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### Course: Mechanics (Essentials) - Class 11th > Unit 8

Lesson 3: Can you push a car from inside?- Conservation of momentum
- Momentum conservation derivation
- Conservation of linear momentum (basic)
- Conservation of momentum calculations
- Bouncing fruit collision example
- Momentum: Ice skater throws a ball
- Apply: conservation of momentum calculations

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# Conservation of momentum

Let's learn one of the most powerful principles of physics, the conservation of momentum with some examples. Created by Mahesh Shenoy.

## Want to join the conversation?

- what happens when both bodies stick together, rather than separate? Is the formula different and how does that affect the momentum?(4 votes)
- The conservation of momentum formula is m1u1+m2u2=m1v1+m2v2 and there is a reaction force acting on the 2 bodies of different masses but in the case bodies sticking together there will be a single body with combined mass of the 2 bodies.Hence the new formula for conservation of momentum in case of bodies sticking together will be m1u1+m2u2=(m1+m2)v(5 votes)

- 7:18Shouldn't it be Newton Second law in terms of momentum ? like what you have demonstrated, because it state : The net external force equals the change in momentum of a system divided by the time over which it changes. The coin one was Newton Second law in practice, after the brown coin was pushed into the blue coin, it will have the force of the brown, which will repel the Blue coin in the direction of the brown coin force?(2 votes)
- This is what ive been tring to avoid now i have no choice but to do it now....(2 votes)
- Is Conservation of Momentum only evident in specific types of collisions? For example, do only elastic collisions demonstrate conservation of momentum, or do some non-elastic collisions show conservation of momentum as well?(1 vote)
- 6:40isn't that because of the 3rd law of motion?(1 vote)

## Video transcript

- [Instructor] Check out this carom shot. We see that the black coin goes, so here is it if you look at it again black coin goes and hits the blue coin. Now imagine we knew the speed at which the black coin is coming and hitting the blue coin. The question is can we
predict with what speed the blue coin takes off? Well, we can solve problems like this by using forces and Newton's laws and accelerations and everything, but it might take a lot of steps. In this video we'll see a shortcut. And this shortcut is based on one of the most powerful principles of physics called the conservation of momentum. So we'll explore what this principle says, why it is so powerful, and we'll also use that to
explore how rockets work. Okay, so what does
conservation of momentum mean? Well, first of all,
remember what momentum is? If you take the mass of any object and multiply it by its velocity, then that number is what we
call momentum of that object, right? So what does conservation
of momentum mean? Well again let's bring
back our carom example. Let's say we looked at the
situation before collision, before the black coin hits the blue coin, and let's say we calculated
the total momentum of both these coins. Meaning you calculate the mass
times velocity of this coin, you calculate the mass
times velocity of this coin, and let's say you
calculate its total value, which we'll call total initial momentum. Initial means before collision over here. And then, let's say you look at the
situation after collision, after the coin hits it, and then again calculate
the total momentum. We'll call this the total
final momentum after collision. Then, this principle says
these two will be equal to each other. Think about what this means. You see, after the collision, the black coin has slowed down. It has stopped actually and the blue coin has speeded up. So clearly their individual
momentum has changed, right? But the principle says the
total value will not change. So even after the collision the total momentum remains the same. And that's why we say the
total momentum is conserved. That's the meaning of
conservation of momentum. So this might bring so
many questions to us like are there any other examples of this, or why does it even work, and does it always work? And, why do we even care about this? So let's try and answer all
these questions one by one. So let's start with why do we care about this? So what? What's the point? Well, this principle helps us
solve problems on collisions in few steps. So let's take an example. Let's put some numbers to this. I have zoomed in so that
we can see this better. So let's say that the mass of
the black coin is 10 units. Let's not worry about the units. Let's keep things simple. We'll solve more rigorous
problems in other videos. And let's say the blue coin
has a mass of 15 units. It was a little heavier than this one. Okay, now if the black coin was coming in with a velocity of say six units, the question is with what velocity would
the blue coin take off after collision? How do we solve this? Well we can use conservation
of momentum to do that. First let me change the background though because I want to use the same colors and it's not visible on black. Okay now to use conservation of momentum first we need to calculate the total momentum before collision. That will be mass into
velocity of the black coin which is gonna be 10 into six plus the mass into
velocity of the blue coin which is 15 into zero because the blue coin
is not moving at all. It's at rest. That should equal its total
momentum after collision. Again that's going to
be mass into velocity of the black coin which
now is 10 into zero because now the black coin is at rest. That what we saw. After collision it comes to rest. Plus 15 into v which is mass into
velocity of the blue coin. And v is what we need to find out. And if you look at this we have setup the equation. Now if you just simplify, we can calculate what v is. So on the left-hand side this goes to zero so we get 60. On the right side this goes to zero we get 15 v, which means we get 60 equals 15 v and if we divide by 15 on both sides we get v equal to four. 60 by 15 is four and that's our answer. So the blue coin after collision takes off with the speed or with the velocity of four units. So within few steps we were able to calculate what is the velocity. Imagine we didn't have this. Then we will have to use force and acceleration and maybe use some of Newton's laws. Ah, that would be so tedious! But with conservation of momentum within few steps we get the answer. That's why we love it so much. Now although this principle is amazing, it has a condition: it doesn't always work. But before we look at
what that condition is let's quickly take some more examples and see this principle in action. Take this rifle for an example. Not to encourage violence but it's a good example of this principle. Now before firing the bullet both the bullet and the gun are at rest. So the total initial momentum is zero. Now what happens after firing the bullet? Well once you've fired the bullet (whoosh) the bullet gains a forward momentum. But the conservation principle says if the initial total value was zero even the total final
momentum should also be zero. It should remain conserved. It should be same, right? So then how does this conserve momentum? Well, you might know that
the gun recoils back. But not just that. To make the total momentum zero the gun gains an exactly equal but negative backward momentum. So that now again if you
calculate the total momentum it still remains zero. Momentum gets conserved. Cool, right? And think about this. The more bullets it keeps on firing the more backward momentum
it keeps on gaining and the gun can actually speed up. And that's how rockets work. They don't shoot out bullets of course but instead they shoot
out hot gases downwards giving them a downward momentum, and you can think the rocket
sort of recoils upwards. And since it's continuously
shooting these gases down the rocket continuously keeps recoiling up gaining speed conserving momentum. That's how rockets work. So now that we looked at some
examples of where it works, the next question we might
have is why does it work? Why should momentum be conserved? Well, we'll look at a
complete mathematical proof in a separate video but let's try to get some sense for it. The main reason for this
is Newton's third law. Again let's bring back
our carom board example, and when the black coin
goes and hits the blue coin it puts a force, a forward force on that blue coin and as a result the blue
coin gains some momentum. However according to Newton's third law the blue coin will put a backward, equal and opposite backward
force on the black coin and as a result the black coin loses an
exactly same amount of momentum because the forces are exactly equal. And as a result see what's happening. One coin gains some momentum. The other coin loses the same amount. And so as a result can you see the total
value remains the same. And that's why after a collision the total momentum has to remain the same. It's just like money. Think of momentum as money. Imagine we have two kids who
have a total of 400 rupees and let's say you know one person decides to
transfer 50 rupees to another. Now she will gain 50 rupees, he will lose an equal amount 50 rupees, but the total will still
remain 400 rupees, isn't it? So just like this during the collision the momentum got transferred
from one body to another. That's it. And as a result the total
value still remains the same. Thinking of momentum as money really helps me understand this. Finally does this principle always work? Answer is no. It will work as long as
there are no external forces acting on our bodies. What do we mean by that? Well again let's come
back to our carom example. As long as these coins keep
putting a force on each other their momentum will stay the same. It's like how as long as these people keep exchanging money within themselves the total money will remain the same. But what if there's a third person who starts putting a force on these coins? So lets say the carom board starts putting a frictional
force on this coin. Now the coin will slow down and the momentum will get
transferred to the carom board. Right? And since the carom board is
not a part of our equation, we're not considering its
momentum in our equation, now the momentum of these two
coins will definitely change. This is what we call is an external force. It's a force acting by a body whose momentum we're not
considering in our equation. Again if you come back
to the money example imagine there is a third kid whose money we are not
considering in our equation. And if these people start, you know, exchanging money with this kid now their total money
will definitely change. It can change, right? But of course if we consider the money of all the three kids together then that money will still
remain conserved, isn't it? In a similar manner if
we consider the momentum of all the three things the two coins and the carom board then the momentum will
still remain conserved. Right? As long as there isn't a fourth body which starts putting an external force like for example the floor
might start putting friction on the carom board. Makes sense, right? So what did we learn in this video? We saw that if there
are two bodies or more who start putting forces on each other then you do Newton's third law. They will always put
equal and opposite forces and as a result they'll end
up transferring momentum from one body to another. And so the total momentum
of all the bodies together will remain the same, which is what we call
conservation of momentum. This works as long as there
are no external forces. Meaning there shouldn't be
forces acted upon by bodies whose momentum we do not
consider in our equation.