Lesson video

Hello, this lesson's about the energy objects have because they're in the 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 keywords 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 equally in size the force we need to lift up an object.

And the gravitational field strength is the strength of the gravitational field, it's a 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 work 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 our 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 release the first two, then they would each gain the same amount of extra energy in the kinetic store as they fall 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, 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 will 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 upward.

In other words, she's doing work in that direction because the 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 to 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 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 do 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 work is done on 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 is 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 to 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've got those correct.

In the next part of the lesson, we're going to look more carefully at the facts 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 fields 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-kilogram 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 that 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 = m x g.

So 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 a 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 are 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, substituting the numbers, and do the maths.

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 a 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 whilst 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 is 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 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.

We've seen before that the energy and object has in its gravitational store is proportional to its mass and its height.

So to calculate an object's gravitational potential energy, we can use this equation we've got here.

The gravitational potential energy is equal to the mass times the gravitational field strength times the height of the object.

So if we double the mass or the height, we double the gravitational potential energy.

The gravitational field strength is a constant.

In symbols, we say E = mgh, where E equals energy.

The gravitational potential energy is measured in joules, the mass in kilogrammes, the gravitational field strength is measured in newtons per kilogramme, and the height is measured in metres.

Let's look at this example and see how that works.

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're lifted a vertical height of 2.

6 metres? We'll start by writing down the equation, and then substituting the values that were given in the question.

18 kilogrammes mass times 10 newtons per kilogramme, for the gravitational field strength, times by 2.

6 metres of height.

If we do the maths, we get an answer of 468 joules.

Here's another question that I'd like you to have a go at.

Just pause the video whilst you try this one, and start again once you're ready.

Okay, so how did you get on? Hopefully you started off by writing down the equation, substituting the values from the question into the equation, and then working it out.

And you would've got 21.

875 joules.

Now what I've done is one more step, and I've rounded that up to two significant figures, and I did that because in the question it had the height the basketball was thrown to as 3.

5 metres, which was two significant figures, and that means I can't really give an answer that's any more accurate than that.

So given the answer to two significant figures is as accurate as we can sensibly go.

So well done if you've got the correct answer, and especially well done if you've got it to two significant figures.

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

Show all of you working out, pause the video whilst you do them, and once you're ready to check your answers, start the video again.

Okay, so how did you get on? For the first part of the question, you were asked to work out the gravitational potential energy of a shot put of mass four kilogrammes thrown to a height of nine metres.

We can work that out by substituting the values in the question into the equation, and we get the gravitational potential energy of the shot put as 360 joules.

We can do exactly the same to work out the gravitational potential energy of the discus.

This time of mass two kilogrammes and the height of 19 metres.

And putting that into the equation, we get the gravitational potential energy of 380 joules.

Now in the question you were asked which of those two have the most gravitational potential energy? So it's important to write that down, and that is the discus in this case.

For question two, calculate the gravitational potential energy of a small aeroplane of mass 700 kilogrammes at a cruising height of three and half thousand metres.

Again, we can use the same equation and calculate that out.

And this time we get an answer of 24,500,000 joules, or 24.

5 megajoules, just make it a little bit simpler.

A megajoule is equal to a million joules.

For part three, you're asked to calculate the gravitational potential energy of a cricket ball stuck on top of a spectator stand at the height of 27 metres.

So once again, we can use the equation to substitute the values in, and to calculate that out.

The correct answer is 43.

2 joules.

Part B the ask us to state how much gravitational potential energy the cricket ball would have if it was hit up into the air to a height of 27 metres.

Well, this is the same height as the cricket ball when it was stuck on the roof of the spectator stand, and it's the same mass, and it's in the same gravitational field, so it's gonna have the same gravitational potential energy.

And because it says state, we don't need to show any calculations there.

So well done if you've got all of those answers, and very well done if you've got that last answer without needing to calculate it.

So congratulations on reaching the end of the lesson.

This is a short summary slide that sums up the key learning points from the lesson.

We learned that the energy an object has in the gravitational store is referred to as the object gravitational potential energy, and we can calculate that using the equation gravitational potential energy equals the mass times the gravitational field strength times the height, or in symbols, E = mgh, where energy is measured in joules, mass is measured in kilogrammes, the gravitational field strength is measured in newtons per kilogramme, and the height is measured in metres.

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

I do hope to see you next time.

Goodbye.