Okay students, so let's get started with the next topic that is dynamics. So dynamics, first of all, we will see Newton's laws, first, second, third, we will see momentum equations and then we will move on to principle of conservation of momentum. Okay, so first of all, let's see Newton's first law.
It basically tells us that if there is an object which is at rest, it will remain at rest if there is no external force on it. And let me tell you one more thing about Newton's first law that if an object is moving at a constant velocity it will keep moving at that constant velocity until and unless what you apply on it? Don't apply any external force on it. Until and unless you apply any external force on the green one, it will continue to move at a constant velocity. Why does this happen?
This happens because both at rest Both at rest and at constant velocity, resultant forces are zero. And when resultant forces are zero, then your state of motion remains the same. If object is at rest, then it will remain at rest.
If it is at constant velocity, then it will remain at constant velocity. Now let's come to Newton's second law. What does Newton's second law say? Newton's second law says that force is equal to the rate of change of momentum.
You have got this equation. Force. is equal to the rate of change of momentum. Simple si second law ki ye wording hai.
Jo humne O level mein pada tha ya IGCAC mein pada tha first of all ki force is equal to M that is wrong. That was not the correct definition of the second law. We just studied to matab usfak hume isle ye study kya tha F is equal to M to simplify things. Lekin asal definition is this force is equal to the rate of Change of momentum and this is basically the second law second law You need a physical through ma f is equal to ma is a derived version of the second law ticket It is not the correct version TK correct version here hey K4 is equal to the rate of change of momentum or a good exam map for second law like not at all You look okay, not this gap physicals to emmett. Okay, a physical so maybe I'm drive curtain is equation second You just wait a second.
Okay What is the symbol of momentum? P is the product of mass and velocity. Till now, everyone knows this from O level. If you don't know that, P is equal to mv.
Okay. And vector quantity is units. Kgms minus 1 and Newton second. Okay. Now, we will derive that formula from this formula which we have studied in O level.
That is, F is equal to mv. So, just keep watching. Okay.
Okay. Now what we will do? We know that force is equal to rate of change of momentum.
So when rate of change happens, then what we do? Momentum final minus momentum initial divided by time. Okay? Whenever change sign comes, we can divide it into two quantities. P final minus P initial.
If change in temperature happens, then what we do? T final minus T initial. Whenever change sign comes, you minus the final from the initial.
Okay? Now what will be the final momentum, kids? M V F minus M. V divided by T, V would be the final velocity, V would be the initial velocity and mass remains same.
So, if I take the mass constant from here, then what will be left? V minus V divided by T. Now, if I replace V, that is final velocity with V and consider V as U, that is initial velocity as U and final velocity as V. And do the equation V minus U divided by T. So, there will be no difference. Now, I had studied in kinematics that V minus U divided by T is equal to what?
Acceleration. So, what is the final answer? F is equal to M. This is how the equation is derived.
So, let me clear this up so that I can show you the easy working. This was just for the explanation. F is equal to change in momentum divided by time.
Final minus initial momentum divided by T. Final velocity into mass minus initial velocity into mass divided by T. And we took mass commonly from those two. And we got V minus Q divided by T. That is equal to acceleration.
Place it and the result is derived. So, in IGCSE, we used to read F is equal to M. That is basically a derived formula from the second law. That is not the second law.
What was the second law? Force is equal to rate of change of momentum. Okay.
And if we multiply the time with force. If we multiply the time with force. And make change in momentum the subject.
The thing that this comes out to be. F into T. The thing that comes out to be F into T. Force into time. This is also known as impulse.
How did we get this? We have just rearranged the equation. We have cross multiplied T here.
and change in momentum is the subject so we got impulse equation that is F into T just remember this see here it is written, define impulse how it will be defined, simple is product of force acting on an object and time taken for which it acts, ok, force and time's product is your impulse ok, which are the formulas of impulse simple, all are derived force into T, ok, force into T whose equals is change in momentum change in momentum How can we write final minus initial momentum? It is written. And how can we write it?
mv minus mu. v is the final velocity. u is the initial velocity.
Simple. What is the unit of impulse, children? Newton per second. Or Newton second.
Not Newton per second. Only Newton second. Okay. If a graph of force versus time is drawn, the area under it will be the impulse.
Why we have found this out? Because f into t is what? change in momentum or we can say impulse.
And what is the area under this graph? The area under this graph is also f into t y axis into x axis. So, that would be also equal to impulse.
So, if you are given in an exam force or time graph, you can calculate the area under it to get the impulse. Do remember this sometimes there are MCQs like this. Now let's move on to examples on how to calculate change in momentum.
Simple logic. What did we study? How can we divide? Means how can we divide change in momentum in two quantities?
Final minus initial. What was final momentum? M into final velocity minus M into initial velocity is your initial momentum. For final velocity, what do we have in this scenario?
V is there. But. it is on the left hand side so we will take negative v so m minus v okay m and u is in the right hand direction so we will take it as positive v so what does this become minus mv minus mv what would be the change in momentum minus 2 mv okay i think that i forgot i forgot one thing before asking this question was that to define the scales what is scales or axis Whenever you ask any question related to vectors, always define the scale.
Let's say right hand side is positive. You have defined it. So, it will make work easier for you. Whatever velocity is on left hand side, you can take that as negative. Whatever velocity was on left hand side, you took it as negative.
See, in P final, you took B as negative. You kept U as positive because it was in the direction of the right hand side. M minus V minus M into V. That is minus M.
minus M so the total answer is minus 2 MB. Let's see it again. Let's see it again. Let's do it one more time so that it gets clear.
First of all, whenever the question of change in momentum comes, you have to see whether the collision is elastic or inelastic. In this case, it is elastic. Now we have to find change in momentum. What was the formula of change in momentum? P minus P.
P is the final momentum. P is the initial momentum. How will be the final momentum?
m into final velocity How will be the initial? m into initial velocity What is m into final velocity? It is v but it is going to the left hand side So it will become negative v And initially before you ask the question We have defined that right hand side is the positive side What is minus mu?
What was the initial velocity? v But in the right hand direction So we will take it as positive So it will become minus mv minus mv is equal to minus 2 mv. This would be your final answer of change in momentum.
Okay. I hope it is clear. See here also I have worked.
You can see it again. Come on. One more question came.
In this also we have to find change in momentum. Given that ball comes to rest after collision. What does this mean?
What is the final velocity? Zero. So let's calculate the change in momentum. Change in momentum is a formula of P F minus P I. What is P F?
What is the final velocity? Zero. What is M into zero minus M?
M into V on the right hand side. If we define the right hand side as positive, then V will also be positive. So, what will be the final answer? Zero minus M which equals to minus M is your change in momentum.
So, is it clear? Let's see the answer. yes, this is done by minus mv and you have another option of taking the left hand side as positive here we have taken right hand side as positive, if you take left hand side as positive then your answer will be plus mv so it basically depends on which side you have considered as positive ok, let's suppose we have a mass of the ball 0.05 kg and time of impact with the ground is 10 ms now how do we convert 10 ms milliseconds into seconds we know that one milli is equal to 10 minus 3 seconds okay so do remember this conversion that milli is equal to 10 minus 3 okay now let's solve this question calculate the change in momentum first we have to calculate the change in momentum so that is really really easy how do we calculate change in momentum final momentum minus initial momentum okay guys for final momentum we will take m v minus m u What is mv?
And one more thing before doing this question we can define the upward direction as positive. Okay, we defined the upward direction as positive and 6th sum of upward direction as final. So this would be positive or negative?
This would be obviously positive 0.05 into 6. Now 14 is going down. So would it be positive or negative? Negative. Okay, what would be the overall change in momentum? The overall change in momentum would be 1 Newton per second.
Okay, let me revise it again. What we did? We considered the upward direction as positive.
We know that change in momentum is final minus initial momentum. What do you do for final momentum? Mass into final velocity. What do you do for initial momentum?
Mass into initial velocity. Mass is 0.05 into 6. That is the initial velocity. We will take it as positive because it is going up.
Minus 0.05 into minus 14. That is your final momentum. initial velocity which is going down and going downward. Okay.
You add them and you get the answer of 1 Newton per second. Why adding them? Because this minus and this minus becomes plus. Okay.
Now, let us do the next part. Okay. Calculate the force during the impact. Now, we have to calculate the force during the impact.
So, do we remember what was the formula of force? Formula of force was change in momentum divided by time. Did we able to calculate change in momentum?
Yes, we won. What was the time? We saw that the time is 10 milliseconds. So let's put that down. How can we write 10 milliseconds?
10 into 10 minus 3. Okay. Here we have written it here. So we will calculate it using a calculator and get an answer of 100 newtons. Simple.
Okay. I hope all these questions are clear. Now let's move on to our next topic.
Now we will be seeing how to apply F is equal to M formula. How to apply it? In.
marking forces and how to calculate result in forces and acceleration through that ok, so we will get all the questions in this, so do watch this till the end ok, let's first of all do some basic questions mark the forces on this diagram, ok in this diagram what will be the forces one will be tension away from the object and second will be weight because it has some weight, it has mass so obviously it will be weight and tension will be away from the object Tension is always, remember this word, tension is always directed away from the concerned object. Okay. Now, what do we have to find?
Calculate t if the object moves at constant velocity of 6 meters per second. Okay. Now, tell me, kids, if you are moving at constant velocity, if you are moving at constant velocity, then what does this mean? What is your acceleration? what is your acceleration acceleration is zero okay acceleration is zero so this means what happened in F is equal to ma if this becomes zero so what will the resultant force become force will also become zero resultant force should be zero now how can resultant force be zero see there are two forces applied tension or weight this is your first force this is your second force In which case the resultant force will be zero?
When tension would be equal to weight. Okay, up would be equal to down Yeah, right would be equal to Left this case may result in for zero you can up key force down key force will cancel the right key force left key Force will cancel the simple thing is okay So in which case we would be moving at constant velocity here Look since forces are balanced constant velocity tension would be 20 newton 20 newton How did we get the tension because what is weight? weight would be mg 2 into 10 that would be 20 Newton or Agar constant velocity be move can I talk you on a chair attention must be equal to weight Okay, the weight attention is equal to 20 Newton simple stuff ticket I'm a gentleman X about this we have to calculate the Mk T. Nika I have if ball accelerates upwards at 2ms minus 2 What to do guys?
We have to find the value of t if ball is accelerating upward at 2ms-2. Now tell me one thing, there are only two forces. So in which direction acceleration is happening, obviously it will be greater force.
So can I write this that resultant force is equal to bigger that is t-w. Why is T bigger? Because T is applied in upward direction and acceleration is done in upward direction Now I know that F is equal to m So can I do this T minus W is equal to m?
What is 2 and what is acceleration in upward direction? 2 Do I know the weight as well? Do I know the weight?
Yes I know 2 into 10 is equal to 20 Newton is correct So what will happen? T minus 20 is equal to 4 What will be the tension? 24 Newton So let's see if we did it right or not.
Let's go to the answer. What will be the tension? It will be a big force because acceleration is happening in the direction of tension.
Hence, what did we do? We did t minus w. This equals to ma. m was acceleration, 2. 20 was minus on the left hand side. What will come on the right hand side?
It will be positive. We will get the total answer of 24 newtons. Simple. Now calculate t if the ball D accelerates downwards at 4ms minus 1. Now, it is accelerating downward. Acceleration in which direction?
In the direction of weight. So, which force will be greater here? Weight will be greater than the T.
Always remember, the direction in which it is accelerating, that force will be more. So, can I write the resultant force like this? W minus T is equal to M.
What is W, kids? 20 minus T is equal to 2 into 4. What will this be? 8. If we subtract 8 from 20, what will be the tension? 12 N. Keep it simple.
The direction in which the acceleration is more, the force of that direction will be more. Keep this simple. Now let's move on to the next similar question. This is a little tricky, but if you put in some logic, you will understand.
Calculate T if ball decelerates downwards at 5 ms-2. till now we have seen many questions in which accelerates and constant speed accelerates means positive acceleration decelerates means negative acceleration it means that calculate t if in downward direction your acceleration is minus 5 Remember this, if in downward direction acceleration is minus 5, then it would be equal to plus 5 acceleration in the upward direction. Always remember this. This is also applicable for velocity.
If it is 4 in downward direction, then it will be plus 4 in upward direction. Do remember this. So, we had minus 5 in downward direction.
We have reverted it and made it plus 5 in upward direction. So, tell me. The direction in which acceleration is happening, that is the upward direction, the force will be more there.
Tension will be more. T minus 20 is equal to 2 into 5. What is the tension? 30 Newton. Simple. If you didn't understand it still, you can ask me in the comments below.
Or you can repeat the video again or download the notes and try to re-go it once. Till now, what forces have we seen? With up-down forces, we have applied a physical sway.
Now let's apply F is equals to M with forces of right and left. There can be two types of forces, up down or right left. Now let's apply F is equals to M with forces of right and left. So here you can see we have two forces, one is on the right and one is on the left.
So what we will do to get the resultant force? F that is the resultant force will be right minus left. Calculate F if object travels at constant speed.
Now kids you know what happens at constant speed. Right value force is equal to left. force. Okay. So right pe abhi kya force lagri hai?
Let's label this as F. Theek hai? So what will be 2000-fe? 0 is equal to 0-2000 What will be fe?
2000 I have just replaced like R with E Because here 2 2 F was happening So it might get confusing What we did basically? We did this that at constant speed We know that F becomes 0 Resultant force becomes 0 Okay When will the resultant force be zero? When right force is equal to the left force. Right force is 2000 N acting on the right. What will be left?
2000 N acting on the left. Simple. F if object accelerates at 5 m per second.
Let's label this as F. F will confuse you guys. Now, what we have read previously?
The direction in which acceleration is taking place, the force of that direction will be more. So, what is he saying? That in this direction, 5 m.
meters per second acceleration is happening so obviously this is more force let's label this as 2000 minus what minus fe what is this resultant force resultant force is equal to ma is equal to m what is this 2 what we have to get out acceleration is given to us 5 we have to get fe out see here fe so fe would be equal to 2000 minus 20 into 5 is equal to 100 is equal to 1900 newton So let's see if our answer is correct or not. Yes, 1900 Newton. Now what is written? Third question. If object decelerates at 6 meters per second.
Let's see its diagram too. What is it telling us? It is telling us that if object is decelerating.
Means what is happening in front? What is its acceleration in front? Minus 6. Okay.
So what will be the acceleration in back? Positive 6 means what will be the acceleration in this direction Positive 6, I have already taught you that if there is a minus 6 on the right, then the vector will be positive 6 on the left And if there is a minus 6 in the up, sorry, there is a plus 6, then what will happen in the down? Minus 6, we have already studied this in this lecture, so do rewind it if you haven't understood it yet So what will happen basically, we have the acceleration of plus 6 on the left hand side Now which force is on the left hand side?
F means F is big F-2000 is equal to M20 into acceleration What is acceleration? Acceleration was 6 This will equal to F is equal to 2000 plus 20 into 6 is 120 N Is equal to 2120 N is your F Is it clear? See here 2120 is written with Newton Now we come to the next type of question which is pulley questions. These are really really easy. We make two equations in it and then we solve simultaneously.
We have to do this in every question. So let's start. See guys, in pulley questions, first of all, what will be applied?
Two weights will be applied. First of all, the thing you have to remember is how to mark the tension and how to mark the weights. Tension is always away from the object.
See, this is our object. This will always cause tension. this is your tension this is your tension okay away from the weight what will happen always from the center of mass and downwards center of mass here and mark down weight from this okay second thing kids what we have to remember about pulley questions is that on which side will be higher weight kids like which is the higher weight of these two 3 kg so pulley will move on that side okay The side with higher weight will move fully So you understood this much And on that side you will have acceleration and resultant force So weight is more on the side of 3 kg So all things acceleration, force and movement will be on this side Means downward movement will be there and acceleration and force will be on this side Ok Now let's make some equations. Now we know that since the pulley is moving downward, why?
Because the 3 kg mass is on the left hand side, so it is moving downward. So the pulley would be moving downward. So tell me, which side is the weight of 2 kg moving if it is moving downward?
This one is moving upward. We have basically learned that first of all, in pulley questions, we mark tension and weight. Second of all, the side where the weight is more, the pulley will start moving on that side. In this, the weight is more on the side of 3 kg, so the pulley will start moving downward on the side of 3 kg. Okay.
Because of this, what will the weight of 2 kg do? It will move up. Okay.
Now, if it is moving up, then which force is greater, tension or weight? Tension, obviously. So, we will write T minus 20 is equal to mk2 acceleration. We don't know.
Okay. Now come to this weight, 3 kg weight. Now 3 kg weight is moving downward. So what force is moving downward? 30 N, that is weight.
So that will be big because it is moving downward. Minus T is equal to what? 3A. Now you have two equations, 1 and 2. Can you solve them simultaneously? Yes, you can obviously solve them simultaneously.
From this equation, make T a subject. T is equal to 2A plus 20. Okay? now substitute this 2a plus 20 instead of this t simple 30 minus 2a minus 20 is equal to 3a now if I will put 2a on this side then what will happen?
5a and 30 minus 20 will be equal to 10 so what will happen? 10 is equal to 5a acceleration will be equal to 2ms minus 2 now if we put acceleration in this equation then what will be the answer of tension? it is equal to 2 into 2 plus 20 is equal to 24 newton okay so i hope it was clear see here i have worked cleanly so you can apply that simple rule is remember in pulley questions that on which side weight is more on that side pulley will start moving and you can draw your equations like this okay let's move to next question okay now tell me in this where is the most weight is 8 kg bigger or 4 kg bigger If it is 8 kg, then obviously the side of 8 kg will start moving down and the side of 4 kg will start moving up.
So what will be the two equations in this? Is the tension more in the 4 kg or is the weight more? Is the weight of 40 N more or is the tension more? Obviously the tension is more because we are moving up, so T-40 is equal to 4A.
This is our first equation. What will happen in the second? Come to 8 kg, 8 kg is moving down, whose weight is 80 N. What will happen? 80 minus T is equal to 8A.
This will be the equation. Why did I take 80 as big? Always keep big forces first.
Why did I take 80 as big? I took 80 as big because this A or 8 kg mass is moving down. And which force is moving down? Weight of 80 N.
80 minus T is equal to 8A. Okay. If you solve these two equations, you will get your acceleration answer. Let me get the acceleration. Yes, 3.33.
Okay. Now the second question is related to kinematics. So do pay a little attention. If you pay a little attention, you will be able to understand that as well. What is acceleration?
Acceleration is 3.33 ms-2. What is it saying in part 2? Calculate the speed when a and b are at the exact same level.
When will a and b be at the exact same level? When it moves 10 meters up and 10 meters down. So what distance we have to move?
10 meters on this side and 10 meters on this side If we move 10 meters overall then our work will be done Because if 10 meters will move down, let's suppose See the pulley is covering the distance on both sides, it is not like this that it is covering on one side only If it moves 10 meters down then obviously B will also move 10 meters up simultaneously So total distance will not be 20 but 10 Okay, what is acceleration, kids? 3.33 ms minus 2. We have to calculate the speed when a and b are at the same level. We have to calculate v. What is u? Since it starts from s, it is 0. So, is there any formula in which if we know s, a, u, so we can calculate v? Is there any formula in kinematics?
Yes, there is a formula. v square is equal to u square plus 2 as u square 0 will be 2. As will be equal to 3.3 into s cat 10 and we will take the under root and get the answer, okay? I hope it is clear here.
Okay, man. I'm working he kiwi. Okay, so this question is also similar You can do it on your homework my notes met at around let's see if sometime you can do it at your homework Okay, or koi bhi cheese unclear Oh, you can ask me in the comments below yeah, pen note could go through Carlo it will be perfectly clear I chaiye a court that I guess about Latin this may Pulley is horizontally lying instead of vertical Horizontal ball is lying and vertical ball is lying Examiner always puts friction force to trick you There will be two equations in this too Let's make it Which two equations will be made?
If I am at point A One is adding weight and one is adding tension This overall system is moving down So tell me, will the weight be increased or tension? Weight W-T is equal to 5 acceleration W will be 50 50 minus T is equal to 5 a will be a first equation okay second equation what will be second equation frictional force is moving it backwards and what force is moving forward tension okay so what will be the second equation it is moving this way so tell me in this tension will increase or friction obviously tension tension minus friction 10 a is equal to 2 into acceleration. This will be your second equation. If you solve these two simultaneously, you will get your T and A. And then you can solve for any other thing that the examiner asks.
The main thing here is that whenever the pulley is horizontal, you have to consider this frictional force as well. And tension minus friction is equal to 2A. Why did I take tension as big? Because we are moving in the right-hand side. And hence, tension will be big.
Okay? Clear?