lesson one momentum and impulse we'll start with a review of scalars vectors and units just a basic overview we'll get a little bit more deep into vectors and units later in the course scalars are measurements that have magnitude only magnitude is the word we use in physics for amount or the number part of a measurement vectors our measurements that have magnitude and direction this means they have an amount but they also have a part of it that tells you which way that magnitude points examples of scalars include speed time mass distance and energy the math that we do with scalars is much simpler you can just add scalars together without worrying about addition or subtraction or direction because scalars have no direction vectors on the other hand have more complicated arithmetic associated them because of the direction part these are quantities like velocity acceleration force and the topic for today's lesson momentum when you're using velocity acceleration force and momentum it's not just enough to know how much their magnitude is you also need to know which way they're pointing so you can really understand how they're interacting with the objects associated with them vector notation notation is a series of rules use in math and science for how things should be written in vector notation you should always draw an arrow over the vector symbol so for example if you're using velocity to distinguish it from speed we draw a little arrow over top to show that it's a vector we also put the direction in square brackets next to the unit so for example if you have a velocity of 10 meters per second you put the direction in square brackets next to the unit using vectors and calculations again we're just going to go for a basic overview later looking more deeply at vector addition you should know that there are positive directions positive directions are all given a positive sign when used in calculations these are North East Ford up and right if we're looking at our XY coordinate system positive directions are the directions that form the positive y axis and the positive x axis negative directions are South West backwards down and left these are the directions on our XY coordinate system that are associated with the negative x axis and the negative y axis now the plus or minus sign is considered to be a direction indicator don't write the negative and the direction you would write velocity equals 10 meters per second West or velocity equals 10 meters per second negative don't write the negative and the West negative West means east the plus or minus sign is considered to be a direction indicator itself so you don't actually have to write the direction the negative is the directions if you write negative a direction you end up flipping your direction and your answer doesn't mean what you think it means units in the SI unit system which is the unit system we use in science there are seven base units in physics 20 you only learned about three meters seconds and kilograms but in total in the SI unit system there are actually seven the meter the second and the kilogram are the ones that we're going to matter to you the most now now be careful in physics we use the kilogram whereas in chemistry they tend to use the gram more often don't mix up physics and chemistry the other units are called derive units and they're constructed from these base units for example acceleration has the unit meters per second squared this comes from the formula for acceleration where acceleration equals velocity over time so that's meters per second divided by a second gives you a meter per second squared for force the unit for the force is generally called the Newton but it can be constructed from the meter the second and the kilogram for example formula for forces F equals MA which is a kilogram times the meter per second squared for the acceleration so we know that one Newton a force is the kilogram meter per second squared the Newton itself is a derived unit it's not a base unit it's made of the kilogram the meter in the second energy also has a derived unit for example one formula for energy that we use is potential energy equals M G H the unit for mass is kilogram G is a type of acceleration so it has a meter per second squared and height is a meter a kilogram times a meter divided by second squared times an their meter gives you a kilogram meter squared per second squared now that's a little bit too much to write every time you write a write out a measurement for energy so they give that a single simple symbol called the Joule so one Joule is a kilogram meter squared per second squared finally we have energy and reduce another concept or power is another concept associated with energy the typical symbol for power is the watt power is energy over time we've already seen that energy is measured in joules so that's joules per second or a Joule is a kilogram meter squared per second squared that divided by a second is a watt so a watt is a kilogram meter squared per second cubed there are some basic unit conversions you should be able to do you should already be able to convert metric units from one bait prefix to another but here are some of the most common ones you need to be able to convert a kilo to the base unit whether it's a kilogram or a kilo meter the conversion factor for kilo is a thousand kilo means a thousand so a kilometer times a thousands will give you a meter and a meter divided by a thousand will give you a kilometer the same goes for kilograms and grams you need to be able to convert kilometers per hour which is the most common unit of speed used in everyday life into a metre per second which is the unit used in physics for speed and velocity the conversion factor is three point six a kilometer per hour divided by three point six gives you meters per second meters per second times three point six gives your kilometre per hour one of the ways I remember this is I noticed that a kilometer per hour has three letters a K and M and an H and the division sign has three parts so if I want to divide a kilometre per hour if I want to convert a kilometre per hour into meters a second I know to divide because it has three letters meters per second has two letters and the time sign has two parts so I know that if I want to convert meters per second to kilometers per hour then I would multiply because of that finally you need to be able to convert for hours which is the unit we use in everyday life for time two seconds which is the unit used in physics the conversion factor for this is a thousand times three point six is three six zero zero or 60 times 60 because there's 60 seconds in a minute and 60 minutes in an hour an hour times 3600 will give you a second a second divided by three points three six zero zero will give you at an hour next we're going to look at two fundamental concepts for this unit momentum and impulse momentum is defined as a product of an object's mass and velocity mass given in kilograms with the symbol m and velocity given in meters per second with the symbol V don't confuse the Amazon mass with the M as in meters one is a symbol the other is a unit momentum is given by the symbol P with an arrow over top of it to say that it's a vector I don't know why they chose to use the letter P it's got not much to do with momentum it might because they'd ran outta letters of the alphabet M was taken by mass and meters so it couldn't be used again so they chose P the unit for momentum is the kilogram meters per second there isn't a special symbol for this derived unit it's just the collection of kilogram meters per second that forms momentum the formula for momentum is P equals M times P where P is Momentum's measured in kilogram meters per second M is mass measured in kilograms and V is velocity measured in meters per second the direction of the velocity will be the direction of the Momentum's an object can have a large omentum either by having a very large mass and a total slow velocity or a tiny mass and a very fast velocity for example an elephant is a fairly slow moving creature an elephant has a very large mentum because it has a very large mass on the other hand a bullet could have a similarly large momentum but it's a very small object a bullet because it moves very fast also has a high momentum when you think about momentum I want you to think about how much you would hurt if that object were to collide with you at that speed an elephant moving very slow would still probably hurt quite a bit if it ran into you a bullet though small is moving so fast that it also hurts when it runs into you momentum is all about how much force an object is capable of transferring here's an example for the elephant an elephant with a mass of 1,800 kilograms walks at 0.21 meters per second what is the elephant's momentum mentum equals mass times velocity so the momentum is the mass of the elephant times the elephant's velocity giving us a momentum for the elephant equal to three point eight times 10 to the 2 kilogram meters per second and again the direction for the mentum is the same as the direction for the velocity so in this case it's east here's a second example what is the Wrentham of a point zero five zero kilogram bullet moving at 2000 meters per second to the left the momentum of the bullet will be given by M times Z so this is the mass of the bullet bullet times its speed or velocity so the momentum of the bullet is equal to 1.0 times 10 to the 2 kilogram meters per second and again the direction is the same as the velocity so that will be to the left you can see these two objects even though they're quite different in size have similar momentum because the elephant is going slowly and the bullets going quite fast simples is the second concept associated with momentum momentum is most useful in physics problems involving collisions and explosions remember momentum is most useful when you think about how much force the object could transfer if it was traveling at that speed transfer force usually occurs during a collision or an explosions a collision is a short interaction between two objects during a collision and impulse is transferred from one object to another this is the same as saying a force is transferred from one object to other but it's a more precise definition impulse has the formula impulse equals Force Times change in time impulse has no symbol if we just write out the word impulse the unit for impulse comes from the formula Force Times time gives you the Newton's times seconds force is in Newtons and time is in seconds now Delta notation is something you should be familiar with from physics 20 Delta means change in Delta or triangle is a Greek letter and it's used to symbolize a quantity that has changed so the impulse is the force times the change in time or the time interval that the force took place over here's an example during a collision between a tennis ball and a racket an impulse of 0.425 Newton seconds is transferred to a ball in a time interval of 0.025 seconds what was the force on the ball impulse is equal to the forest transferred times the time interval it was transferred in we can rearrange this to give us force equals impulse divided by the time interval which is 0.425 divided by the time interval of 0.025 seconds this gives us a force imparted of 17 news we can connect the concepts of impulse and momentum now I've already explained to you that momentum is most useful in an event where you have a collision or an explosion impulse is the force transferred in that time interval that if there is a collision or an explosion now we can connect these two formulas by looking back at some of the formulas we need before recall Newton's second law which is F equals MA now impulse equals F times delta T and force equals mass times acceleration so we can rewrite this to give us impulse equals MA to steep also remember back from physics 20 that acceleration is change in velocity over change in time this gives us impulse equals M Delta V over delta T times delta T and whenever you have the same quantity on the top and bottom of a fraction it can be cancelled out so this gives us impulse equals M Delta V now M Delta V looks very familiar momentum is MV so it makes sense that M times change in velocity would be a change in momentum or Delta P equals M Delta V what this tells us is a really important thing about physics impulse is equal to the change in momentum the way we would write this out is f delta T equals M Delta 3 impulse F delta T change momentum M Delta V now if you examine your formula sheet for momentum and energy you'll see some familiar formulas that we've gone through in this video so far well mentum formula p equals MV is there but you won't see the impulse formula that's because the impulse equals change in momentum formula is listed and they don't want to list it twice so f delta T impulse is given there M Delta V change in momentum is also listed but they don't list them individually it also shown as usual because it shows this relationship F delta T equals M Delta B or impulse equals change momentum and analysis now I showed you for impulse impulses F delta T which has the unit's Newton seconds change in momentum is M Delta V and we use the momentum units kilogram meter per second I'm going to show you that the Newton's second and the kilogram meter per second are interchangeable even though when you're using impulse use the Newton's second and when you're talking about momentum use the kilogram meter per second they actually are the same unit so we know because the Newton is a derived unit that the Newton is the kilogram meter per second squared now the kilogram meter per second squared times a second means that we end up cancelling out one of the seconds this gives us a kilogram meter per second so in other words we can also show using unit analysis that impulse is equal to momentum here's an example a racket hits a 0.057 kilogram tennis ball for the 0.03 four seconds that the collision occurs a force of 47 Newtons is exerted what is the change in speed of the ball will use this impulse momentum relationship that we derived f delta T equals M Delta V to calculate the change in velocity change in velocity would be f delta T divided by M which is 57 times the change in time divided by the mass which gives us 34 meters per second another good useful example of this F delta T equals M Delta V relationship is airbags airbags lengthen the amount of time and victim's head takes to stop during the collision so delta T becomes bigger or a longer number now we know that the change in velocity can't change during a collision you go from the same initial speed to the same final speed the airbag isn't gonna change the speed to originally going at and it's not going to change the fact that you stopped also know that mass can't change - due to the airbag the airbag isn't gonna change the mass of your head at all there's nothing that can be done it's your head so the only thing that can change is the force in order for F Delta t to the M Delta V where these the M Delta V can't change stays the same delta T becomes bigger in order for the relationship F times Delta team to still equal M Delta V the force has to become smaller so the purpose of an airbag is to increase the amount of time your head has to stop in so that the force on your head becomes smaller final example and this one's going to be a little bit longer a 5 kilogram puck slides to the right at 10 meters per second on a frictionless surface and it collides with a stationary eight kilogram puck the five kilogram puck rebounds at 2.5 meters or second to the left what is the final velocity of the eight kilogram puck so it's helped sometimes to draw a picture of the situation so we can properly visualize what's happening in this situation we have a collision and we have a before the collision and after the collision so before the collision we have a 5 kilogram puck sliding to the right at 10 meters per second colliding with a stationary eight kilogram puck now we then have a collision and after the collision the motion changes the five kilogram puck is now going to point five meters per second to the left and the a kilogram puck is probably also moving and we want to find out how now to solve this problem it's best to realize that in the moment of the collision Newton's third law still applies Newton's third law is during an interaction an equal and opposite amount of force is exchanged between the up two objects so the five kilogram puck experience is the exact same amount of force during the collision as the eight kilogram talked since impulse equals F delta T is the change in momentum and F is equal and opposite so the force it's equal and opposite during the collision for the two pucks therefore the change in momentum for the two pucks must also be equal and opposite same amount different direction so the omentum of the five kilogram puck before is equal to M VB 4 which is 5 times 10 is 50 kilogram meters per second to the right and the omentum of the 5 kilogram puck after is M V which is 5 times 2.5 to the left here's 12.5 kilogram meters per second to the left the change in momentum for the 5 kilogram puck would be momentum of the 5 kilogram puck after minus the momentum of the 5 kilogram puck before which is 12.5 negative because its left minus 50 positive because it's right there's 62.5 kilogram-meters per second negative which means left now we know that the change in momentum of the Akal grandpa must be equal amount and opposite in direction this means that the a kilogram puck must experience a change in momentum of sixty two point five kilogram meters per second to the right since the change in momentum of the eight kilogram puck is equal to momentum of the eight kilogram puck after minus the lenten of the eight kilogram puck before and before the eight kilogram puck wasn't moving so sixty two point five kilogram meters per sec to the right is equal to the momentum of the eight kilogram puck after minus zero or just the mental of the eight kilogram puck after is equal to sixty two point five kilogram meters per second to the right this allows us to calculate the velocity of the a kilogram puck after the collision since p equals MV V equals P over m the sixty two point five divided by eight kilograms which gives us seven point eight meters per second to the right