulums though this applies to waves as well so what you learn here waves a pendulum it&amp;#39;s just a thread and a mass that&amp;#39;s allowed to swing I mean honestly a swing and like push you on the swing you are literally a pendulum you&amp;#39;re just a living pendulum how do I find the time taken for a pendulum to finish one oscillation meaning starts here goes to the other end and comes back how do I do that okay I do that by measuring the time of 20 oscillations I do that by measuring time of 20 or 10 like at least 10 oscillations with 10 20 15 several oscillations and you divide the reading by their number sheets of paper so the technique to measure thickness oh sorry the thickness of a sheet of paper is the same Technique we use to find the time of one oscillation of a swing or pendulum which is measure the time then divide by the number it&amp;#39;s always the time over the number of things or the value over the number of things it&amp;#39;s like taking an average but it&amp;#39;s not really an average after you do that it&amp;#39;s always best to repeat your readings and take an average it&amp;#39;s always best to repeat your readings and take can average okay why because it improves reliability makes your readings more reliable finally sometimes questions like these ask you to describe the entire process one of the precautions we use to ensure that our reading is accurate is to reset the stopwatch before we start making measurements I know it&amp;#39;s very obvious I know it&amp;#39;s very basic to you like it really shouldn&amp;#39;t even be a point of question but it is that&amp;#39;s the first part easy write measurements together let&amp;#39;s talk about Mass because Mass affects what we call weight which is the force of gravity state that mass is a measure of the quantity of matter in an object at rest relative to Observer meaning this is the definition that he wants you to memorize if asks you in the new syllabus to Define mass okay we&amp;#39;re not going to see a lot of definitions in our questions we don&amp;#39;t actually ask you to define a lot but it&amp;#39;s still there next state the weight sorry state that weight is a gravitational force on an object that has mass so it&amp;#39;s the force of gravity essentially Define gravitational field strength as the force per unit mass and use the equation gal w m andise as in how do I calculate weight and what does g even mean and know that it&amp;#39;s equivalent to the acceleration of Free Fall remember revision I&amp;#39;ll send you this document and I want you to you know check these things as you understand them know that weights and masses can be compared using a balance so I can measure mass and I can compare language I can compare weights you don&amp;#39;t measure weight with a balance you compare weights with a balance but you can measure mass with a balance describe and use the concept of weight as the effect of a gravitational field on mass gravitation field but first let&amp;#39;s Define mass what is mass we know that mass is the amount of matter in an object how much stuff is in an object but if you&amp;#39;ve studed studied chemistry at any level have you studied the mole before you can answer in chat yeah and if you remember the definition of mole it&amp;#39;s the amount of it&amp;#39;s a unit that measures the amount of a substance which is matter so Mass isn&amp;#39;t just the amount of matter it&amp;#39;s okay like even if you haven&amp;#39;t studied it the mole is just a unit that measures the amount of a substance which is very similar to Kit amount of matter oh okay so what is mass mass is something that is one affected by gravity and two affects the [Music] what the motion of an object this is why we said it&amp;#39;s a measure of the quantity of matter in an object at rest relative to an observer because when an object moves the mass affects that motion with the reason he says relative to The Observer and honestly it&amp;#39;s not for o LEL it&amp;#39;s because for higher level physics unless theory of relativity maybe if you&amp;#39;ve watched Interstellar Mass actually is affected by motion it&amp;#39;s not our thing but this is why he wants that kilit relative to observe he&amp;#39;s keeping himself safe The Examiner is keeping themselves they&amp;#39;re keeping themselves safe what do we use to measure mass a balance whatever the type of balance is the only technique you need to remember when measuring mass is how to get the mass of a liquid why because a liquid has no fixed shape you can&amp;#39;t put it on a balance we put an empty container on a balance it gives us a reading we pour a liquid into the Container it gives us a second reading all right the difference between these two readings is the mass of the liquid that&amp;#39;s inside okay very good so what do we do measure the mass of the empty container or the liquid inside and measure the mass of the container with the liquid calculate the difference between the two so that&amp;#39;s Mass what&amp;#39;s weight now we&amp;#39;ve gone into the territory of forces a force is a push or a pull that has many different effects and the most common force that we experience every single moment of Our Lives unless our lives are like in outer space far away from planet Earth very far away from planet Earth is weight what is weight weight is defined as the force of gravity the gravitational force on an object planet Earth like any other planet or Celestial body like body in space has a lot of mass and attracts objects towards it that General force of attraction caused by a planet or a star on other masses that pulls other masses towards it is called gravity so the gravitational force is called weight like the the action itself is called weight the phenomena is called gravity why there&amp;#39;s a difference in the phrasing oh this is my gravity it&amp;#39;s not your gravity it&amp;#39;s the gravity of the planet it&amp;#39;s the phenomena of Attraction of the planet the amount of pull like the force of the pull that&amp;#39;s what we call weight how do we calculate Weight here&amp;#39;s your equation equation wal mg weight is equal to M so that&amp;#39;s mass that depends on mass The more mass the more weight n g which is the gravitational field strength as in how strong the planet&amp;#39;s gravity is the value of G on Earth that we have to memorize is 9.8 Newtons per kilogram the value of G is 99.8 Newtons per kilogram it also is equal to the acceleration of freeall which is what if you hold an object and you drop it like here&amp;#39;s my pen and I drop it and it falls it will fall with an acceleration of 9.8 m/s squared it just so happens to be equal to weight uh sorry uh the gravitation field strength which is .8 discuss falling the concept of falling we&amp;#39;ll discuss in a bit for now I want your only focus to be what weight what is it it&amp;#39;s the pull of gravity on an object the gravitational force on an object and it&amp;#39;s calculated using mass times G on Earth it&amp;#39;s 9.8 other planets have different values of G we don&amp;#39;t care we don&amp;#39;t care about other planets we only care about Earth and field strength is the strength of Earth&amp;#39;s field and it&amp;#39;s defined as the force per unit Mass if you make G the subject W over m w over a m which is why it&amp;#39;s defined as Force per unit Mass force over Mass that&amp;#39;s if you make it the subject Newton per kilogram a unit that Force newon Mass kilogram now weight as a concept does not show up on its own a lot calculating weight shows up as parts of other questions it almost never shows up as its own idea it&amp;#39;s part of other questions so when it comes to multiple choice questions I mean we can give you questions that are just about weight because questions are small on enough so these are two questions from the multiple choice paper paper two an object in space uh sorry an object in a space probe above Earth weighs 3.5 Newtons the gravitational field strength at the height of the space probe is 7 Newtons per kilogram here&amp;#39;s a planet here&amp;#39;s our planet and we have a probe I can say satellite think of a satellite and it&amp;#39;s orbiting our planet As you move farther and farther away from a planet the gravity gets weaker so the G here is 7 Newtons per kilogram the gravitational field strength on Earth is 9.8 like the G on Earth is 9.8 what are the mass this is one question and the weight of the object on earth mass does not change I actually wanted to put that X on the change the mass of any object does not change okay so if I calculate the mass of this object when it&amp;#39;s far away from Earth in space it&amp;#39;s the same mass on Earth and when it&amp;#39;s in space w g when it&amp;#39;s in space g seven he has to give you the value of G if it&amp;#39;s not on Earth Earth somewhere else you have to begin the value of G wal mg what&amp;#39;s m w over g w 3.5 will G 7 3.5 over 7 which is half a kilogram if this is the mass in space in space probe it&amp;#39;s also the mass on Earth so the answer is 0.5 that&amp;#39;s either A or B then he asked me a second question what is the weight of the object on earth and I equation weight is mg we know the mass is 0.5 and we know that g is 9.8 on Earth not in space on Earth so 0.5 * 9.8 calculator I&amp;#39;m working it out 4.9 so the answer here is B Mass W mg in space and then weight on Earth next which statement about mass or weight is not correct let&amp;#39;s read masses can be compared using a balance this is a correct statement literally checklist mass is a force absolutely not mass is the quantity of matter of an object that rest relative to Ober weights can be compared using a balance yes they can balance weight is a force absolutely correct but what&amp;#39;s the correct answer here B it&amp;#39;s the only one that&amp;#39;s wrong very good talk about something else that&amp;#39;s also easy density yeah density and my favorite one of my favorite density jokes or questions is which is heavier a kilogram of steel or a kilogram of [Music] feathers and the trick is and they&amp;#39;re the same they&amp;#39;re both a kilogram exactly they&amp;#39;re both a kilogram they&amp;#39;re both 1 kilog and 1 kilog so volume and therefore their densities define density before we go density is defined as mass per unit volume recall and use the equation density is mass over volume describe how to determine the density of a liquid oh of a regular shaped solid okay and the regular irregularly shaped solid which sinks in a liquid including a appropriate calculations determine whether an object floats based on density we know that objects float in a liquid if it&amp;#39;s less dense determine whether one liquid will float on another based on density data given that the liquids do not mix like I can pour some oil on water and I know these liquids don&amp;#39;t mix if I see that the oil floats on water the oil is more less dense if oil floats on water is it more or less dense exactly first what is density it&amp;#39;s the mass per unit volume basically the more dense and this is the symbol for density the more dense an object is The more mass it has and the smaller its volume basically think like a coin a metal coin whereas the less dense something is the less Mass it has and the more volume it has think of a balloon balloons are very large but they have very low mass almost less than can a the coin even though they&amp;#39;re larger so density is just the ratio mass and volume and the equation is density equals mass or volume you don&amp;#39;t have to say row because most of the time you just write it down so the pronunciation is not very important it&amp;#39;s just density equals mass over volume the unit of density is either kilogram per meter cubed or gram per ctim Cub type how do you measure density well measure the mass and measure the volume but the trick isn&amp;#39;t density when it comes to measurement the trick is how do you measure mass and how do you measure volume so if it&amp;#39;s a regular solid object like a box how do you measure mass with a balance how do you measure volume length and width and height and calculate the volume and then calculate density m one what if it&amp;#39;s a liquid oh well first I need a measure measuring cylinder and keep an empty measuring cylinder mass then we fill that measuring cylinder with the liquid you give Mass two so the mass of the liquid is Mass 2 minus Mass one and the volume is obtained from the cylinder volume and we also got the volume so what&amp;#39;s the density mass over volume finally an irregular solid just like my keys as long as it&amp;#39;s a solid how do you measure mass balance and if you want volume what do you use a measuring cylinder or some water put your keys inside the water level rises at ULU V2 minus V1 gives you the volume of this of these keys and that allows you to calculate density using mass over volume okay now we already talked about floating and sinking but I&amp;#39;ll remind you why do objects float because they are less dense their total density is less dense than liquid why do objects sink because their total density is more than the liquid it&amp;#39;s in so if I throw a piece of wood like a plank of wood in some water why would it float because it&amp;#39;s less dense Sal but that&amp;#39;s wood density value like let&amp;#39;s say water has a density of 1,000 kilogram per met cubed and this wood has a density of 800 it makes sense that it floats and if I have a of Steel it will sink because Steel m has a density of around 5,000 kilg per meter cubed it&amp;#39;s very dense so it sinks but how does a ship float a boat float when I make a boat out of steel how can a boat float ah it&amp;#39;s no longer longer about the density of the material it&amp;#39;s about the density of the entire object a total object what we do with a boat and steel boats is like what we do with a balloon we take it and we get a very thin layer of Steel and we bend it so that we fill it up with air inside this means that it has a very large mass but sorry a very small Mass I meant volum very small mass in sheet of metal is very thin but it takes up a very large volume less dense the reason why ships can float like if you go on a cruise or if you ride a boat they float [Music] because and the air inside and the people inside they take up so much space and the density which explains why ships can sink like the Titanic for example Titanic I hope you do I hope I&amp;#39;m not too old to reference Titanic do you know the Titanic please Titanic do you know the Titanic yes aldah ald I&amp;#39;m not too old yet do you know the Titanic was like No And then I will kill all anyway why did the Titanic syn ah I&amp;#39;m explaining it now again why did the Titanic sink because overall it&amp;#39;s made of a very thin sheet of Steel that&amp;#39;s full of air so the density of the ship is not 5,000 like the steel it&amp;#39;s a lot less than 5,000 it&amp;#39;s a lot less than 5,000 we take that piece of metal we spread it out we make it super thin as thin as we can and still maintain structural Integrity so the reason it floats it&amp;#39;s because it&amp;#39;s less dense than the liquid but the reason the Titanic sank was because when it was broken into by the iceberg you&amp;#39;ve got water flowing in so that started filling in the ship with water M but the volume of the ship did not so what happens to the density it increases which makes it sink goodbye Titanic okay so why do things float if they&amp;#39;re not like a block but they&amp;#39;re actually like a balloon blown up they in size because the air space in size increases the volume without increasing the mass the mass of the air is negligible so this decreases the density do you understand that is that clear just like a balloon other details as long as objects have the same material they have the same density I don&amp;#39;t care if you have a small coin made of wood or a large door made of wood if you put them in water they will both float why because they have the same density if you put them on water they will have the same density because they&amp;#39;re made of the same material wood the only thing that can change the density of any substance is temperature for unit two and unit 2 we&amp;#39;re going to study something called thermal expansion if you increase the temperature of an object its volume increases the volume increases and according to the equation of density density is mass over volume if if the volume increases and the mass does not change the density will decrease Le because density and volume are inversely proportional that&amp;#39;s their relationship Max they inversely proportional so the less then something is the more space it takes up this can happen due to thermal expansion that&amp;#39;s why heating something makes it less dense and hot stuff can float like hot air balloon when I heat up the air in a hot air balloon it fills up the balloon with very hot air Which is less dense than the surrounding air like it&amp;#39;s even less dense than the surrounding cold air so the entire balloon starts to float okay let&amp;#39;s solve a quick question a rectangular swimming pool is 50 m long 25 5 m wide and has a depth of 2 m so now I have the length and the width and the height depth is another way of saying height the density of the water is 1,000 kg per M cubed what is the mass of the water in the pole uh what yeah well let&amp;#39;s write this down density is mass over volume he wants Mass so mass is density times volume what density oh it&amp;#39;s 1,000 what&amp;#39;s the volume you have length you have width you have height so it&amp;#39;s going to be length time width times height 50 * 25 * 2 what does that give us 1,00 * 50 * 25 * 2 cuz it&amp;#39;s a regular shape it&amp;#39;s like like a rectangular swing pool 25 00 0 so D is your answer any questions before we move on to scalers and vectors and slightly harder things any questions very good next let&amp;#39;s talk about scalers and vectors what&amp;#39;s a scalar and what&amp;#39;s a vector let&amp;#39;s check the checklist first understand that a scalar quantity has magnitude only and a vector quantity has magnitude and Direction so whenever we describe an object like or State a value of a property or a quantity some quantities only need a value to be understood for example if I tell you uh because of my poor diet the past few months I&amp;#39;ve gained some Mass I&amp;#39;ve gained 5 kilograms do the 5 kilograms that I&amp;#39;ve gained care about Direction 5 kg 5 kg towards the forward backward so they don&amp;#39;t need a direction to be understood but if I tell you for example uh somebody pushed me forward with a force of 100 Newtons you now know in which direction I&amp;#39;m going to move and if I omit the direction sh Direction somebody applied the force on me with 100 Newtons and in which direction will I move forward or backwards left or right or up down I don&amp;#39;t know you need to know what the direction is to know what the effect of that quantity is vectors scalar quantities only have size or magnitude know that the following quantities are scalers distance speed and time and mass and energy and temperature makes a lot of sense because none of these things care about Direction know that the following quantities are vectors force and weight weight is a force so it&amp;#39;s a vector velocity and acceleration and discuss them through motion momentum also something we&amp;#39;ll discuss today electric field strength and gravitational field strength we will study this in electricity but it does have a direction like because we draw an electric field from positive to negative electric Fields have a direction a d Direction but the gravitational field strength also has a direction because gravity acts towards the center of the planet it pulls you in so there is a direction I know it&amp;#39;s constant but it does have a direction finally determine by calculation or graphically the resultant of two vectors at a right angle limited to forces or velocities what does that mean we already understand scal vector scalers are quantities like Mass 75 Kg it&amp;#39;s my mass it doesn&amp;#39;t have a direction whereas Force for example could be 100 Newtons to the right right our moments could be 30 newon met clockwise or anticlockwise you need the direction determine by calculation or graphically the resultant of two vectors at right angles as the and if I have two vectors like a 10 Newton Force to the right and a 10 Newton Force pushing an object up top right or forward and to the right if this was a ball for example this ball would move to the right and to the top somewhere for no but what we want is to find out deep C this is called the resultant the result of these two forces and I want to know what the value of this force is and the exact Direction and when I say exact Direction I mean the angle between the horizontal line and the line of the result so I know exactly how many degrees above or below or to the left or to the right it is so how do we add them we have two methods you can either calculate them my preferred method is calculation or you can draw what we call a vector diagram to find the resultant and here&amp;#39;s how you take these two forces the 10 and the 12 we&amp;#39;ll call them fub1 and F2 and then you draw them it&amp;#39;s just a sketch one after the other head to tail you take the head of one arrow and stick it to the tail of the other if you close off this line or draw a line from the starting point to the ending point this will look like a right angle triangle which means geometry is going to start working by now we have something called the Pythagoras Theorem which states what do you guys remember the Pythagoras Theorem that a that b and this is C Pythagoras states that c^2 is equal to a 2 + B ^2 that&amp;#39;s what the Pythagoras Theorem States this also applies to the resultant result hypoten this is called the hypoten resultant hypoten C this means that if I want the resultant C I can use square root a s plus b s that&amp;#39;s squ that squ under a under root the resultant so that&amp;#39;s the rule that you use the resultant force or velocity whatever it is is F1 s+ F2 ^ 2 under root a Pythagoras but we also said vectors have magnitude and Direction magnitude and tell you what like let&amp;#39;s find out 12 my calculator square root 10 2 + 20 s uh sorry 12 s 20 square otk 10 s + 12 s this gives us 15.6 Newtons so this Force this resultant force is 15.6 Newtons okay Mr I want the direction angle D how do I get this angle over here I want the angle trigonometry for trigonometry we have three functions called the S and the cosine and the tan if this is a triangle and this is your angle Theta the opposite divided by hypotenuse is called s the adjacent divided by the hypotenuse is called cosine which is the ratio of these lines and the opposite divided by the adjacent is what we call Tan I don&amp;#39;t care which one you use just pick one and memorize it s or cosine or tan but wait you want Theta you want the angle s Theta you want the angle or tan you want the angle but for example opposite is 10 F2 10 and fub1 is 12 so if I say tan theta equals opposite 10 over adjacent 12 to get the angle Theta shift because what I want is formula on one side to the other shift tan answer 39.8 de which is about 40° please be careful guys if you ever lend your calculator to an as student like it could be a sibling it could be a friend at school make sure your calculator has the letter D written on top in dark you know black because that&amp;#39;s the unit of angles degrees there are two other units called radians and gradients so R and G so if you ever see RNG G on top please change your mode like literally press shift mode and click degree three on your calculator press shift mode and you&amp;#39;ll find a few options just click the option for degrees which is three on this calculator finally how do you get the resultant vector by drawing I don&amp;#39;t really like the drawing method it&amp;#39;s time consuming but here&amp;#39;s how you do it step one you need a scale and 1 cm is 1 Newton so we draw a scale diagram but for the resultant of these two forces 12 or 10 12 to the right or 10 up top you measure a line that&amp;#39;s 12 cm long to the right and from the end of it you draw a line that&amp;#39;s 10 cm high but to scale then to connect a line from that starting point to the ending point this is your resultant it&amp;#39;s length to scale 16 16 cm which is 16 newon roughly so you measure it and you get it to scale finally dire Pythor trigonometry get a protractor in order to get the angle put it here and then just measure what this angle is lot like 40° roughly 39 40 somewhere like that and that&amp;#39;s how you can get any resultant V VOR if they&amp;#39;re at 90° and let me interject H for a second the syllabus changed in 2023 before the syllabus changed students were required to know how to find the resultant Vector of two vectors not at 90° at different angles this has changed it is now only vectors at 90° so let&amp;#39;s look at a question from March 23 a boat crosses a river I always like to sketch by the way and why do I like to draw because it helps me visualize the question don&amp;#39;t have to do it just in my head a boat crosses a river the boat points at right angles to the river bank so if this is a river for example like the river is this way and here&amp;#39;s a boat and the boat is going up top because it travels at right angles any perpendicular to the a to the river at a speed of 3.5 m per second so it&amp;#39;s traveling at a speed of 3.5 Ms per second the river acts at right angles to the boat and the river has a speed of 2.5 m/s meaning two vectors to the right of 2.5 the up top 3.5 and the resultant will be somewhere here which makes sense this means that the boat is not going to travel upwards boat travel somewhere to the right and upwards by drawing a scale diagram or by calculation see he&amp;#39;s giving you the option determine the speed and direction of the boat relative to the river bank and relative to the river bank R relative the River Bank horizontal it&amp;#39;s almost always the horizontal measure this angle let&amp;#39;s call it Theta how do we solve this well I want the resultant when I resultant Vector our resultant velocity is square root 1 squ + 2 squ 2.5 S + 3.5 s this gives us 2.5 S + 3.5 squ this gives us 4.3 okay so that&amp;#39;s the speed me/ second what about the direction H use any trigonometrical function you want I like tan thet is equal to shift tan tan minus one opposite over adjacent 3.5 which is the opposite of the angle like it&amp;#39;s facing the angle over 2.5 and we&amp;#39;ll shift tan 3.5 over [Music] 2.5 and that&amp;#39;s 54.5 de 54° next uh speed is a scalar Quant and velocity is a vector State the names of one other scalar and one other Vector what else is a scaler mass mass is a scaler what else is a vector you have acceleration you have Force you have momentum all of these are vectors that was a mouthful for it next see we have a lot to revise for the motion almost guaranteed p l motion or movement and motion is actually very simple like if you think about it it&amp;#39;s very simple see if details okay Define speed what is speed we know what speed is it&amp;#39;s distance over time and recall the equation speed is distance over time speed is distance over time how fast you travel you can measure speed in meters per second or kilometers per hour that&amp;#39;s depends on the question Define velocity as the speed in a given Direction meaning velocity speed with a direction a vector speed is a scaler recall and use the equation average speed is total distance uh divided by I forgot to slash here divide by total time so average speed is total distance over total time it&amp;#39;s speed But it includes the time when the object stops so it&amp;#39;s just total distance travel divide by total time and you get the median or the average or the mean speed so for example somewhere somewhere like I don&amp;#39;t know on school in the morning the only thing I can think of think I think of a school right now and I drive 50 kilometers right in 30 minutes if I drive a distance of 50 kilom in 30 minutes half an hour if you calculate my speed with 50 over 0.5 which is 100 kilm per hour this makes no sense why because realistically half hour day I didn&amp;#39;t travel at 100 to I had to slow down a bit for Speed bumps or stop for traffic lights or speed up even faster when I&amp;#39;m on like a nice big open road it&amp;#39;s like nice and wide and super free so I can just drive at 120 so usually when you calculate speed you do you are getting the average speed next sketch and plot and interpret distance in speed time graphs distance with speed time graphs determine qualitatively from the given data or shape of a distance or speed time graph when an object is at rest moving at constant speed accelerating or decelerating being able to look at a graph and tell what type of motion this is calculate from the gradient of straight line section of distance time graph calculate speed from it calculate the area under a speed time graph I&amp;#39;ll stop here for a second because now he&amp;#39;s talking about speed time graphs distance time a distance time graph shows you how distance changes over time if the line is going up you&amp;#39;re moving at constant speed if it&amp;#39;s horizontal you&amp;#39;re at rest because you&amp;#39;re not changing your distance you are changing the distance the slope of the line shows you the speed the steeper the line is like the higher the line is the higher the speed and the lower the line is the lower the speed which means slope gradient Y2 - y1 / X2 - X1 and if you take two points and calculate the gradient that gradient gives you speed but what if the line is not straight what if the line is curved right what if the line is curved a if it&amp;#39;s curving upwards this acceleration if it&amp;#39;s curving downwards it&amp;#39;s not going physically down that it&amp;#39;s just curving and becoming more and more horizontal less steep it&amp;#39;s called deceleration so you can&amp;#39;t actually calculate acceleration which is speeding up or deceleration which is slowing down from a distance time graph before we talk about the speed time graph let&amp;#39;s Define acceleration what is it it&amp;#39;s defined as the change in velocity over time change in velocity over time and keep in mind that the word change in something has a symbol which we call Delta it&amp;#39;s a triangle so if I tell you acceleration is Delta V / T I mean it&amp;#39;s a difference in speed over time the speed increase the speed could decrease still works increase and decrease is all called acceleration however deceleration is just the special name given to when speed decreases and since the speed is decreasing like if a speed is decreasing it&amp;#39;s decelerating we call it negative acceleration we call it negative acceleration because you&amp;#39;re not really accelerating positively you&amp;#39;re accelerating negatively and your speed is dropping we just call it deceleration what about speed time graph what can we learn from a speed time graph well first this doesn&amp;#39;t have to be speed this could be velocity by the way this could be a VT graph and it&amp;#39;s exactly the same thing for now when the goes up that&amp;#39;s called acceleration when the line is horizontal that&amp;#39;s called constant speed when the line goes down that&amp;#39;s called deceleration line is horizontal is at rest zero speed that&amp;#39;s at rest which means the steeper a line is the higher the acceleration and the less steep Aline is the lower the acceleration steeper means more change in speed over less time so what do we call this the slope that slant is the slope and the slope is the acceleration but I could use Y2 - y1 / X2 - X1 to get the acceleration of any line but there was another thing another very very important thing whenever you solve questions involving speed time graphs he would usually ask for distance you would usually ask for distance and we know that distance is speed times time this speed is not always constant for graphs instead rearrange distance speed times time when speed with time because the speed is not always constant we have to resort to another method calculating distance only from a speed time graph and that&amp;#39;s by getting the area of the shape under the line so if I take this shape and I split it up and the triangle and and the square or rectangle okay if you calculate the area of the shape of this triangle using the numbers from the graph triang if I get the area under the graph here so as a friendly reminder triangles half Bas time height a rectangle is base time height a trapezium is half base 1 plus base 2 * height next finally if the line can curve any of these lines can curve this means that acceleration doesn&amp;#39;t have to be constant if the line slopes upwards it&amp;#39;s called increasing acceleration because the slope is increasing because it becomes steeper whereas this is called decreasing because it becomes less a steep I don&amp;#39;t know why it&amp;#39;s so thick just give me a second yeah finally a regularly shaped line when the slope is becoming steeper speed a increases left the acceleration increases and it&amp;#39;s accelerating us it&amp;#39;s already speeding up but the increase in speed is even higher with this decreasing acceleration speed Z with the decreasing amount you is it 0 10 20 30 the constant zero 20 and then 25 and then 26 this decreasing acceleration that change in speed is not increasing it&amp;#39;s decreasing if the line is going down this means you&amp;#39;re decelerating you&amp;#39;re slowing down so if the slope is becoming steeper it deceleration with zed and slope less steep deceleration with a very good any questions so far acceleration before we head into forces and because it&amp;#39;s got a lot of questions that we want to solve it&amp;#39;s just forces and momentum but first let&amp;#39;s solve this question a car accelerates uniformly in a straight line from rest at a time of zero I want to change the color to Red there we go at 3.2 seconds the speed of the car is 13 m/ second so you have the time you have the starting speed it&amp;#39;s at rest and you have the final speed what what&amp;#39;s the acceleration acceleration is change in velocity over time Delta V and change in velocity so the velocity was Zero it became 13 it&amp;#39;s 13 minus 0 over how much time is this 3.2 seconds you pull out the calculator F 13 IDE 3.2 this gives us 4.0 625 huh how many significant figures should I write my final answer what do I like how many significant figures do I have to write three you must stay consistent and use three significant figures round up if you have to but D6 two two won&amp;#39;t round up the six so it&amp;#39;s 4.06 m/ second squared Why is it meters per second squared because acceleration units are m/s over second the m/ second per second m/ second squ okay explain in words what&amp;#39;s meant by the term acceleration what is acceleration the change remember what&amp;#39;s the definition of the change in velocity per unit time okay next the car travels at 13 m/ second from a time of 3.2 to a time of 12 seconds so it&amp;#39;s giving me the time and the speed which is constant plot the speed time graph from 0 to 12 going back he said that it starts at rest time zero and at 3 2 it&amp;#39;s 13 and it accelerates uniformly so from zero so from zero to how many seconds sorry oh there we go from 0 to 3.2 that&amp;#39;s how many 20 seconds it accelerated to 13 which means from0 to 3.2 mister I can&amp;#39;t see the 3.2 I can&amp;#39;t read the scale it&amp;#39;s getting blurry so what do I do every you need to find out every small square became like what&amp;#39;s every small square if oh 10 small squares there four which means every small square is 0.4 0.4 0.8 1.2 1.6 2 so what does he want again why is from 0 seconds to 3.2 seconds in 3.2 okay that&amp;#39;s two it&amp;#39;s 2.4 yellow 2.8 3.2 for 3.2 a again DET distance traveled by the car from 0o to 3 oh sorry plot a gra from 0 to 12 3.2 speed of 13 so we go up to 13 and we Mark a point just for me because I know it&amp;#39;s going to accelerate from 0 to 13 and then from 13 to 12 12 it travels at the speed of 13 which means constant speed but here&amp;#39;s what I will draw straight line going up because he said it accelerates uniformly K it uniform wait k it uniform means at constant a rate so constantly uniformly and then it&amp;#39;s constant speed until 12 so he wants this plot from 0 to 12 G plot Mister we&amp;#39;ve drawn what does he want determine the distance traveled by the car between 0 and 3.2 seconds what how do you get distance in G area under speed time graph we get the area under the speed time graph when I want distance what I actually want is the area under the graph what shape is this the trapezium so I can use the trapezium rule I can say base 1 plus base 2 over 2 * height but does he want the entire graph thank you very much huh do you see do I want the entire graph I would use this that I wanted the whole graph he doesn&amp;#39;t want the whole graph he only wants it until 3.2 so if I close this off till 3.2 what&amp;#39;s the area of this shape ah he wants the triangle I would have used the trapezium if I wanted to get the whole thing but I don&amp;#39;t I just want the triangle so it&amp;#39;s halftimes base times height that&amp;#39;s halftimes 3.2 * the height which is 13 how do I know it&amp;#39;s 13 because again this was given to us earlier in the question5 * 3.2 * 13 this gives me 20.8 see how we get the area under the graph so you&amp;#39;ve now seen how to use the equation for acceleration how to get the area under the graph how to plot a graph Define acceleration these are some of the very important things to keep in mind okay now before we move on to the last two sections which is forces and momentum we&amp;#39;re going to take a short break let&amp;#39;s continue let&amp;#39;s talk about forces so what is a force we know that a force is a push or a pull it has many different effects like you know changing the motion of an object or the size size and shape of an object all of these are effects of forces so let&amp;#39;s look at the checklist quickly know that that forces May produce changes in size and shape yeah Springs like that&amp;#39;s the main thing sketch plot and interpret so you should be able to draw this or plot points if I&amp;#39;ve given you a table and interpret as in understand and explain a load extension graph for an elastic solid and describe the associated experimental procedures like the steps that we take to do this and uh where is it Define the spring constant as a force per unit extension and recall the equation K = FX and Define and use the term limit of proportionality for a load extension graph and identify this point on a graph an understanding of the elastic limit is not required you&amp;#39;re going to notice something in a bit regarding the term elastic limit and limit of proportionality but let&amp;#39;s first explain this how does a force affect shape and size if you have a spring you apply a force on that spring that spring will will stretch as in it will get longer the greater the force the greater the stretching of that spring and that stretching is called the extension that increase in length is called the extension right so force and extension are proportional Force increases extension increases Force decreases extension decreases very good how do you get the extension you take the total length that you&amp;#39;ve measured minus the original length of the spring and the difference is the extension but here&amp;#39;s the thing every object like a spring has a limit if you stretch it too far and you let it go it will not go back to its original size or original length this means that it has exceeded what we call the limit of proportionality or what we can for now call the elastic limit the Mr Leo like why is it up here why up here sorry uh did he say an understanding elastic limit is not required because when you start studying as and A2 and college level physics you start realize that there are two different points like there&amp;#39;s a point called the limit of proportionality and another called the elastic limit they&amp;#39;re very close and they have very similar features but for now in O Lev we&amp;#39;re going to assume they&amp;#39;re the same thing right so elastic limit and limit of proportionality are the same thing for us if you plot a graph of force and extension it&amp;#39;ll be a straight line why because it&amp;#39;s proportional but after the limit of proportionality the line stops becoming straight and it starts to curve now keep in mind it will always curve towards where the extension is so if the extension is on the x-axis it curves to the right if I draw the same graph but the force and extension extensions on the Y y AIS it&amp;#39;ll be straight and then it&amp;#39;ll curve up extension okay this is called hooks law now what is the spring constant that he&amp;#39;s talking about the spring constant is defined as the force per unit extension in engineering if you remember we said that this actually represents what we call the stiffness of the spring how tough a spring is the higher this value is the harder it is for you to stretch a spring it needs more Force per extension needs more Force per centimeter or per millimeter and the lower this is like if you have a very weak spring weak materials like plastic Springs they stretch very easily they have a low spring constant so how do you calculate it k equals FX but I prefer to remember this equation like this FAL KX and you can just rearrange it you can rearrange it to K = FX or calculate X which is the extension and so on now that&amp;#39;s basically it when it comes to the effect of forces a on the shape and size of an object what about the effect of forces or sorry the resultant of forces in a straight line this is very straightforward compared to the previous thing if forces are in the same direction you add them if forces are in opposite direction you subtract them and the resultant direction is always in the direction of the larger Force so n is to the right you the resultant is to the right next what is friction a very important Force because the rest of our discussion here is about movement and motion so what is friction there are two different types of friction solid friction which is the friction between two two surfaces like if you put your hands on each other and you start rubbing them this is what we call solid friction when one surface moves relative to another but they&amp;#39;re in contact with each other you experience a resisting Force meaning it tries to slow you down if you&amp;#39;re the one moving that friction depends on the roughness of the surface if it&amp;#39;s rough there&amp;#39;s a lot of friction if it&amp;#39;s smooth or if you put a lubricant on the surface like oil it&amp;#39;ll slip and there will not be friction additionally friction is a force that produces heat the friction produces heat because it&amp;#39;s a very common thing when we start discussing energy next time because when we press the brakes the brakes do what they slow down your car how do they slow it down by converting kinetic energy into heat energy or thermal energy but if you have friction with water or air we call this drag water or air resistance is called drag it&amp;#39;s exactly like friction but it&amp;#39;s not between two Solid Surfaces it&amp;#39;s between a solid object and a liquid which again is basically friction but with a liquid or a gas water and air resistance or drag depends on two things your speed and your surface area the faster an object is moving like for example if you have an object that is fall through the air the faster it moves the more drag or air resistance act on and the larger it is the more a resistance or drag it experiences so it depends on your surface area and your speed finally let&amp;#39;s get into motion what is Newton&amp;#39;s first law now you don&amp;#39;t have to memorize the law or the statement but you have to understand it and be able to describe the statement here&amp;#39;s the statement an object either remains at rest or continues in a straight line at a constant speed unless acted on by a resultant Force what does that mean this means that if there is no resultant Force forward equals backwards and they cancel each other out an object either stays at rest or moves but at constant speed if the object is at rest already it stays at rest if an object is moving it continues to move thank you very much I know my art is fantastic so please don&amp;#39;t feed this to an AI okay we&amp;#39;re going to ruin AI art forever or maybe do if you don&amp;#39;t like AI art that&amp;#39;s another story but anyway the opposite of this statement is this if there&amp;#39;s no resultant Force you&amp;#39;re at rest or you move in a straight line but what if there is a force and this is very important what if there is a force if there is a resultant force acting on an object the object can change its speed you can change the velocity by either making it move faster or slower you can change speed or you can change direction to simplify this you have three cases if the resultant force is forward you speed up if the force is backwards air resistance driving force for example you slow down and if the force is sideways it&amp;#39;s not forward and it&amp;#39;s not backwards you change a direction this is like turning your steering wheel or turning your a uh steering wheel on a bike what what happens you turn your wheels to the side which creates a sideway force and that Force changes your direction that&amp;#39;s the first law what&amp;#39;s the second law it&amp;#39;s an equation f equals m a force is equal to mass times acceleration that&amp;#39;s literally it it&amp;#39;s it&amp;#39;s just a very important law because we use it a lot but keep in mind keep in mind in it must be the resultant backwards resultant so what does this mean this means that any resultant force acting on an object causes it to accelerate which makes sense because first resultant Force you speed up Force you slow down this is called acceleration resultant Force sideways and you change direction this is still considered acceleration because motion acceleration was defined as the change in velocity over time change in velocity includes change in Direction Change in speed it also includes change in a direction okay now the force and acceleration are always in the same direction acceleration is a vector which means it has a direction the direction of the acceleration is in the same direction of the force they are in the same direction next what about circular motion this is a special version of what we talked about here if a force is sideways not forward or backwards if a force is sideways this causes you to turn if you keep that sideway Force you continue to turn until you move in a circle we call the circular motion so what causes it it is caused by a force acting perpendicular to the direction of motion and you&amp;#39;re moving to the right it&amp;#39;s downwards or to the right and you&amp;#39;re moving forwards but it always acts towards the center of the circle you&amp;#39;re going in so if you&amp;#39;re going in a circle the force is always towards the center of the circle this Force depends on three things your speed the radius of the circle and your mass the faster you move like at I&amp;#39;m in a car I&amp;#39;m driving I am pressing the gas pedal I&amp;#39;ve turned my steering wheel a certain amount I move in a circle if I press the gas pedal and I start moving faster I need more Force to stay in my circle like if I&amp;#39;m moving faster I have to turn my steering wheel harder and I need to apply more Force like the car has to apply a bigger sideway Force to stay in a circle or if I&amp;#39;m moving at the same speed if I&amp;#39;m moving slowly but then instead of going around a big circle urn which is a very short turn like very start hard turn you need to turn very hard I need to turn the steering wheel a lot to create a very big sideway Force so if the radius of the circle decreases you&amp;#39;re going in a tighter Circle you need more Force and finally what if you&amp;#39;re not driving a car what if you&amp;#39;re driving a big truck truck Furniture bricks whatever it is your truck is very heavy because you have more mass you need more for which makes sense because mass as a property makes it harder for you to move again mass as a property makes it harder for you to move the more mass you have the more Force you need to make you turn so keep these in mind but can I say something really quick circular motion as a concept doesn&amp;#39;t show up in questions a lot you look through M the past seven or eight questions variant in 2023 and 2022 and 2021 it doesn&amp;#39;t show up on its own a lot usually it&amp;#39;s a multiple choice question maybe it&amp;#39;s like part of a little question but it doesn&amp;#39;t appear a lot so it&amp;#39;s not a very very important part of this chapter but it&amp;#39;s there you need to revise it and let&amp;#39;s move on to the last bit of motion this one is very easy falling objects if you drop an object and you allow it to fall and there is no air resistance as in vacuum it falls at a constant acceleration of 9.8 m/s squared which is the acceleration of Free Fall G this is just like the value of G because if there is no air resistance the only force acting on an object is weight and the weight causes it to accelerate at 9.8 m/s squ that&amp;#39;s if the question says there&amp;#39;s no air resistance air resistance is ignored you&amp;#39;re falling in a vacuum it falls with a constant acceleration have a nice day there&amp;#39;s nothing else to explain but if an object is falling through air like a sky diver for example and there&amp;#39;s air resistance any object falling through air experiences three different stages of motion stage one when you just start to jump you like you&amp;#39;ve just jumped there is only gravity acting on you so what do you do you fall with a constant acceleration so this is the sentence you say only weight acts on the object downwards so the object falls with a constant acceleration resistance depends on your speed So the faster you start to move the more air resistance starts to act on your body so as your speed increases the air resistance increases I&amp;#39;ve mentioned the direction huh direction is very important so the downward resultant Force decreases wait 100 80 Newtons the resultant is now 20 when before it was 100 Newtons pulling me down now it&amp;#39;s 20 now it&amp;#39;s 10 now it&amp;#39;s zero eventually your air resistance increases and becomes equal to the weight so they cancel out and what did we say happens resultant Force you a zero you move at a constant speed when the air resistance is equal to the weight the resultant force is zero acceleration is zero you move at constant speed this speed is called terminal velocity speed terminal velocity if I ask you to draw a speed time graph for this motion this is what it should look like it shouldn&amp;#39;t be colored obviously you just draw it with your black or blue or pencil black or blue pen or a pencil but the first stage doesn&amp;#39;t take a lot it&amp;#39;s just a quick straight line Le because it&amp;#39;s you know constant acceleration then this line starts to curve downwards my decreasing acceleration like we said earlier earlier and finally you move at constant speed constant speedly because air resistance is now equal to weight as an extra thing which sometimes shows up if we have a parachute like if I&amp;#39;m skying with a parachute and I open the parachute the moment the parachute opens I slow down and I drop to a new constant speed why do I slow down like why would I slow down if I open a parachute because the air resistance is more than the weight the weight is less than the air resistance so you start to slow down you don&amp;#39;t go upwards you just slow down suddenly then you move at a new constant speed let&amp;#39;s solve a couple of questions some of these are super hard by the way like this this question is actually very hard like I chose a very hard question to solve on purpose this is from June 22 variant 2 figure 2.1 shows an object of Mass 2 kilograms on a bench so it&amp;#39;s a 2 kilogram object the object is connected by a cord over pul to a 3 Kg object the 2 kilog object is released and then it accelerates at four accelerate why would it accelerate accelerate to the right with an acceleration of 4 m/s squ acceleration with an acceleration of 4 m/s squar to mister you just said in when an object falls and there&amp;#39;s no air resistance be acceleration 9.8 that doesn&amp;#39;t work here because there is a force resisting you it&amp;#39;s not air resistance not yet at least it&amp;#39;s what it&amp;#39;s this object tension C we pull it up even though they&amp;#39;re both falling it does apply you know a stretching upward Force so the 3 kilog object two forces the weight of the 3 kog object it&amp;#39;s not friction or you could consider it friction me okay if there&amp;#39;s any friction I&amp;#39;m not sure because he didn&amp;#39;t say if there&amp;#39;s a rough force or not but I do know and there&amp;#39;s tension here because this is a thread or a string that&amp;#39;s is stretched but the thread itself is a pulling it up I don&amp;#39;t have enough data to say if there&amp;#39;s friction but it&amp;#39;s a good thing to assume and I don&amp;#39;t need that assumption upward Force F the resultant Force makes you accelerate with 4 m/s Square like I&amp;#39;m just going to answer each question separ calculate the resultant force acting on the 2 kog object fals M Force 2 kg 4 eight came newton8 Newtons but it shed with resultant force of 8 Newtons that&amp;#39;s all we&amp;#39;re saying Cate the upward Force this is the hard question exerted by the chord on the 3 kog object you need to understand two things first this 3 kilog object exper expences two forces weight will upward Force F okay it&amp;#39;s a very bad I don&amp;#39;t know why called it and second and second in this object is moving with an acceleration of 4 m/ second because he said they&amp;#39;re both connected and if they&amp;#39;re both connected they&amp;#39;re moving with the same acceleration and if they&amp;#39;re moving with the same acceleration it&amp;#39;s four but this mass is 3 kilog step one I&amp;#39;ll do what I can which is force [Music] I which is mass time acceleration if I say 3 * 4 which is 12 Newtons would F this is weight minus F object it&amp;#39;s falling downwards I can guarantee you up I can guarantee he&amp;#39;s moving at constant speed he said it&amp;#39;s accelerating 12 because remember fals M A give resultant Force give it a resultant force wus not directly directly weight weight questions don&amp;#39;t show up on their own a lot but weight questions show up in the middle of other questions M which is 3 kilog times in 2022 G can new per kilogram 9.8 this is new syllabus starting 2023 9.8. weight 30 Newtons and W 30 Newtons minus FAL 12 fals a 30- 12 18 18 okay this is a hard question why you needed to use FAL ma to get the resultant of a weight will upward force and second you need to understand and if you weight we upward force and their difference is 12 Newtons then you need to get the weight of the block this is a separate question so you get the weight 30 - 12 the objects have a constant access acceleration show that the speed of the objects 0.08 seconds yeah that&amp;#39;s time after release is 3.2 L speed the wait if they have a constant acceleration acceleration before rule just write down the rule acceleration equals change in velocity over time therefore change in velocity is equal to acceleration time time acceleration before will time of 0.8 4 * 0.8 3.2 m per second he wants to see the working show questions mean you need to show the working finally a card of width 2 cm the distance is fixed to the 2 kog object in Mass maybe I don&amp;#39;t need it maybe I do as the 2 kog object moves to the left the card passes through a beam of light that is perpendicular to the card basically we got a laser pointer once we press the button creates a laser and then this object has a card sticking out of it this block has a card sticking out of it and as the block is being pulled forward this card cuts the laser like it touches the laser and it cuts the laser K use the speed given in CI which is 3.2 to calculate the time taken for the cart to pass through the beam of Light how long is the card I should pass through the beam of Light 2 cm how long is this card two cmers and how fast is it moving 3.2 what does he want time speed is distance over time equation speed therefore time is distance over speed the distance is 2 cm wait to change from C meter you divide by 100 okay over speed 3.2 0.02 3.2 0625 0.00625 seconds okay okay okay let&amp;#39;s move on uh I&amp;#39;ll answer that right after the session okay finish up momentum vectors Springs because we have to finish this and momentum and then when we&amp;#39;re done I&amp;#39;ll answer your question okay a force is a vector quantity state two features of a vector this is easy vectors have magnitude oh wow okay okay sorry uh that&amp;#39;s huge have magnitude and Direction State the names of two other quantities that are vectors so he said Force so we could say velocity we can say acceleration they both work okay actually I want this question for this a student suspect a spring from a clamp stand and measures the length L the student then suspends loads of different weights from the spring and measures the length of the spring for each load this is the experimental procedure that we follow expansion extension length and so on he then plots a graph of the length of the spring against w weight figure 2.2 is the graph the students plot they ploted the graph if I look at the line it&amp;#39;s curving upwards the limit we can easily tell that the limit is somewhere here because that&amp;#39;s when it stopped being straight or maybe here but let&amp;#39;s continue use figure 2.2 to determine the initial length of the spring to Y AIS is not extension it&amp;#39;s length so the original length original length or initial length is the length of the spring at a force of zero oh uh well I don&amp;#39;t know how to read the small square .02 this is after five squares this is 0.1 s012 0.2 since each one small square is 0.02 but the answer is 0.12 I need to I need the unit it&amp;#39;s meters from the graph it&amp;#39;s meters next state what is meant by the limit of proportionality and determine the weight of the load that causes the spring to just reach that limit here&amp;#39;s how we Define it it is the a it is the maximum the maximum force or low after which the spring does not return to its original limit to only after which the spring no longer obeys Hook&amp;#39;s law or does not extend proportionally the limit of proportionality what is the weight liity so like we said we&amp;#39;ll look at the graph oops and we&amp;#39;ll see when did it start it is the force not at which after which the load force is no longer proportional to extension you can okay after which they&amp;#39;re not proportional now there it is uh this was straight and I want to show you a trick I do cuz sometimes you know what graphs are not very clear value what I do is I put my ruler on the line line and then value when the line started to curve away from the ruler this is good this is very obvious so I go down down down down down this is should use a ruler it&amp;#39;s not 11 it&amp;#39;s what it&amp;#39;s 10.8 it&amp;#39;s 10.8 this is what I like to do I put a ruler down when did the line start to deviate away from the ruler because it&amp;#39;s sometimes hard to see with your eyes cuz Mister can&amp;#39;t I just say 10 look it&amp;#39;s nice and easy oh but it&amp;#39;s still straight after 10 11 you mis it&amp;#39;s easy you&amp;#39;re right it&amp;#39;s it&amp;#39;s it&amp;#39;s curved at 11 but when did it start to leave the line the the straightness of the line so 10.8 next determine the spring constant of the spring a to find the spring constant K is equal to F over X what is f f liit so choose any point on this graph and I would prefer to choose a point where the intersection is nice yeah like the line intersects at a really good point it&amp;#39;s a very annoying graph s so let&amp;#39;s say I like this one this is clear to an extent this is a nice intersection here this is also a nice intersection this is also a nice intersection like what I&amp;#39;m looking for is an intersection where it&amp;#39;s not like halfway through a square or a quarter way through a square or like kiding like this is an okay intersection board okay on looking at a graph that&amp;#39;s printed in front of you is so much easier on the eyes compared to a screen or a monitor&amp;#39;s let&amp;#39;s pick this point let&amp;#39;s pick this point pick any point force and extension force and 1 two 3 four five so this is 5.2 Han 1 2 3 4 5 this is 0.34 the mister is this the extension extension 0.34 like this is the force 5.2 Newtons extension length in order to get the extension extension is what original length minus it total oh total length minus original length so if I decided that this is my point to use you can use any other point but if this is my point to use the length extension sorry is not 0.34 it&amp;#39;s 0.34 minus 0.12 and 5.2 by 0.34 minus 0.2 2 23.6 or so 23.6 what&amp;#39;s the unit unit a table Newton for the force per divided by x x can be meters on the graph I said table accidentally earlier I meant Li a graph length is M and weight is n so it&amp;#39;s n over M because it&amp;#39;s Force overextension very good last bit this is a very small bit by the way like momentum is very simple because what is momentum momentum is just mass times velocity there&amp;#39;s nothing special about it it&amp;#39;s just masstimes velocity Newton velocity he multipli them and how do we calculate them how how do we calculate momentum it&amp;#39;s Mass velocity so the definition is the equation or the equation is the definition the symbol for momentum is p but if you don&amp;#39;t like it don&amp;#39;t use it like M what is momentum Mass velocity the unit of mass is kilogram and the unit of velocity is meters per second so momentum is kilogram m per second what is impulse impulse is when you apply a force on an object in a very short time like you smack an object you hit it very fast that&amp;#39;s called an impulse and it&amp;#39;s calculated using force times time ft force times time both of these equations momentum have Force mass times velocity which is how much okay of course uh how much movement an object has and I have a truck at the same speed we say that the giant truck has more momentum more motion more movement simply because it has more mass it&amp;#39;s harder to stop and that&amp;#39;s what momentum is how hard it is to stop an object from moving depending on its mass and velocity impulse impulse is force time time momentum is mass time velocity these two are related because of a rule resultant Force Newton&amp;#39;s Second Law or resultant Force defines resultant Force as change in momentum over time but this is the original Second Law in force is equal to the change in momentum over time if force is changing momentum over time Delta m t but ft equals change in momentum this means that impulse is also equal to the change in momentum impulse is equal to the change in momentum as a meaning because a lot of questions will ask you to calculate momentum and then ask you to State the impulse he or I can ask you to calculate the impulse but you only have mass and velocity so what do you do you calculate change in momentum they are the exact same thing in terms of calculation but in terms of definition impulse is force times time and momentum is mass times velocity and what is force change momentum over fine but you also need to know how to use this the principle of conservation of momentum and solve simple problems simple is uh in quotes because some questions are not simple as I&amp;#39;ll show you in a bit in one dimension what is the principle of conservation momentum it states that the total momentum of a a closed system is always conserved or constant meaning the total momentum of the two objects before they Collide if you calculate the momentum of the objects before they Collide and you add them up so in this case it&amp;#39;s m * UA like the velocity and mass of this object before the Collision Plus the mass times velocity of this object after before the Collision as well M Au UA plus MB U equals like when they bam Collide the sum of their momentums after the Collision total momentum is conserved is constant and before equals after but if I calculate the momentum of the objects of each object separately before and after the Collision before totally equal after so look at this formula m a UA plus MB U equals m a v a plus MB VB for example z z and we cancel it out and if a question gives you mass and U and mass and V and mass but not VB you try to find it and this is the LA this is the law and this is the law the exact same scenario an object called a that&amp;#39;s going to hit an object called B okay truck a this is from June 2016 okay truck a of mass 6,000 kilg is moving at 5 m/s it is approaching a truck B of mass 5,000 kilog which is stationary calculate the momentum of truck a so this is a simple momentum question first like he was like hey here&amp;#39;s truck a what&amp;#39;s the momentum so mass time velocity which is 6,000 * 5 6,000 * 5 so that&amp;#39;s 30,000 30,000 what unit mass time velocity so kilogram time met per second so kilogram met per second if you want to put a dot put a dot next the trucks Collide their buffers compress and they bounce off each other remaining undamaged after the Collision truck B has a momentum of 27,000 he kind of skipped a a few steps and he said hey after they collided and truck a a but I know [Music] Tru with a momentum of 27,000 kg M momentum a what was the momentum of truck B before the Collision like before it was hit uh zero if it&amp;#39;s stationary and it&amp;#39;s not moving it has no velocity momentum was Zero now the momentum is 27 determine the impulse we know that impulse is force times Time s but we also said that impulse is changing momentum I don&amp;#39;t have force or time but I do have the momentum I even have the change in momentum okay I even have the change in momentum because the momentum before it was hit was Zero the momentum after it was hit is 27,000 so what&amp;#39;s the change 27,000 minus 0 27,000 kilogram m per second it&amp;#39;s 27,000 kilogram meters per second yeah it&amp;#39;s two marks but it&amp;#39;s the same answer all he needs to see is oh impulse is change in momentum and the change momentum is 27,000 I don&amp;#39;t need even have to calculate next the trucks are in contact for 0.6 seconds it&amp;#39;s giv me time the only formula momentum is force equals change in momentum over time this is the only formula with time okay this is the only formula with time what&amp;#39;s the force change in momentum over time impulse impulse is force times Time Force is impulse over time I already have the impulse 27,000 I and I have the time 0.6 27,000 IDE by6 45 th000 45,000 Newtons how I use this like how did I work this out impulse divide by time listen you need to memorize the formulas you need to memorize so you can put them down and choose the correct one based based on what the previous value was calculate the final speed of truck a calculate the final speed of truck a this is the last thing I&amp;#39;ll solve I know there&amp;#39;s one more question left I&amp;#39;ll let you solve it on your own and we can revise it next time but what&amp;#39;s the final speed of truck a find speed of truck a and speed of truck a after the Collision which means we will use the law of conservation of momentum yeah total momentum before equals total momentum after then total momentum before equals total momentum after oh What&amp;#39;s the total momentum before you don&amp;#39;t need to calculate it you don&amp;#39;t need to calculate it the total momentum before is shown we already have it it&amp;#39;s 30,000 because that was the momentum of truck a before it collided and truck B was Zero now did he say he rebounded or did he just say they bounce off each other he said they bounce off each other I don&amp;#39;t know in which direction did it go because he didn&amp;#39;t say rebound and second look at the value of the momentum of B after the Collision if the total momentum was 30,000 kilogram m/s and this is zero to the left like the total momentum has to be 30,000 to the left after the corion what happened B went to the left 27,000 30,000 momentum I&amp;#39;m not asking speed momentum the total has to be 30,000 that 27 3,000 he didn&amp;#39;t say it went to the left it didn&amp;#39;t say it went to the opposite direction he just said they bounc up as in they did not stick to each other like they bounced off as in did not stick to each other if he wanted rebound he would say rebound question rebound okay mister what does he want en total momentum before is 30,000 What&amp;#39;s the total momentum after truck a plus b huh remember a plus b a mass times velocity plus b which is 27,000 mass time velocity Tru a is equal to 30,000 minus 27,000 3,000 remember I want the speed up speed subject VA is equal to 30,000 what was the mass of a forgot a there it is became 6,000 kilog 6,000 kilog velocity 0.5 m per second so again what was the concept total momentum is constant since the total momentum before the Collision was 30,000 after the Collision 30,000 literally the momentum was split B 27,000 a gets the rest which is 3,000 since we already have the momentum of a which is 3,000 we can get the velocity since momentum is mass times velocity and I want velocity but velocity equals momentum over Mass 3,000 over 6,000 but 0.5 m/s okay before I end the session I won&amp;#39;t solve this I want you guys to try and solve this but keep in mind this is also a momentum question there are two tricks here units [Music] and look at this after hitting the object like a ball is going to hit the object the ball bounces back H did you notice back if a question changes the diction and you&amp;#39;re solving momentum you don&amp;#39;t add the total moment and if I said M here&amp;#39;s ball that before the Collision the to the right and this is stationary after the Collision if this is moving to the left and this is stationary this is moving to the right M VA plus Z because it&amp;#39;s stationary minus m a vaa plus MB VB minus so I&amp;#39;ll just quickly show you the working mass times velocity is 0.19 because I changed this from grams to kilogram time 6.9 which gives me19 * 6.9 is 1.31 kilogram m/s but Mister did you need to do this GRS you would have left this as 190 you don&amp;#39;t divide it by th and this answer would be uh what 2 three so 1,310 gram meters per second so going to keep it as kilog after hitting the object the ball bounces back with a speed of 1.5 the object has a mass of 1.8 what&amp;#39;s the speed of the object after it&amp;#39;s hit by the ball but basically momentum before which is this which we which we already calculated equals momentum after which is this minus because it&amp;#39;s moving to the left relax but what was the velocity of this ball 1.5 mass time velocity 0.19 time 1.5 minus plus mass times velocity of this pin 1.8 time moment equals total momentum after before 1.31 after minus 0.19 * 1.5 it&amp;#39;s moving to the left sign it&amp;#39;s not added you don&amp;#39;t add them subtract them minus this is 1.31 = 19 * 1.5 which is is 0.285 + 1.8 V but therefore V is equal to 1.31 + 0.285 over 1.8 this is just some algebra that I&amp;#39;ve done I assume you can do the same divided by 1.8 this gives me 0.886 m per second and that&amp;#39;s unit or half of unit one

Transcript for:General Physics and Mechanics (Unit 1)

Transcript for:
General Physics and Mechanics (Unit 1)