Lesson video

Hello, there.

I'm Mr. Forbes and welcome to this lesson from the Forces Make Things Change unit.

In this lesson, we're going to be looking at conservation of momentum.

And momentum is a property of a moving object that allows us to analyse collisions and explosions.

By the end of this lesson, you're going to have an understanding of what we mean by the momentum of an object and be able to calculate momentum.

You're going to be able to use momentum to calculate how objects move before and after explosions or collisions.

Here are the key words that will help you with the lesson.

And first, we have momentum.

Momentum is the product of the mass and velocity of a moving object, and we use the symbol p for momentum.

Then we have the unit of momentum, kilogramme metres per second.

Then conservation of momentum is a principle that says that for any closed system for a collection of objects where there's no external forces, the momentum is always conserved in any interaction within that system.

And then, we've got collisions, which is when two objects move together and hit each other and explosions, where a single object splits or a combined objects separate and those pieces of the object move apart.

You can return to this slide at later in the lesson if you need to.

The lesson is in three parts.

And in the first part, we're going to look at what momentum is and how it's calculated.

In the second part of the lesson, we'll look at what happens to momentum during collisions of objects.

And in the third part, we'll look at what happens to momentum when there's explosions and how we can use it to calculate the motions of objects.

So when you're ready, let's start by looking at what momentum is.

When you have moving objects, some of them are much more difficult to stop than others.

You need a larger force to act on the object to bring it to a stop or that force needs to act for a longer period of time.

And that's because objects of a property we call momentum, the momentum of an object.

I've got two objects here, a large van and a smaller car.

And let's imagine they're both travelling at the same velocity of five metres per second there.

The lorry's going to be much harder to stop than the car when they're moving at that velocity.

It's going to need a larger force or a force that acts for a longer period of time.

And that's because the momentum of the lorry is greater than the momentum of the car, because it has that greater mass.

So, momentum depends upon the mass and the velocity of an object.

The momentum of an object is directly proportional to the mass of the object.

So the more mass of the object is, the greater it's momentum and it's proportional to its velocity as well.

The greater the velocity of the object, the greater the momentum will be.

Let's check if you understand that concept.

I've got two cars here and they've got the same mass, but car X, the top car there in red, is moving at twice the velocity of car Y, the green car at the bottom there, which statement is correct? Have a look at the three statements, make a decision, and then restart please.

And welcome back.

Well, the momentum of car X, the red car, is twice the momentum of car Y, the green car, and that's because it's got a lighter velocity and momentum is proportional to the velocity.

So if you double the velocity, you double the momentum.

Well done if you got that.

We define momentum by this equation here.

Momentum is mass times velocity, and if we write that in symbols that's p for momentum, m for mass, and v for velocity.

Momentum p is measured in kilogrammes metres per second.

That's a fairly unusual sounding unit.

It's just kilogrammes multiplied by metres per second.

The mass is measured in kilogrammes and the velocity in metres per second.

Let's try a couple of examples of calculating momentum.

I'll do one and then you can have a go.

I've got a bowling ball of mass 7.

4 kilogrammes.

It's moving with the velocity of six metres per second.

Calculate the momentum of the ball.

And I'll write it out in words for this example.

Momentum is mass times velocity.

So, I substitute in the values.

Momentum is 7.

4 kilogrammes times the velocity of 6.

0 metres per second, and that give me a momentum of 44 kilogramme metres per second.

Now, it's your turn.

I'd like you to calculate the momentum of this runner with a mass of 60 kilogrammes moving at 4.

5 metres per second.

So, pause the video, work out the momentum, and then restart please.

Welcome back.

Well if you use the symbols, you've written p equals m times v.

Substitute the values of 60 kilogrammes and 4.

5 metres per second, gives us a momentum of 270 kilogramme metres per second.

Well done if you've got that.

Sometimes, we're giving the momentum of an object and we need to find it velocity or its mass depending on what the question asks.

So, let's see how we can rearrange the momentum equation to get those.

If we want to find the velocity V, we can start with the original equation.

p equals m times v, momentum is mass times velocity, and divide both sides of that equation by m.

That gives us this relationship.

So, you can see I've divided both sides by m.

I'm gonna cancel those two m's on the right hand side, so those two there, and they cancel each other, m divided by m is one.

So, we don't need that in the equation any longer and that gives me this expression, momentum divided by mass is velocity.

And we usually write that in this order.

Velocity is momentum divided by mass.

So, there's my first rearrangement.

Similarly, if I wanna find the mass m, again, start with the original equation.

This time, I'll divide both sides by v the velocity.

So, we'll get expression like this, cancel the velocities on the right hand side there.

So, both of those cancel each other out.

That gives me this equation.

And finally, I'll rearrange it and I've got an expression, mass is momentum divided by velocity.

Here's my three versions of the equation.

Let's try and use those versions in the equation in some calculations now.

So, I'll try one and you can have a go as well.

A skateboarder of mass 60 kilogrammes has a momentum of 300 kilogramme metres per second.

Calculate the velocity of the skateboarder.

I let her write out the version of the equation for velocity.

Velocity is momentum divided by mass.

Write down the values taken from the question, and that gives me an answer of 5.

0 metres per second.

Now, it's your turn to calculate velocity.

We've got all the information here, so please calculate the velocity of that golf ball, and then restart the video when you're done.

Okay, welcome back.

The answer should be something like this.

Again, write out the equation, substitute values, and that gives 20 metres per second.

Well done if you've got that.

Now, let's try calculations of the mass, our third and final version of the equation.

So, I've got a radio controlled toy car travelling at five metres per second, with a momentum of 15 kilogramme metres per second.

Calculate the mass.

So, I write out the version of the equation that starts with m equals so or mass equals momentum's divided by velocity.

Write down the values taken from the question, and that gives me an answer of 3.

0 kilogrammes.

And your turn again.

So, I'd like you to calculate the mass of the rock based on the information you can see here.

So pause the video, calculate that mass, and then restart please.

Welcome back.

Well, you should have written an expression like this and that gives us 15 kilogrammes.

So, the massive rock was 15 kilogrammes.

Well done if you've got that.

One of the important properties of momentum is it's a vector quantity.

It has size, so you can have different sizes of momentum, but the direction is important as well.

So if I have objects travelling in opposite directions, they have opposite signs of momentum.

So, let's see an example of that.

I've got opposite objects travelling in opposite directions.

So, I've got two cyclists here.

I've got one cyclist travelling towards the right at four metres per second, and they'll have some momentum.

And I've got a cyclist travelling towards the left at minus three metres per second.

'Cause the directions are opposite, I've got the state of velocities using positive and negative numbers.

So if I calculate the momentum of the first cyclist, you get an answer like this, 240 kilogramme metres per second.

Then, I calculate the momentum of the other cyclist.

I get an answer like this, minus 210 kilogramme metres per second.

So, they're in opposite signs.

The momentum direction is important and we can have positive momentum and negative momentum.

Okay, let's see if you understand why momentum is vector.

What I'd like you to do is to look very carefully at these six diagrams. All are balls with different masses and different velocities and I need you to identify which pair has exactly the same momentum.

So pause video, work out which pair has the same momentum, and then restart please Welcome back.

The selections you should have made were c and e.

If you multiply those out, you find that the momentum of each of those is minus 12 kilogramme metres per second.

The momentum of the others, well some of them are 12 kilogrammes per second, you can see the a is 12 kilogramme metres per second, but that isn't the same as minus 12 kilogramme metres per second.

And similarly, I've got an eight and a minus eight and they're not the same as each other either.

So, well done if you selected c and e.

It's time for the first task of the lesson and I've got three questions here.

I'll let you to work your way through each of those.

So pause the video, read the questions carefully and answer them, and then restart please.

Welcome back.

And here's the solution to the first couple of questions.

You were asked to calculate the magnitude of the momentum of some objects.

And the rock has got a momentum of 2.

4 kilogramme metres per second.

The car has got a much higher momentum.

It's got a much greater mass and a much greater velocity.

So, you'd expect that and that's 45,000 kilogramme metres per second.

Then, you can rearrange a momentum equation to find a speed or a velocity.

I've started with the original equation, substituted the values for the momentum and the mass, and that gives me 1.

5 metres per second.

Well done if you've got all of those.

And the question three here about the drones and they're travelling in different directions.

So, we've got drone Y moving upwards and drone Z moving downwards at the same speeds and with the same mass.

They've got different momentum, because momentum's a vector property.

And so, the direction is important.

So, they'll have equal amounts of momentum going up the direction.

So, one will have negative momentum and one will have positive.

So, the momentum is actually opposite each other.

Drone Y reverse the direction and we can find the change in momentum where we can find out the initial momentum it had by having its initial velocity and mass.

And that gives 6.

0 kilogramme metres per second.

And its new momentum, what we do is, well, the direction is opposite, so now it's moving at minus 4.

0 metres per second and that gives us minus 6.

0 kilogramme metres per second.

So overall, the change is the difference between those.

It's minus 12 kilogramme metres per second.

Well done if you got that one.

Now, we're gonna look at why momentum is so important in physics.

And to do that, we'll look at some collisions and the concept of conservation of momentum.

So, let's start that.

Momentum is so useful because of a principle we call the principle of conservation of momentum.

And that is expressed here as the momentum in a closed system is always conserved in any interaction.

You can't increase momentum or decreased momentum in a closed system.

There's always the same amount of momentum no matter what happens.

Now, we need to explain what a closed system is.

And a closed system is any collection of objects that are not affected by any external factors or outside things.

So, it means that there's no outside forces affecting the system.

And there's also no transfer of energy into or outta the system.

No energy is lost or gained by it.

So, that's the rules to define a closed system.

But that thing in the box there, the conservation of momentum thing is a very important principle that we use all the time.

We can explain why momentum is conserved based upon Newton's third law.

And if you remember Newton's third law is this, if object A exerts a force on object B, then object B will exert an equal size force in the opposite direction on object B.

So, force cause change in momentum.

And when one object produces a force that's acting, there will be a change of momentum due to that force, but also it's going to be a second force, which is changing the momentum of another object.

And overall, the change in momentum of one object will cancel out the change in momentum of the other one.

So, the total amount of momentum will be conserved.

So, what I'm saying is that pair of force is caused equal and opposite changes in momentum.

So overall, there's no change in momentum.

Let's try and explain that in a little more detail using an example and Newton's third law.

So if you imagine they've got two objects approaching each other here are ball A and ball B, and then they collide with each other.

Once they're in contact with each other, object A is gonna cause a force in object B and that is going to cause a change in momentum of object B.

That force is gonna act on object B, change its velocity, and therefore change its momentum.

But at the same time that change is happening, ball B is going to place a force on object A and that force is going to be the same size in the opposite direction and it's going to change the momentum of ball A.

So, both of those forces are gonna cause changes in momentum but they're gonna be of different objects.

And overall, the forces are the same size yet in opposite directions and they last for exactly the same amount of time.

And that means the momentum of ball A has changed by exactly the same amount as the momentum of ball B, but in an opposite direction.

So, momentum must be conserved.

Let's have a look at an example.

I've got about two objects here, X and Y colliding as shown.

The momentum of X changes by three kilogramme metres per second.

What's the change in momentum of object Y? So pause the video, make your decision, and restart please Welcome back.

Hopefully, you selected minus three kilogramme metres per second.

If one object changes by plus three kilogramme metres per second, the other must change by minus three kilogramme metres per second 'cause the overall amount of momentum hasn't changed.

Well done if you got that one.

We can use the principle of conservation of momentum to analyse things we call collisions, where objects bump into each other.

The stages in these analysis at ease.

So first of all, we find the momentum of each object before the collision happens.

That allows us to find the total momentum of the system before the collision.

And what we know by the principle of conservation momentum is the total momentum after the collision is going to be exactly the same as it was before the collision.

And we use that fact to find any missing momentum and that will allow us to calculate the velocity or masses of the objects involved.

I'm gonna show you an example of that 'cause it's much easier to understand when you have an example.

So, I've got two objects here.

We've got the first one, object X, it's moving up to two point millimetres per second and it's got a mass of five kilogrammes.

And I've got object Y here and that's got a mass of four kilogrammes and that's not moving before the collision.

So, this is my situation before the collision.

After the collision, I've got this.

Object X is as velocity slowed to now 0.

4 metres per second and object Y is now moving towards the right there.

An unknown velocity, I'm gonna call that vY.

The masses of both objects are still the same mass.

That doesn't change during the collision.

So, my question is to find the velocity vY of that second object or stone Y after the collision.

So, what I do is look at the momentum before the collision and find out the total momentum of the system.

And I do that by looking at the first object.

That's the only moving part in it, but it's mass and its velocity.

And I calculate the momentum by multiplying those two together and that's 10 kilogramme metres per second.

And now after the collision, I know that the total momentum is still 10 kilogramme metres per second.

The momentum of the first stone, the blue one, X there, I can calculate 'cause I've got its mass and its velocity and that's 2.

0 kilogramme metres per second.

And that must mean that the momentum of object Y, stone Y, is the difference in those values.

So, there's a total of 10 kilogramme metres per second, two kilogramme metres per second of that is in stone X and that means that 8.

0 kilogramme metres per second is in stone Y.

So, the final stage then is to try and find the velocity of stone Y.

And I can do that by taking its momentum, which I know is 8.

0 kilogramme metres per second and dividing it by its mass, which is 4.

0 kilogrammes.

And that gives me the velocity of Y of 2.

0 metres per second.

So it's multi-stage process, but it allows you to calculate the missing velocity of stone Y there.

Let's have a look at a second example.

I've got two stones sliding and colliding again.

So, here's the situation beforehand and here's the situation after the collision.

And again, I'm going to calculate the missing velocity and this time, the velocity of stone X.

So to find that, I find first of all the total momentum before the collision.

And in this case, I've got two objects moving.

So, I've got to add the momentum of both of those two together and I'm being very careful here.

And I put brackets around each objects momentum to make it easy to see which mass goes with which velocity.

So, you can see there for the first one, I've got my stone at two kilogrammes and it's moving at 2.

5 metres per second.

And I'm gonna add that to the momentum of the second stone.

That's a three kilogramme stone and it's moving at minus four metres per second and that's very important.

I need to take into account that direction.

I work out all of those and get a total momentum of minus 7.

0 kilogramme metres per second.

After the collision, the total momentum that I can see in my diagram is just the stone Y there.

So, that's got a total momentum of minus three kilogramme metres per second.

And what that means is I can find the momentum of stone X.

So again, looking at those values and taking into account the direction, I can find that stone X has a total momentum of minus 10 kilogramme metres per second.

Using that momentum allows me to calculate it to velocity.

Its velocities is momentum divided by mass and that gives me a velocity of minus five metres per second.

Okay, I'd like you to try out that process for yourself.

I've got a collision here between two stones.

Again, you can see the before collision situation and the after collision situation.

And what I'd like you to do is define the velocity of stone Y after the collision.

So pause the video, work out your answers to that, and restart please.

Welcome back.

Well, the answer to that is six metres per second.

Again, I'll show you the calculation.

The total momentum before the collision is 17 kilogramme metres per second.

That must mean the momentum of the stone Y is 12 kilogramme metres per second.

Once you've worked out the missing momentum in that second diagram, then that allows you to calculate its velocity as six metres per second by dividing that momentum by its mass, which was two kilogrammes.

Well done if you got that.

We're gonna look at a third example of a collision where we can use the momentum to find out that information.

So during collisions you can have objects that don't bounce off each other.

They stick together.

The masses combines to create a new object.

So, I've got an arrow.

It's got a mass of 0.

3 kilogrammes.

It's travelling at 20 metres per second.

And let's imagine that hits a coconut that's got a mass of two kilogrammes.

And they stick together and they move off together.

So, a situation like this beforehand.

Before the collision, I can work out the total momentum.

That's just the momentum of the arrow and that's 6.

0 kilogramme metres per second, multiplying the mass by the velocity.

After the collision, the momentum will be the same.

It's still 6.

0 kilogramme metres per second.

So, I've got this object where the arrow and the coconut combined together, but I still know the total momentum.

So, what I can do is find the total mass of the two objects joins together.

I know the momentum, so I divided the momentum by the total mass and that gives me a velocity of 2.

61 metres per second.

So, the arrow is slowed down considerably and the calculators started moving as they're joined together.

Okay, it's time for you to try some momentum and collision calculations, and I've got two questions here for you.

So, what I'd like you to do is pause the video, read them carefully, work out the answers, and then restart please.

Welcome back.

And here's the solution to the first of those questions.

We find the momentum before the collision of 8,000 kilogramme metres per second.

Then, we find the combined mass of the two objects, 20,000 kilogrammes.

So, we divide that initial momentum by that mass and that shows that the objects move off at 0.

4 metres per second.

Well done if you've got that.

And the second question's here, we find the total momentum before the collision 0.

48 kilogramme metres per second.

Then after the collision, we can find out the momentum of ball W, the white ball there.

It's minus 0.

16 kilogramme metres per second.

Remember, we take the direction into account.

That allows us to find the momentum of the yellow ball, ball Y.

That momentum is not 0.

64 kilogramme metres per second.

Again, we're very careful with the directions there.

And finally, we can use the momentum of the yellow ball and its mass to find its velocity, which is 4.

o metres per second.

Well done if you got that.

Now, it's time to move on to the next part of the lesson.

And in it, we're going to look at principle of conservation and momentum and how it applies to explosions, situations where objects move apart from each other.

So, let's start that.

Momentum is conserved in any situation in a closed system.

So, it's not only conserved when objects collide with each other, it's conserved to when object break apart.

When objects break apart, we call our situations explosions.

So, let's have a look at example.

I've got an object here and it's made up of two parts, part X and part Y.

And let's say that this object isn't moving initially, so it's got an initial momentum of zero, because no matter what its mass was, 'cause it's got a velocity of zero, if you multiply any mass by a velocity of zero, that's gonna give a momentum of zero.

So, I've got a momentum of zero kilogramme metres per second.

Now, imagine that this object breaks apart.

There's springs or something between the two sections and they're released and the object flies apart at different velocities like that.

The two objects are moving in opposite directions, we call that event the explosion.

The momentum after that event is also going to be zero.

There was no momentum before the explosion.

So after the explosion, the total momentum of the system is going to be zero again.

We can investigate momentum in explosions using dynamics trolleys.

The dynamics trolleys are those small wheel vehicles you use in motion experiments.

So imagine, I've got two trolleys here next to each other and initially, they're stationary, so the total momentum of this system is zero.

Now, the trolleys can have little springs between them and you can trigger those springs to push the trolleys apart to make the explosion.

If we release it, the trolleys are going to be pushed apart and the momentum are gonna be something like this.

I've got trolley A moving off to the left here and that's gonna have a momentum and we call that momentum A or PA.

And the other trolley is gonna have a momentum PB.

Now, what we can say is well the total momentum is still zero after that explosion, what's gonna that's gonna mean is the trolleys have got equal and opposite momentum.

For the momentum to still be zero, PA and PB added together must equal zero or PA is equal to minus PB.

Let's have a look at an example of using the conservation of momentum to find out the velocity of an object after an explosion.

So, I've got two dynamic trolleys here.

Before the explosion, before I release the spring, they're not moving, they're at rest.

And I've got the masses of the two trolleys written down there.

After the explosion, you can see the trolleys are both moving.

Trolley A is moving to the left at 0.

5 metres per second, and trolley B is moving to the right at an unknown velocity.

So, the first thing I can say is I'm gonna find the velocity of trolley B after the explosion.

Before the explosion, the total momentum must be zero because the trolleys were at rest.

So, I've got total momentum of zero.

After the explosion, I know that the total momentum must be zero.

So if you add the momentum of the two trolleys, PA and PB, that's equal to zero kilogramme metres per second there.

So, PB is minus PA.

So, I can then write out PB equals, and I work out the momentum of trolley A.

It's 2.

0 kilogrammes times 0.

5 metres per second, and it's minus that for trolley B.

And that gives me a momentum of trolley B of minus 1.

0 kilogramme metres per second.

Now, I can find the velocity of trolley B.

It's the momentum divided by the mass.

I've got the momentum.

It's minus 1.

0 divided by the mass, 0.

8 kilogrammes, and that gives me a velocity of trolley B of minus 1.

25 metres per second.

And it's minus because it's moving in the opposite direction to trolley A.

Okay, I'd like you to try an example of that.

Now, I've got two stationary trolleys again.

They're both at rest.

The momentum of trolley X after the explosion is four kilogramme metres per second.

What must the momentum of trolley Y be? So, pause the video, work out your answer, and restart please.

Welcome back.

Well, it must be answer c, minus four kilogramme metres per second, because they must gain equal and opposite momentum during the explosion.

Well done if you've got that.

Okay, now it's time for the final task of the lesson.

I've got two questions here.

The first of them, I'd like you to complete those statements and in the second one what I want you to do is go through the process of calculating momentum and I want you to find the velocity of trolley B after an explosion.

So, pause the video, work out your answers, and restart please.

Welcome back.

Here's the answer to the first one.

So if two joint objects are at rest, the total momentum is zero kilogramme metres per second.

And the momentum is zero kilogramme metres per second when they break apart in an explosion, because momentum is always conserved.

Well done if you've got those.

And here's the calculation for the second part.

Again, we find the momentum before the explosion.

It's zero.

We know that the momentums are opposite to each other, so PB is minus PA.

So, we can find PA and just put a negative sign in front of it and that gives the momentum of PB as minus 1.

8 kilogramme metres per second.

And finally, we can use that momentum and the massive of the trolley to get a velocity for B of minus 0.

9 metres second.

Well done if you've got that.

We've reached the end of the lesson now, and here's everything we've learned.

The momentum of an object is given by momentum is mass times of velocity or in symbols, p for momentum is m for mass times v for velocity.

Momentum is measured in kilogramme metres per second, and it's a vector.

It has direction and that direction is very important.

The principle of conservation momentum states.

The momentum in a closed system is always conserved in any interaction, and that's always true.

This includes collisions and explosions, and we can analyse those by remembering that the total momentum before an event is equal to the total momentum after an event.

Well done for reaching the end of the lesson.

I'll see you in the next one.