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 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 equally 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 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 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's 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 the gravitational field.

We're going to measure what we call is 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 where 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 some of that energy from a 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 are in very different situations, but what they have got is the same amount of energy in the gravitational store.

Now, first at 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've 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 Sofia.

Sofia'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 the 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 she 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 100 metre cliff.

They go different routes.

In which example does that cyclist have 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's 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 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 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 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 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, masses 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 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 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 the 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 go at this question.

Forklift Y is used to lift three times the mass as forklift 1 but lifts to just half the height.

How much work does forklift Y do compared to forklift 1? 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 1? 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 if you only lift it to half the height and half of three times as much, it's 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 gravitational potential of an object is directly proportional to its mass and also to its height.

And we can put those ideas together and calculate the change in gravitational potential energy using this equation, which is the change in gravitational potential energy is equal to the mass times of gravitational field strength, times of change in height.

And if we double the mass of an object or if we change its height by twice as much, we double the amount of gravitational potential energy that we're transferring to it.

We've seen before that the gravitational potential energy is directly proportional to mass and also to height.

And we can combine those ideas into this equation for calculating the change in gravitational potential energy when an object rises up or falls down.

And gravitational potential energy is equal to the mass times the gravitational field strength times by the change in height.

And in symbols, this looks like this, where the funny triangle symbol is the Greek letter delta, meaning a change.

So we've got the change in gravitational potential energy equals mg delta h, which is a change in height.

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

Let's use that equation and see if we can solve this problem with it.

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 of vertical height of 2.

6 metres? Well, let's start with the equation and then substitute in what we know.

The change in gravitational potential energy equals the 18 kilogrammes mass times 10 newtons per kilogramme times by the change in height, which is 2.

6 metres.

If we do the maths, we get 468 joules.

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

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

Okay, so how did you get on? Hopefully you started with the equation, substituted the numbers in from the question and then did the math, and you get an answer of 21.

875 joules, which is very precise, but we only said she threw it to 3.

5 metres, which is quite a general measurement.

So sensibly we should only give our answer to two significant figures as well.

So let's change that to 22 joules by rounding it up.

So well done if you've got that answer and especially well done if you chose to round it up to two significant figures.

Here's another example.

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

What height did she go up to? Well, we'll start with the equation again and her gravitational potential energy was 85 kilo joules, which is 85,000 joules.

We must remember to convert that before we put the numbers into the equation.

And once we've got that in, we can multiply the 50 by 10 to get 500 and we can divide both sides by that 500 newtons that we get.

And then to work out the change in height, that's going to be 170 metres by doing the maths.

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

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

Start again once you've got your answer ready.

Okay, so how did you get on? Hopefully you started with the correct equation, substituted in your values.

This time 3,000 kilojoules is 3,000 thousand joules or three million joules.

Multiply the 85 by the 10 on the right, which is 850 and divide both sides by 850.

And we can use that to calculate the height, which is 3,529.

41176 metres.

Hopefully you remembered to round off your answer to two significant figures, which gives us 3,500 metres.

So well done if you've got that answer.

Here's another example to look at.

Sam has a mass of 50 kilogrammes.

When she has a riding hot air balloon, she gains 85 kilojoules of gravitational potential energy.

So what height does she go up to? Well as usual, we start by writing down the equation and then we substitute the values we've got given to us in the question.

But first of all, 85 kilojoules of gravitational energy needs to be converted to 85,000 joules.

So that's what it looks like when it's substituted into the equation.

We can multiply the 50 and the 10 on the right hand side to get 500 and divide both sides by 500 to get the height on its own.

And if we do the maths there, we get the height as 170 metres.

Here's a similar question for you to have a go at.

Just pause the video whilst you do this one, and once you're ready to check your answers, start the video again.

Okay then, so how did you get on? Hopefully you started by writing down the equation and substituting in the numbers, and then if you do the maths you end up with the answers, the height is 3,529.

41176 metres.

You were asked to give your answer to two significant figures, so that rounds down to 3,500 metres.

So well done if you got that answer correctly.

What I'd like you to do now is to have go at these calculations, pause the video again whilst you do these ones and start again once you're ready to check your answers.

Okay then, so how did you get on? Let's start with part A.

How much gravitational potential energy did the shot puts have four kilogrammes at a height of nine metres? We substitute the values into the equation and we get the gravitational potential energy of the shot put as being equal to 360 joules.

If we do exactly the same for the discus, we get the gravitational potential energy of the discus as 380 joules.

Now the original question asked which of those two had the most gravitational potential energy.

So in an exam situation, it's very important to write that down to get the final mark.

The discus has got the most gravitational potential energy would get you a simple, easy mark the end and you'd lose it if you missed that part out.

For question two, calculate the gravitational potential energy for a cricket ball that is stuck on top of a spectator stand at the height of 27 metres.

Again, we substitute the values into the equation, and this time we get an answer of 43.

2 joules.

And then part B asks you to state how much gravitational potential energy a cricket ball would have if it was simply hit up into the air.

And we can assume it's moving at this point.

Well, it's got the same height, the same mass, and it's in the same gravitational field, so it's gonna have the same gravitational potential.

It's probably gonna have a little bit more energy 'cause it will have some energy in its kinetic store as well.

Now because this question said state, it means you don't need to calculate your answer and you should be able to find the answer, work out what the answer is from other parts of the question.

So very well done if you got that right.

For the final question, we have a hot air balloon of mass 2,200 kilogrammes and a gravitational potential energy of 600 kilojoules.

What height is it flying at? If you put the numbers into the equation going to work it out, you end up with a height of 27.

27272727 metres.

Those two dots I've put above the final two and the seven in the answer show that those last two digits keep repeating to infinity.

We need to round that to two significant figures, so our height is simply 27 metres.

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

And congratulations for reaching the end of the lesson.

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

We found out that the energy that an object has in the gravitational store is referred to it as that object's gravitational potential energy, and we can calculate that by using the equation the gravitational potential energy is equal to the mass times the gravitational field strength times by the height, or in symbols E equals mgh, where the 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.

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

I do hope to see you next time, goodbye.