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Hello and welcome to this lesson about calculating energy changes.

It's from the physics unit "Energy of moving objects," and my name is Mr. Fairhurst.

In this lesson you're going to find out about how you can use the principle of conservation of energy to calculate changes in energy of moving objects, and in particular you're going to think about how energy is transferred between the gravitational store and the kinetic store.

These are the keywords that you're going to come across during the lesson.

Conservation of energy is the principle that energy cannot be created or destroyed, but it can only be transferred from one store to another store.

And when it's transferred, some energy is usually dissipated, it's transferred into the surroundings by warming them up slightly.

The energy that an object has in its gravitational store is what we call its gravitational potential energy, and the energy an object has in its kinetic store is what we call its kinetic energy.

These are the definitions of those keywords.

Any point during the lesson you want to come back and have a look at these and remind yourself of what the definitions are, just pause the video and come back to this slide.

The lesson's divided into three parts.

In the first part, we're going to consider how energy is transferred between stores, in particular between the kinetic store and the gravitational store.

We're then going to look at how the conservation of energy affects this transfer of energy.

And then in the final part of the lesson, we're going to use all of those ideas in order to calculate the amount of energy transferred in a range of different situations.

Okay, then, let's make a start with the first part.

We'll start off by thinking about how energy can be transferred from one store to another store, and we'll do that by considering this toy cannon.

Inside the cannon is a spring that when is compressed the toy cannon has got energy in the elastic store.

And when the spring is released, the cannon fires a small ball up into the air.

Now when that spring is compressed and before it's released, the cannon has got a lot of energy in the elastic store and it's got a little bit of energy in the gravitational store because the ball is raised a little bit up into the air.

And then when the spring is released, the ball is shot up into the air and energy is transferred between the stores.

All of the energy or most of the energy in the elastic store is transferred into making the ball move, so it's got energy now in the kinetic store, and the ball has also risen up into the air, so some energy has also been transferred into the gravitational store.

Now I've got a couple of questions I'd like you to have a go at.

This first one, what energy transfer takes place between firing the toy cannon and the moment the ball reaches its maximum height when it's shot straight up into the air? Just pause the video whilst you choose your answer and then start again once you're ready.

Okay, so how did you get on? The ball shot straight up.

It starts with energy in the elastic store inside the cannon and at its maximum height it comes to a momentary stop before it starts falling back down again, so it's only got energy in its gravitational store, so the correct answer is B.

Well done if you've got that one.

This is the second question.

Again, have a look at the question, pause the video whilst you think about it and choose your answer, and start again once you're ready.

Right then, this time you were asked what happens when the cannon is fired horizontally, and at the moment the ball has just left the cannon before it starts to fall.

All of the energy in the elastic store has now been transferred to making the ball move and it hasn't changed its height yet, so no energy has been transferred into the gravitational store.

So this time the correct answer is A, energy has been transferred from the elastic store just into the kinetic store, so well done if you've got that answer correct.

The point of this lesson is that we want to be able to calculate the amount of energy transferred between stores, and we're gonna start from this principle that the total amount of energy after firing the cannon, or after an energy transfer, is always the same as the total amount of energy at the start.

Now in this case, if we add up before the cannon was fired the energy in the elastic store and the gravitational store, and compare that to the energy in the different stores afterwards, then what we find is we get the same total amount of energy both times.

This is the principle of conservation of energy.

We can't destroy or create energy, we can only transfer it from one store into another store, or from a few stores into other stores.

Now, if we were to ignore the energy that's dissipated when energy is transferred, it will be quite straightforward to calculate the amount of energy transferred.

But energy is dissipated.

When this toy cannon is fired, there's still friction between the ball and the cannon that heats up the barrel of the cannon.

And as the ball moves through the air, there's air resistance between the ball and the air.

And this makes it really difficult and challenging to calculate the amount of energy transferred in this instance to the gravitational store when that ball reaches its maximum height.

And that's because we don't know exactly how much friction there was, we don't know how much air resistance there was, so we can't easily calculate that.

But what we can do is we can use the principle of conservation of energy to calculate the maximum height that the ball could have reached if there was no air resistance and friction involved at all, if we ignore those.

So that's what we're to do in a lot of these physics calculations, we're going to ignore the energy that's dissipated so that we can work out the maximum transfer of energy assuming that these were non-existent or very, very low.

Have a look at this question and see what you think.

What is the maximum amount of energy transferred to the kinetic store as the gannet dives into the water, assuming that we can ignore the air resistance that's involved in this case.

Pause the video whilst you think about this one and start again once you're ready.

Okay then, so what do you think? The correct answer is exactly 98 joules of energy.

If the gannet starts off with 98 joules of energy in the gravitational store, as it dives down and reaches the surface of the water, it's got no energy left in the gravitational store.

And if none of that energy has been dissipated, then all of that energy will be transferred into the kinetic store into making the gannet move faster and faster.

Now gannets will enter the water at an incredibly high speed, so well done if you got that right.

What I'd like to do now is this task.

I want you to think about a heavy pendulum that swung from a height of 2 metres, 2.

00 metres in the air.

It swings down, speeds up, and then goes back again to a maximum height where it pauses.

What I'd like you to do is to have a go at those questions and then once you've got the answers start the video again and we'll check your answers.

Okay, so how did you get on? The first question was, where will the pendulum have the maximum speed? Well, as it's moving down and the energy's being transferred from the gravitational store into the kinetic store, it's speeding up.

And then as it rises again from the lowest position, energy's being transferred back from the kinetic store and into the gravitational store, so it's losing speed.

So its maximum speed will be at the bottom of the swing.

Question two says, what is the maximum height it will swing up to? Well, we're assuming here that no energy has been transferred to the surroundings, no energy has been dissipated.

So all the energy in the gravitational store at the start was transferred to the energy in the kinetic store at the bottom, and it's been transferred back to the energy in the gravitational store at the top.

So it's got the same energy in the gravitational store at the end than it had at the start.

In other words, it's at the same height it was before, 2.

00 metres.

Question three was to explain why it can't reach the maximum height.

Why is it not going to rise up again to exactly 2 metres? And that's because in real life there's air resistance, there's friction where the string is attached, the pendulum is attached to the pivot at the top, so that's gonna cause rubbing and it will slow the pendulum down and it will dissipate energy into the thermal store of the surroundings rather than the gravitational store again.

So that essentially is the answer.

Well done if you've got a good description of that.

We'll now go into part two of the lesson where we think a little bit more carefully about the conservation of energy and what that tells us about the quantity, the amount of energy in different stores.

To do that, we're going to think about a roller coaster.

I don't know if you've ever been on a roller coaster, but you'll notice that as you get pulled to the top, there's some sort of mechanism that cranks you to the very top, and at the top there's that moment when the roller coaster is released from the mechanism just before it starts to fall, and then it freewheels all the way along the track.

It just coasts along, hence the name a roller coaster.

Now what we can calculate about the roller coaster is that the amount of gravitational potential energy it has at the start, and we can calculate it using this equation.

The gravitational potential energy equals the mass of the roller coaster times the gravitational field strength times by its height above the ground.

So we can calculate the energy it's got at the start before it starts moving and coasting down the track.

Now as it rolls along the track, friction and air resistance will cause some energy to dissipate into the surroundings.

And when it reaches the top of the next rise, the roller coaster will have energy in the gravitational store and the kinetic store, and there'll be some energy in the thermal store of the surroundings as well.

Now bearing that in mind and thinking about a real roller coaster, what I'd like you to do is to answer this question.

Just pause the video while you do so and start again once you're ready.

Okay, so how did you get on? We can imagine the roller coaster starting at the high point there on the left, rolling along, some energy is dissipated, and it will climb up the right-hand side and it will stop when it reaches its maximum height, when it's run out of energy in the kinetic store, it's all been transferred back into the gravitational store.

And the correct answer here is B.

It won't be quite as high as it started from because some of the energy has been transferred into the surroundings, it's been dissipated.

So well done if you got that answer.

What I'd now like you to do is to think of the same question, but this time for an ideal roller coaster, one in which no energy is dissipated.

What height will it reach now if there's no dissipation of energy? Pause the video and start again once you're ready.

Okay, so how did you get on? The correct answer here is C, the same height as when it started.

Because no energy's been transferred into the surrounding, so it's got the same total amount of energy at the end as it had at the start and where it stops at C, so therefore it's got all of its energy in the gravitational store, so well done if you got that one.

That means that for an ideal roller coaster in which no energy is dissipated, all of the energy in the gravitational store at the top is transferred to the kinetic store at the bottom.

And that idea helps us to calculate the amount of kinetic energy it's got at the bottom.

And the amount of kinetic energy is exactly equal to the amount of gravitational potential energy it had at the top, and the gravitational potential energy is equal to the mass of the roller coaster times the gravitational field strength times the height the tip falls from the start.

What I'd like you to do is to have a quick look at this question and see what you think.

Pause the video whilst you do it and start again once you're ready.

Okay, so how did you get on? A ball was calculated to have 80 joules of gravitational potential energy and is dropped.

How much energy did it have in its kinetic store when it hits the floor? And the correct answer is exactly 80 joules.

We're of course assuming that there's no air resistance and so that no energy has been dissipated.

So well done if you got that right.

I'd now like you to think about the same ball as it hits the ground.

But this time, rather than hitting the ground, it's hitting a trampoline.

How much energy will be in the elastic store when the ball first stops moving? Pause the video and start again once you're ready.

Okay, so this time, as the ball hits the trampoline, it stretches the elastic of the trampoline and the energy from the kinetic store is transferred into the elastic store.

And again, because no energy dissipates, exactly 80 joules of energy is transferred into the elastic store.

So again, well done if you got that right.

What I'd now like you to do is to have a go at these four questions and where it's appropriate, show your working out.

Pause the video and start again once you've got all your answers ready.

Okay, so how did you get on? Let's start with the first question.

Calculate the gravitational potential energy of the ball at the top of its flight.

The ball's got a mass 0.

2 kilogrammes and it's shot up into the air with a catapult and it reaches a maximum height of 15.

0 metres.

So to work out its gravitational potential energy, we can use the equation gravitational potential energy equals the mass times the gravitational field strength, which here is 10 newtons per kilogramme, times by the change in height.

And if we do the sums we get 30 joules of energy, so well done if you got that one right.

The next questions all say state.

That means that you don't need to do a calculation.

So question two here, state how much energy was in the kinetic store the moment the ball left the catapult.

Well, if no energy is dissipated, it's got the same amount of energy as it has when it reaches the top height and it's got no energy left in the kinetic store.

So the correct answer there was 30 joules.

The amount of energy it had in the elastic store just before the catapult was released, again, that is all of the energy, which is 30 joules.

And state again how much energy was in the kinetic store the moment the ball hit the ground.

So it's reached the top, where it had 30 joules of energy.

It then starts speeding up and then hits the ground having lost all of that gravitational potential energy and transferred it into kinetic energy, so the answer is again 30 joules.

So well done if you got all of those answers correct.

In the final part of the lesson, we're going to use the equation for calculating the kinetic energy of an object and the equation for calculating the gravitational potential energy of an object together with the principle of conservation of energy in order to calculate energy transfers.

And these are the ideas that we're going to use to do that.

First of all, for an object that changes height, we know that we can calculate the energy transfer to or from the gravitational store using the gravitational potential energy equation, which is the gravitational potential energy equals the mass times of gravitational field strength times the change in height.

We also know for an object that changes speed that we can calculate the energy transferred to or from the kinetic store using the equation for kinetic energy of the object, which is the kinetic energy is equal to 1/2 times the mass of the object times its speed squared.

And if we assume that there's no energy dissipated, then when an object changes height or speed, we know that the change in gravitational potential energy is equal in size to the change in kinetic energy.

So those two equations are equal to each other and energy is conserved.

So let's put those together and have a think about what happens.

Have a go at this question and see what you think.

Pause the video as you do so and start again once you've got your answer.

So how did you get on? A pupil drops a cricket ball from a height of 1.

5 metres.

Which equation or equations need to be used to calculate the total amount of energy in the kinetic store when the ball hits the ground? Well, the correct answer is A.

We know the height of the ball and we know the mass of the ball and we know the gravitational field strength, so we can calculate the energy it has before it's dropped and we know that that is equal to the kinetic energy when it hits the ground.

Well done if you got the right answer.

We're now going to have a look at some example calculations.

So this first one, a roller coaster has got a mass of 850 kilogrammes.

How much energy will it have in the kinetic store after falling 40 metres from rest? Well, we always start by stating the principle in which we answer the question, which is that the change in gravitational potential energy is equal to the change in kinetic energy.

Now in the question we've got the mass of the roller coaster, we've got the height it falls, and we know the gravitational field strength, so we can calculate the gravitational potential energy it had at the start.

We use this equation and we put the numbers in, so we got the gravitational potential energy is equal to 850 kilogrammes times 10 newtons per kilogramme times 40 metres.

If we do the math, we get 340,000 joules, or 340 kilojoules.

And that's the amount of gravitational potential energy we have at the start.

And that is equal to the energy in the kinetic store at the bottom.

So that's our correct answer there.

Here's a second example for you to have a go at.

Just pause the video whilst you do so, show all your working out, and start the video again once you're ready.

Okay, so how did you get on? A cyclist got a mass of 75 kilogrammes.

How much energy would she have in the kinetic store after freewheeling down a 23-meter hill from rest? So it's the same sort of question as before.

And again, we'll start off by stating the principle that the change in gravitational potential energy is equal to the change in kinetic energy.

And we can calculate the change in gravitational potential energy using this equation.

We can substitute the numbers in from the question and we get 75 kilogrammes times 10 newtons per kilogramme times 23 metres, which gives us 17,250 joules or 17 kilojoules if we round it up to two significant figures, like the advice we were given in the question.

We need to remember to state the final part of the question, which is what the kinetic energy or what the energy in the kinetic store is at the end, which is the same, it's 17 kilojoules.

So well done if you got that answer.

Let's look at the slightly different question using the same principle.

In this case, a ball of mass 1/2 a kilogramme is kicked up into the air at a speed of 8 metres per second.

And the question is, how high will it reach? Well, we got the same principle that we're going to use again.

The change in gravitational potential energy equals the change in kinetic energy.

And this time we've got the mass of the ball, its speed, and we can use that to calculate the kinetic energy it starts off with.

So the equation for kinetic energy is 1/2 times the mass times the speed squared.

And if we substitute our values in now, we've got 1/2 times 1/2 a kilogramme times 8 metres per second squared, which gives us 1/2 times 0.

5 times 64, which is 16 joules.

And that is equal to the gravitational potential energy when it's at the highest point.

Now our question asked us to say how high it reached, so we now need to use the gravitational potential energy equation which is equal to mass times gravitational field strength times the height.

And if we put the values we've now got into that equation, we've got the gravitational potential energy, 16 joules, equals 0.

5 kilogrammes times 10 newtons per kilogramme times the height.

In other words, the height is equal to 16 joules divided by 5, which is 0.

5 times 10.

And that gives us an answer of 3.

2 metres.

Now that's quite challenging 'cause it's a two-part question.

What I'd like you to do is to answer a similar question.

Just pause the video whilst you do so and start it again once you're ready.

Okay, so how did you get on? Hopefully you started by stating the principle that we're using, that a change gravitational potential energy equals a change in kinetic energy.

You'll have then used the equation for kinetic energy and substituted the values in, and that will give you the kinetic energy of 1,215 joules, which is equal to the gravitational potential energy when the toy rocket reaches the highest point.

You were asked how high it would reach, so you'll need to use the equation for gravitational potential energy.

Substitute the numbers in again.

And we end up with a value for the height as 1,215 joules divided by 12, which is equal to 101.

25 metres.

In the question, we got our values given to two significant figures, and if we round up our answer to the same two significant figures, it comes to 100 metres.

So very well done if you got that question right.

In this question we're asked at what speed a 0.

5 kilogramme ball is kicked up at if it reaches a height of 10 metres where the gravitational field strength is 9.

8 newtons per kilogramme.

We've got a mass, a height, and the gravitational field strength, so we can calculate the gravitational potential energy of the ball when it reaches its maximum height, and we know that that is equal to the kinetic energy it has at the moment it is kicked up from the ground because of this principle.

So we'll state the principle, and then we'll use the equation for gravitational potential energy to calculate the gravitational potential energy, substitute the values in, multiply them through and we get 49 joules, which is the same as the kinetic energy at the moment the ball is kicked up.

Now we were asked for the speed of the ball, so let's substitute the values we've got into the equation for kinetic energy, and we get 49 joules is equal to 1/2 times 0.

5 kilogrammes times speed squared.

Rearranging that we get the speed squared is 196.

We need to square root both sides and we get the speed equal to 14 metres per second.

So that's quite a challenging two-step calculation.

What I'd like you to do is to have a go at this one.

Pause the video whilst you do so and start again once you're ready.

Okay, how did you get on? You were asked to find the speed that a toy rocket of mass 1.

8 kilogrammes has when it shoots up if it reaches a height of 150 metres.

We start with the principle, that a change in gravitational potential energy equals a change in kinetic energy, because we can calculate the gravitational potential energy and then we need to use the kinetic energy equation to find the speed.

Let's start with the gravitational potential energy.

Substitute the values in, multiply them out, and we get the gravitational potential energy is equal to 2,646 joules, which is equal to the kinetic energy at the moment the rocket is launched.

We can then use the kinetic energy equation, substituting the mass and the energy, and we get a value for the speed squared, which is 2,940.

We need to square root both sides to find the speed, which is 54 metres per second.

So very well done if you've got that answer.

What I'd now like you to do to finish the lesson is to have a go at these questions and for each one show clearly your working out.

Again, pause the video whilst you do so and start again once you've got all of your answers ready.

Okay then, so how did you get on? Let's have a look at your answers.

Starting with question one, a skydiver with a mass of 68 kilogrammes.

How much energy will she have in the kinetic store after falling 50 metres from rest? Well, we know the energy in the kinetic store after falling is equal to the gravitational potential energy she had before she fell.

So we'll write down that principle and then we can calculate the gravitational potential energy she had before she fell.

We'll substitute the values from the question.

And then we'll multiply those through to get 34,000 joules or 34 kilojoules.

And we need to remember at the end to state that that is equal to the energy that's been transferred to the kinetic store, 34 kilojoules.

Well done if you've got that answer.

In question two, a cyclist of mass 84 kilogrammes stops pedalling at the bottom of a hill.

If he then freewheels up the hill and reaches a height of 4.

05 metres, how much kinetic energy did he have before he stopped pedalling? Well, again, we can use the same principle, the change in gravitational potential energy equals a change in kinetic energy.

This time the kinetic energy was changed into gravitational potential energy.

And because we've got a mass, a height, we can work out the gravitational potential energy he had at the end, so let's do that.

We use the same equation as always and substitute the values in.

We'll multiply those out to get the gravitational potential energy at the end of 3,405 joules, which to two significant figures is 3.

4 kilojoules.

And we need to remember to state that that is equal to the kinetic energy that he had when he stopped pedalling at the start.

So 3.

4 kilojoules is the right answer and well done if you got that.

For the third question, a stunt double of mass 74 kilogrammes is shot vertically out of a cannon at a speed of 22 metres per second.

What height will they reach? Well, we've got a mass and we've got a speed, so we can calculate their kinetic energy at the moment they left the cannon.

And then we can use this principle to work out how much gravitational potential energy they had at the top of their flight.

So let's start by working out their kinetic energy.

We'll use this equation, substitute in the values, and then multiply that out to 1/2 times 74 times 22 times 22.

And that gives us 17,903 joules, which is equal to the gravitational potential energy at the highest point.

We can then substitute the energy into this equation along with the mass and the gravitational field strength to find the height.

Rearranging that, we get the height is equal to 24.

2 metres, which rounds up to 24 metres, which is two significant figures, the same as the values that we were given in the equation.

So that's the correct answer, well done if you got that right.

And then the final question is quite challenging.

A volleyball of mass 280 grammes, which we need to remember to change to 0.

280 kilogrammes, is hit up into the air and reaches a height of 3.

80 metres.

How fast was it moving at the moment after it was hit? Well, we start off again with our principle, that a change in gravitational potential energy equals a change in kinetic energy.

We know that at its maximum height of 3.

8 metres, the gravitational potential energy can be calculated using this equation.

When substituting our values in, we get the gravitational potential energy at the maximum height is 10.

64 joules, which is equal to the kinetic energy at the moment after it was hit.

So we can then use the kinetic energy equation, substituting the values for energy and the mass to find the value of the speed squared.

And by square rooting both sides, we get a value for the speed, which is equal to 8.

7178 metres per second.

And again, rounding up to two significant figures is 8.

7 metres per second.

We round it up to two significant figures here despite both values in the question being given to three significant figures because we used a value of 10 newtons per kilogramme for the gravitational field strength, which is two significant figures, and we have to give our answers to the smallest number of significant figures to any value that we used in our calculation.

So very well done if you've got that right.

So well done for reaching the end of the lesson.

This is a short summary slide of the key learning points from the lesson.

For an object that changes height, we found that the energy transferred to or from the gravitational store is equal to the mass times the gravitational field strength times the change of height.

We found that for an object that changes speed, the energy transferred to or from the kinetic store is equal to 1/2 the mass times the speed squared.

And we also found that if no energy is dissipated as an object height and speed, then the change in gravitational potential energy is equal to the change in kinetic energy.

So very well done for reaching the end of the lesson again.

I do hope to see you next time, goodbye.