Lesson video

Hello.

This lesson's about the energy objects have because they're in a gravitational field.

It's part of the physics unit, the Energy of Moving Objects.

My name is Mr. Fairhurst.

So by the end of this lesson you should really understand what it means for an object to have energy in the gravitational store.

And you should also be able to calculate how much energy is transferred when it's lifted or lowered inside a gravitational field.

These are the key words that we're going to use, and you're gonna come across during this lesson.

The gravitational store is the amount of energy an object has because of its height and its mass when it's inside a gravitational field.

And the work done, that we do on an object, is the amount of energy we transfer to it when we push it and move it with a force.

The weight of an object is the force it's pushing downwards in a gravitational field.

And that's equal in size to the force we need to lift up an object.

And the gravitational field strength is the strength of the gravitational field.

It's the number of Newtons of force that that gravitational field pushes down with on an object, for each kilogramme of its mass.

And the gravitational potential energy is the word that we give to the energy that a particular object has in its gravitational store.

So here are the definitions of those keywords.

If at any point during the lesson you feel that you would like to come back and have a look at those, just pause the video and come back to this slide.

So this lesson is split into three parts.

In the first part of the lesson, we're going to look at the energy an object has in its gravitational store, and the factors that affect how much energy it's got there.

And then in the middle part of the lesson, we're going to calculate the amount of work we need to do in order to lift an object up against the force of gravity.

And then we're going to use those ideas in the last part of the lesson, in order to calculate the amount of energy transferred when an object is lifted up, or indeed, if it falls down within a gravitational field.

We're going to measure what we call its gravitational potential energy.

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

Let's start by thinking about what we mean by energy in the gravitational store.

This crane has lifted up that concrete block, which means that that block has now got more energy in the gravitational store.

It's got more energy because its mass is higher up.

Now, that energy has not come from nowhere, it's come from the crane and the energy that that crane had.

Now, when the crane works, petrol in its engine reacts with oxygen to make its engine work and to lift up that concrete block so energy's come from the petrol.

Now, if we look at the energy diagrams of what we can see there, the crane starts with lots of energy in the chemical store because of its petrol.

And as it lifts the block up, it transfers some of that energy from the chemical store into the gravitational store as the block rises up.

The total amount of energy, as always, will remain the same.

We're assuming here that the crane is 100% efficient and there's no energy dissipated into the surroundings.

Now, all of these three blocks in very different situations, but what they have got is the same amount of energy in the gravitational store.

Now, at first look, that might seem a little bit counterintuitive.

The first two blocks are quite similar, the first block's held and suspended in the air by the crane, and the second block is resting on the tower, so it can't move.

The third block is falling, and often people say that that block therefore must have much more energy, 'cause if you're underneath it, you'll notice a bigger difference when it hits you.

It will hit you with a much faster speed.

But it's not got more energy in the gravitational store, it's simply got more energy overall.

It's got a lot of energy in the kinetic store.

If each of those blocks fell from that position they're at now, we released the first two, then they would each gain the same amount of extra energy in the kinetic store as they fell that last little bit of the distance.

So we do say they've all got the same amount of energy in the gravitational store.

Now, what I'd like you to do is to have a look at this question and have a real think about this.

Which of these identical balls has got the most energy in the gravitational store? Pause the video whilst you think about this and then start again once you've made your choice.

Okay then, so what do you think? Did you choose option B? If you did, then I'm afraid you're wrong.

And that's the option that most people choose, because when they look at this diagram, they think that that ball has got further to fall, therefore it must have more energy in the gravitational store.

But in reality, if you think about it, each of those balls has got the same mass, they're at the same height, they've got the same amount of energy in the gravitational store.

If each of those balls went down to the level of the surface at one metre, they would all still have the same energy in the gravitational store.

Now, ball B can carry on falling and it can lose more energy from its gravitational store and transfer that into the kinetic store.

But all of the other four balls would still have that amount of energy in the gravitational store that ball B had when it was at the surface.

And each of those four balls can then be tipped into the hole, and they will lose, or have more energy transferred from their gravitational store into the kinetic store.

So overall, we can say that all of those balls have got the same energy in the gravitational store, because they've got the same mass and they're all at the same height.

So if you did say that, very well done indeed.

Now, we're going to use this equation about work done for a moment to think about what happens when we lift objects up into the air.

Work done, if you remember, is the energy that's transferred to an object when we move it.

So what happens when we move an object upwards? Well, we've got three little dots after that equation.

Why have I put those in? Well, that equation in full, is work done is force times distance moved in the direction of the force.

And when we're lifting objects up, that becomes very important.

Let's think about Sophie.

Sophie's climbing a hill and what she's doing is work against the gravitational force of the planet Earth.

The gravitational force is pulling her downwards towards the centre of the Earth, and as she's climbing up, she's doing work against that force in order to lift herself upwards.

In other words, she's doing work in that direction because a gravitational force is pushing directly downwards.

She's pushing up against the gravitational force.

Now, if she climbs to the top of the hill, does it matter which route she takes? She's doing her work against the gravitational force.

She could go up this steep side there.

She could go up the more gradual side, or she could find the shortest, quickest, steepest way up the hill.

But at the top of the hill she would still have the same amount of energy in the gravitational store, no matter which route she took.

It's like those concrete blocks or the balls in the earlier examples.

It's her mass and it's her height that are important.

So let's have a think about this question.

Look at each of these different examples of a cyclist cycling to the top of a 100-meter cliff.

They go different routes.

In which example does that cyclist has the most energy when they get to the top? Pause the video and make your selection and then start again once you're ready.

Okay then, so how did you get on? Hopefully this time you were a little bit clearer that they will all have the same amount of energy in the gravitational store, because they've all got the same mass and they're all at the same height.

So, well done if you said that.

Now, what I'd like you to do is have a go at this task.

It's about a cable car that's being pulled up a mountain and some pupils are discussing the work done and the energy in the gravitational store.

The work done pulling the cable car up the mountain and the energy in the gravitational store when it gets to the top.

And what I'd like you to do is to read through each of their statements and pick out which pupils you think are correct and just note that down.

And then for the other pupils, I want you to say, to think about what you would say to them to help them understand their thinking a little bit more clearly, and understand the correct scientific explanation for what's going on.

So pause the video whilst you do that and once you're completely ready, put it back on again.

Okay, so how did you get on? Which pupils did you think were correct? Well, both Laura and Sofia were correct.

Laura said that the energy in the gravitational store increases because the cable car moves upwards.

Its height gets bigger, therefore it's got more energy in the gravitational store.

And Sofia said that works done the cable car by the pulling force that's pulling it up the mountain.

So they're both correct.

So what would you say to the other two pupils? Well, Sam said that the pulling force is constant, therefore the gain in gravitational energy will be the same if you double the height it's lifted to.

But work done is equal to force times the distance.

So if you double the distance or the height that you lift up the cable car, you also need to double the work done.

Work done is not dependent on just the force.

and Aisha said that because less force needed to pull the cable car up if it's a smaller angle, less work will be done overall and it will gain less gravitational energy.

But what she forgot to think about was the distance over which you need to move it.

If it's going to the more gradual angle, a smaller angle, then you're gonna need to pull it a lot further to get it to the top, and overall the force times the distance will be just the same, no matter what the angle.

So the work done and the gain of gravitational energy will be the same, no matter what the force is and the angle.

So, well done if you got those correct.

In the next part of the lesson, we're going to look more carefully the factors involved in working out the amount of work done in lifting an object, and therefore the amount of energy in the gravitational store.

Let's start by thinking about the gravitational field that surrounds the earth, and which pulls all objects around it towards the centre.

And so the further we go from the planet, the weaker that field gets, so objects that are close to the surface are pulled down with a stronger force than objects that are further away.

Although, we do know that the gravitational field of the earth attracts objects that are very far away, objects like the moon that orbits the earth, so we do know that the earth's gravitational field reaches far out into space.

Although, if we do think about the Earth's gravitational field close to the surface, the differences are so small that they're insignificant.

If you're flying in a plane, the gravitational force that you feel will be the same whether that plane is close to the ground, whether it's high in the air, or indeed if it's actually on the ground.

Now, near the surface of the earth, each kilogramme of mass is pulled downwards with a gravitational force of about 10 newtons.

And we call that force per kilogramme, the gravitational field strength.

Now, it's not exactly 10 newtons, in your room it's going to be about 9.

81 newtons per kilogramme, which means 9.

8 newtons is pulling down on each kilogramme of mass.

Now often we just round that up to 10 newtons to make the numbers a little bit easy to calculate.

Bearing that in mind, have a look at this question.

What is the gravitational force acting on a 10 kilogramme plank of wood if the gravitational field strength is 9.

81 newtons per kilogramme? Pause the video whilst you work that out and start again once you're ready.

Okay then, how did you get on? 9.

81 newtons per kilogramme.

There's 10 kilogrammes, so we multiply that 9.

81 by 10 to get 98.

1 newtons.

So, well done if you got the right answer.

Now, the gravitational force of an object is equal to its weight.

The force of that object pushes down onto the surface.

And we know that the weight is equal to the mass times the gravitational field strength.

Or in symbols, weight W equals m times g.

So little g is the gravitational field strength, the symbol for the gravitational field strength.

Weight is measured in newtons 'cause it's a force, mass is in kilogrammes, and the gravitational field strength is the number of newtons per kilogramme.

Let's have a look at an example and see how that works.

A boulder, a rock, has got a mass of 85.

6 kilogrammes.

What's its weight? Well, the gravitational field strength we're going to use is 10 newtons per kilogramme.

So we'll start off, as always, with the equation, weight is mass times the gravitational field strength, substitute in the numbers, and do the math.

So we get 856, and weight is a force, so it's in newtons.

It's the force of gravity pulling down on an object.

Have a go at this example yourselves.

Show your working out and just pause the video whilst you do that, and start again once you're ready.

Okay, so how did you get on? What's the weight of the basketball? Weight is mass times the gravitational field strength.

So that's 0.

625 times 10, which gives us 6.

25 newtons.

And the weight of that basketball pushing downwards, is also the size of the force we need to lift up the basketball.

So the force needed to lift an object against a gravitational force is equal in size to its weight.

If we think about the work done lifting a heavy book onto a shelf, if we lift two identical books with twice the weight, we're going to double the amount of work done.

So in other words, the work done lifting an object, is proportional to its weight.

And weight is mass times the gravitational field strength.

Now, we've seen that the gravitational field strength is a constant value, it doesn't change near the surface of the earth.

So in other words, we could say that the work done lifting an object is also proportional to its mass.

If we double the mass of an object, we double the work done lifting it up.

And if we lift it to twice the height, we also double the amount of work done 'cause we've moved it twice as far, so the work done is also proportional to the height lifted.

Have a think about those relationships and then have a go at this question.

A forklift raises a mass up to 2.

5 metres.

How much work does it do lifting twice the mass to the same height.

Pause the video and then start again once you've got your answer.

Okay, what do you think? Twice the mass to the same height.

So it's going to do two times as much work.

Well done if you got that answer.

What about this question? Another forklift raises a mass up to 1.

6 metres.

How high can it lift twice the mass if it does the same amount of work? Pause the video once you think about this one and start again once you're ready.

Okay, how did you get on? The correct answer was 0.

8 metres.

It's got twice the mass, but it does the same amount of work.

That means it's going to be able to lift it only half the distance.

So, well done if you got that right.

I'd now like you to have a go at this question.

Forklift Y is used to lift three times the mass as Forklift One, but lifts to just half the height.

How much work does Forklift Y do compared to Forklift One? I'd like you to work that out and then to spend a little bit of time explaining your reasoning behind giving your answer.

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

So, what do you think, how much work does Forklift Y do compared to Forklift One? The correct answer is one and a half times more work.

But the important part of this question is the explanation, the reasoning behind that.

If we start with the mass, it lifts three times the mass, so that's three times the force to lift it up, so it will do three times as much work.

But you'll only lift it to half the height, and half of three times as much is going to be one and a half times more work in total.

So, very well done if you got that right.

The last part of the lesson is where we put all of those ideas together in order to work out how to calculate the amount of energy in the gravitational store.

So far we've talked about energy in the gravitational store, but the energy a particular object has in its gravitational store, is often referred to as that object's gravitational potential energy.

And that's not a special sort of energy, it's just the energy that that object has because it's got a mass and it's got a height and it's in a gravitational field.

So for example, this cricket ball's got a height above the ground, it's got a mass, gravity's pulling it down towards the ground, so it's got a gravitational potential energy.

It's got energy in the gravitational store.

In this case, 0.

96 joules.

Now we've already seen that the gravitational potential energy of an object is directly proportional to its mass and also to its height.

But we can combine those ideas by saying the gravitational potential energy is equal to the mass times the gravitational field strength, which is constant, times by the height.

So if we were to double the mass or the height, we would also double the amount of gravitational potential energy that that object has.

This is the same equation in symbols.

The capital E with a subscript P stands for gravitational potential energy, which is measured in joules.

The mass is measured in kilogrammes.

The gravitational field strength is measured in newton's per kilogramme, which close to the surface of the earth is about 10 newtons per kilogramme.

And the height is measured in metres.

Let's have a look at an example.

Laura carries a box of books with a mass of 18 kilogrammes up the stairs.

How much gravitational potential energy do the books gain if they are lifted a vertical height of 2.

6 metres.

And as you can see on the bottom of the screen, the gravitational field strength we're using is 10 newtons per kilogramme.

So let's start, as always, with the equation.

Gravitational potential energy is mass times the gravitational field strength, times by the height.

18 times 10 times 2.

6, and that gives us a gravitational potential energy of 468 joules.

I'd like you to have a go at this example.

Just pause the video whilst you do so and don't forget to show all your working out.

Start the video again once you're ready.

Okay, so how much gravitational potential energy did you calculate was gained at the top of the throw? The gravitational potential energy's mass times the gravitational field strength, times by the height.

Substitute in the numbers from the question, and do the maths and we come up with 21.

875 joules.

Now I've rounded that up to 22 joules, just for simplicity, but also because we were only told some of those values to two significant figures.

Like for example, the the height the basketball was thrown was 3.

5 metres, which is two significant figures.

And that means we can only accurately give the answer to the same number of significant figures, which is why I've rounded it up to 22.

So well done if you've got the right answer and even better if you rounded it up to two significant figures.

So let's look at another example.

Sam has a mass of 50 kilogrammes and when she has a ride in a hot air balloon, she gains 85 kilojoules of gravitational potential energy.

What height does she go up to? Well, let's start with the equation again and substitute in the values that we're told in the question.

So her gravitational potential energy gain was 85 kilojoules, which is 85,000 joules.

So we need to convert that first.

And that's equal to 50 kilogrammes times 10 newtons per kilogramme, times by her height.

So we'll just multiply what we can straight away and divide both sides by 500.

And that gives us a height of 170 metres.

Have a look at this other example.

Try this for yourselves, show your working out, and then start the video again once you're ready.

Okay, so how did you get on? The parachutist started off with a gravitational potential engine of 3000 kilojoules 'cause they jumped out of a plane, had a mass of 85 kilogrammes.

How high did they jump from? So we'll start with the equation and put in the values that we already know.

So 3000 kilojoules is 3000 thousand joules or 3 million joules, equals 85 kilogrammes times 10 newtons per kilogramme, times by the height.

That gives us this sum to work out the height, which is 3,529.

41176 metres.

We can't possibly be that accurate and you were in fact asked to round up your answer to two significant figures, the same number of significant figures as the mass, and that comes out as 3,500 metres to two significant figures.

So, well done if you got that answer.

What I'd like you to do now is to have a go at these calculations.

Show all of your working out for each one, pause the video whilst you do them, and once you've got all of your answers, start the video again and we'll go through the answers.

Okay, so how did you get on? Let's start with one A, the shot put of mass four kilogrammes at a height of nine metres.

What's its gravitational potential energy? Well, if we put all of the values into the equation, we get 360 joules.

Part B was to do the same thing for a two-kilogram discus at a height of 19 metres.

And if we put those values into the equation, we get 380 joules.

So you were asked to say which one had the most gravitational potential energy.

So the correct answer is the discus.

And you need to state that clearly in an exam if you're going to get the mark for that part.

For question two, you were asked to, first of all, calculate the gravitational potential energy of a cricket ball that was stuck on top of a stand at a height of 27 metres.

So putting the values into the equation, we end up with 43.

2 joules of gravitational potential energy.

You were then asked to state how much gravitational potential energy the same cricket ball had when it was hit up into the air and was moving at a height of 27 metres.

Well, it's the same height and the same mass, so it's gonna have the same amount of gravitational potential energy.

So we can simply write down the same answer we got for part A without doing any calculation.

And that's sort of what the word state means.

It means you do not need to do a calculation, but you should be able to work out what the correct answer is from, in some other way.

So, well done if you got that.

Then the third part, the third question, a hot air balloon of mass 2,200 kilogrammes has a gravitational potential energy of 600 kilojoules.

What height is it flying at? Substitute those values into the equation.

We can work that through for height, which is 27.

27272727 metres.

The two dots above the last two figures of that answer show that those figures keep repeating themselves.

Rounding that up to two significant figures, or in this case, rounding it down to two significant figures, gives us a height of 27 metres.

So, very well done if you got all of those right.

So, well done for reaching the end of the lesson.

This is a short summary slide to sum up the key points that we covered during the lesson.

We started off thinking about the energy that an object has in the gravitational store.

And that energy, when we're talking about a particular object, we often refer to as that object's gravitational potential energy, which we can calculate using the equation, gravitational potential energy equals the mass times the gravitational field strength times the height.

Or in symbols, it's E with a subscript P equals mgh, where E subscript P is the gravitational potential energy, measured in joules, m is the mass, measured in kilogrammes, g is the gravitational field strength, measured in newtons per kilogramme, and h is the height, measured in metres.

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

I do hope to see you next time.

Goodbye.