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I can calculate the energy an object has because it is moving.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Energy is measured in joules (J).
Doubling the mass of a moving object doubles the energy it has in its kinetic store.
Doubling the speed of an object increases the energy it has in its kinetic store by four times.
The energy an object has in its kinetic store of energy is found using the equation Ek = ½ mv².

Common misconception

When calculating energy in the kinetic store, pupils often work out ½ mv and then square everything, rather than just the speed.

Scaffold calculations to show how kinetic energy is calculated, taking pupils through how to do this on their calculators without making a mistake.

Keywords

Work done - Work is done whenever a force makes an object move. The amount of work done is equal to the force multiplied by distance moved in the direction of the force.
Kinetic store - If an object is moving and has a mass, then there is energy in its kinetic store.
Directly proportional to - If two quantities are directly proportional, then as one increases, the other also increases at the same rate.
Kinetic energy - The energy an object has in its kinetic store is referred to as the object’s kinetic energy.

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Hello.

This lesson is about calculating the energy that objects have because they're moving.

It's from the Physics Unit: Energy of Moving Objects.

My name is Mr. Fairhurst.

By the end of this lesson you should understand why an objects called energy because of its movement and to be able to calculate the amount of energy it's got because of that movement.

Here are the key words that we're going to look at in the lesson.

Work done is the amount of energy we give to an object by pushing or pulling it.

Energy in the kinetic store is the energy that objects or systems have because of movement.

And when we're talking about relationships that are directly proportional, we mean that if we double one quantity, the other one doubles as well.

And if we make it one quantity three times bigger, the other becomes three times bigger.

Kinetic energy is what we call the energy that a particular object has, that we can calculate, that it can contribute towards the energy in the kinetic store.

This lesson's split into three parts.

In the first part of the lesson we're going to find out about how doing work to change the speed of an object affects the energy in the kinetic store.

And then in the middle part of the lesson we're going to look at the properties of the object, its mass and its speed, and to find out exactly how they affect the amount of energy in the kinetic store.

Then in the final part of the lesson, we're going to combine those ideas in order to calculate a quantity for the amount of energy in the kinetic store that's contributed by particular object or objects.

So let's get on with the first part of the lesson and have a look about how work done affects the energy in the kinetic store.

Pushing this car with a steady force makes it move faster.

Now we can see the car going a little bit faster because we've done some work on it and we can actually calculate the amount of work we do by using the equation work done is force times distance, and if you remember, the work done is measured in joules.

The force is measured in newtons and the distance in the direction that we're pushing it in this case is measured in metres.

Now that work done on the car will transfer energy into the kinetic store by making the car move faster and faster.

And if we think about the energy transfers, the energy starts off inside the person, if you like, as the energy in the chemical store.

That's all the chemicals in the person's body that can react together to cause their to work properly that they can then use to push the car.

And as the car gets faster, some of that chemical store, the energy in the chemical store is transferred to energy in the kinetic store.

So here's a question for you.

Just pause the video whilst you think about this and start again once you're ready.

How much work, so how much energy will be in the kinetic store of a car if the amount of work done on it is doubled? Okay, how did you get on? How much energy in the kinetic store of a car if the amount of work done on it is doubled? Well, the correct answer is twice as much energy by doing twice as much work with transferred twice as much energy into the kinetic store.

Well done if you got that one right.

Now we can use the same ideas when we're slowing things down, when we're doing work on an object to slow it down.

On this train if we apply the brakes with a steady force, it will slow down and again, we're doing work on it and that work is the force we're pushing on the train in order to slow it down, multiplied by the distance we move whilst we're applying the force.

Work done is moved in joules, the force in newtons and the distance in metres as always.

Now when we do work on the train, we're again transferring energy, we're transferring energy out of the kinetic store.

We know that because the train is slowing down.

So that's the energy it's got to start with.

We've assumed it's got no energy in the thermal store though it will have a little bit.

And by doing work on the train to slow it down, we're transferring that energy outta the kinetic store and into the thermal store.

The brakes of the train will get really, really hot as friction and rubbing cause them to increase the temperature and the energy in that thermal store will increase and then it will dissipate into the surroundings afterwards.

So another question for you.

This time, how much energy will be transferred outta the kinetic store if the amount of work done by breaking is doubled? Again, pause the video and start again once you've got your answer.

Okay, how did you get on? How much work will be transferred outta the kinetic store when the work done by breaking is doubled? The correct answer is twice as much energy.

We've done twice as much work, so we've transferred twice as much energy, this time outta the kinetic store and into the thermal store.

So well done if you got that one right.

So here's a shopping trolley and the work done on the shopping trolley is equal to the change in energy in the kinetic store.

As we're doing work on the trolley, we're speeding it up.

And we're starting with energy in the chemical store.

That's all the chemicals in the person that can react to make their muscles work and as they're pushing the trolley, speeding it up, that energy is being transferred into the kinetic store as the trolley gets faster and faster.

If the work's done to slow the trolley, the energy will be transferred from the kinetic store and into the thermal store.

Now for a real trolley, some of you'll be thinking that's not quite right.

Sub energy is always dissipated, there's always a bit of friction, a bit of rubbing, a bit of heating as air particles are pushed outta the way and made to move faster.

So that means that the energy in a thermal store will increase.

So this is a more accurate representation of what will happen.

Energy in the chemical store has been transferred mostly into the kinetic store but a little bit into the thermal store as well.

Now for an ideal trolley, there's no friction, so no energy is said to be dissipated and we're going to talk about ideal trolleys because we can calculate more easily when we talk about situations in which there's no friction, it's really, really hard to measure a quantity of friction.

So for an ideal trolley we say that there's no friction, so no energy is dissipated and we get this transformation of energy when all of the energy in the chemical store is transferred into the kinetic store and the energy in the thermal store stays the same.

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

How much energy is transferred out of a kinetic store when 260 joules of work is done by slowing an ideal trolley, one in which there's no friction? Pause your video whilst you have a go and start again once you're ready.

Okay, what do you think? 260 joules of work is done slowing an ideal trolley, the amount of energy transfer to the kinetic store is exactly 260 joules.

So well done if you got that, there's no energy being transferred anywhere else because we're ignoring all of the friction and air resistance and so on.

Okay, now I'd like you to have a go at these questions.

95 kilojoules of work is done to speed up a car from rest.

State the amount of energy the car now has in the kinetic store assuming that no energy has been dissipated.

And estimate the amount of energy the car has in the kinetic store if energy is dissipated.

And for this question I'd like you to explain your answer and why you put the amount that you chose.

Pause the video whilst you do that and start it again once you've got some answers.

How did you get on? Let's start with the first question.

What's the amount of energy, state the amount of energy the car now has in the kinetic store.

So you shouldn't need to do any calculations and the amount is simply 95 kilojoules.

If no energy is dissipated, that means that all of the work done has been transferred into the kinetic store.

So 95 kilojoules.

And then for part two, how much should energy would the car have in the kinetic store if energy is dissipated? Well the answer's going to be a little bit less.

I put 80 kilojoules, but anything around that would be fine.

The reason for that is that some of the energy has been transferred to heat the surroundings, to transfer energy into the thermal store as well as into the kinetic store.

That rubbing by friction and air resistance to speed up the particles of the air as it pushes outta the way, all of that will be transferred and dissipated into the thermal store.

So well done if you've got the answers right and you've got a good reason as well.

Now in the second part of this lesson we're going to find out how the mass and the speed of an object can change the amount of energy in the kinetic store.

In order to understand how the mass and the speed of a car affect the energy, the amount of energy in the kinetic store, we're going to think about the work done stopping a car on the dry road.

Now car driving at 30 miles an hour on a dry road usually takes around about 14 metres to stop once the brakes have been applied, it'll also travel distance about 14 metres in the time it takes a driver to react to a hazard and to actually press the foot onto the brake pedal.

So the total stopping distance will be about 28 metres, but we're going to consider just the braking distance once the brake has been applied.

And we're gonna think about these two cars.

The red car's got twice the mass of the blue car and it takes more work to stop it.

Now work done is forced times distance.

So if we use the same braking force for both cars, the red car because it takes more work to stop it is going to travel a greater distance than the blue car because it's got more mass.

So here are the two cars lined up.

They're both travelling at 15 metres per second.

The red car's got twice the mass of the blue car.

The blue car takes about 14 metres to stop once the brakes have been applied and it actually takes the red car with the same size braking force 28 metres to stop.

In other words, doubling the mass will double the braking distance.

Have a look at this question.

An 800 kilogramme car, that's its mass, needs a braking distance of 46 metres to stop.

What's the braking distance needed for a 1600 kilogramme car travelling at the same speed and using the same braking force to stop? Just pause the video whilst you think of your answer and start again once you're ready.

Okay, what do you think? Twice the mass of the car, how far does it take to stop? The correct answer is 92 metres.

So well done if you chose that one.

And it's 92 metres because that's twice the distance that the 800 kilogramme car needed to stop.

So twice the mass, twice the distance.

Yeah, so work done doubles if the force acts for twice the distance because work done is force times is distance and we've got the same force each time.

So that means that the car with twice the mass stopping in twice distance means that we need twice the amount of work done to stop that car.

And because we needed twice the amount of work to done, we've transferred twice the amount of work from its kinetic store.

So initially when it's the both cars are travelling at 15 metres per second, the car which has got two times the mass, has got two times the amount of energy in the kinetic store.

The energy in the kinetic store is actually directly proportional to mass.

So if we double the mass, we double the energy in the kinetic store and if we triple the mass, we triple the energy in the kinetic store and so on.

That's what we mean by directly proportional.

Have a look at this question.

How much energy do you think of full 75 kilogramme trolley has in its kinetic store compared to an empty 25 kilogramme trolley travelling at the same speed? Pause the video whilst you think of your answer and start again once you're ready.

Okay, how did you get on? The correct answer is three times more because the full trolley's got three times the mass and the amount of energy in the kinetic store is directly proportional to the mass.

So three times the mass, three times the kinetic, the energy in the kinetic store.

We're now going to think about what happens if we change the speed of a car.

So we're going to consider on the dry road with the same braking force applied to the same car, which is travelling at different speeds.

At 12 metres per second this car takes 10 metres to stop once the brakes have been applied.

But at 24 metres per second it takes 40 metres and at 36 metres per second it takes 90 metres to stop.

So what does this mean? The braking distance clearly increases with speed and we can see here if we look at, compare the car travelling at 12 metres per second to the car travelling at 24 metres per second, a car with two times the speed has got a braking distance here that is four times longer and if you compare the 36 metres per second car to the 12 metres per second car, we can see that a car travelling at three times the speed has got a braking distance here that is nine times longer.

So what's that relationship? We know that work done is directly proportional to the distance of force acts.

So the car travelling at twice the speed here needs four times the amount of work done in order to stop it.

That means that it's got four times the amount of energy in its kinetic store at its initial speed before we try to stop it.

So a car travelling at twice the speed has got four times the amount of energy in the kinetic store.

Bearing that in mind, have a look at this question and see if you can answer it.

A car at 20 metres per second stops in 48 metres.

So what's the breaking distance of the same car if it was travelling at 10 metres per second? Just pause the video whilst you think about that and start again once you're ready.

Okay, what do you think? It's going at half the speed so it's braking distance will be four times smaller and the correct answer is 12 metres.

So well done if you've got that answer.

So let's go back and see if we can come up with the relationship between speed and the energy in the kinetic store.

Work done is directly proportional distance of a force acts.

We keep saying.

So in this case the car that's travelling three times faster takes nine times longer to stop.

So it's got nine time, we need nine times the work done in order to stop it.

That means that initially when it was travelling at three times the speed, it had nine times the amount of energy in its kinetic store.

So before we had the car was travelling twice as fast, had four times the amount of energy in the kinetic store and a car now travelling at three times the speed has got nine times the amount.

In other words, the energy in the kinetic store is directly proportional to speed squared.

So twice speed, two times two, the square of the speed is four, it's got four times the amount of energy in its kinetic store.

If it's going three times faster, three times three, which is a square of its speed means it's got nine times the amount of energy in its kinetic store.

Okay, let's see if you can use that relationship to answer this question.

How much energy does a shopping trolley have in the kinetic store when it's travelling at four times the speed? Pause the video whilst you think about that and start again once you're ready.

Okay, what do you think? The trolley was travelling four times faster so it's got more energy in the kinetic store.

It's got four times four or four squared times the amount which is 16 times more.

So well done if you've got the correct answer.

What I'd like to do now is have a go at this task.

A train has got a mass of 120,000 kilogrammes and is travelling at 12 metres per second.

How much energy does it have in a kinetic store compared to a train with a mass of 240,000 kilogrammes that's travelling at six metres per second? Work out your answer and then see if you can explain how you got your answer.

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

Okay, how did you get on? A train had a mass of 120,000 kilogrammes travelling at 12 metres per second.

How much energy did it have in the kinetic store compared to a different train with a mass of 240,000 kilogrammes travelling at six metres per second? The correct answer is twice as much energy in the kinetic store.

So why twice as much? It's got half the mass.

And so it's gonna have half the energy because the mass is directly proportional to the amount of energy it's got in the kinetic store.

So half mass, half the energy, but it's also got double the speed and double the speed means it's got four times the amount of energy in the kinetic store.

So four times, half the amount gives you two times the amount overall, so it's gonna have twice as much energy in its kinetic store.

Well done if you've got the right answer with the right reasons.

In the final part of the lesson we're going to use those ideas that we've covered so far in order to work out how to calculate the amount of energy in the kinetic store.

So far in the lesson we've talked about the energy that an object's got because of its mass and its speed has been the energy it's got in the kinetic store, but often we refer to that quite simply as the object's kinetic energy.

Now that's not to say the object's got a special source of energy, it's just got energy like anything else, but it's got energy because of its speed and its mass.

And we use the phrase kinetic energy as shorthand.

So for example, this cricket ball has got a mass of 0.

6 kilogrammes.

It's got a speed of 20 metres per second, so that means it's got energy in the kinetic store.

It's got 32 joules of energy in the kinetic store.

But for shorthand, a quick way of saying that we say the cricket ball's got 32 joules of kinetic energy.

We've also seen in this lesson that the kinetic energy of an object is directly proportional to both its mass and to its speed squared.

And we can summarise that in an equation which is this one.

Kinetic energy is equal to 1/2 with the mass times the speed squared.

And that works because if we say double the mass on the right hand side, we will double the amount of kinetic energy, which is what we'd expect.

And if we double the speed on the right hand side, it's speed squared, so double twice the speed is two times two, which is four times bigger and we get a kinetic energy which is four times bigger if we double the speed, which again is what we'd expect.

The half comes in just to make the equation work effectively with the units that we're using.

In symbols the equation's E for energy with a subscript K to show that it's kinetic energy equals a 1/2 times the mass times the speed squared.

And it's important to realise that we're just squaring the speed, we're not squaring the mass and the half as well.

So when you put it into calculator a 1/2 times the mass times the speed times the speed.

Kinetic energy is made in joules, mass in kilogrammes and the speed in metres per second.

Let's have a look at this question.

A formula one has got a mass of 800 kilogrammes and the top speed of 100 metres per second.

How much kinetic energy does it have when travelling at its top speed? Well we'll start with the equation.

Kinetic energy is 1/2 mv squared, which means we need to do 1/2 times the mass times the speed squared.

So let's put the numbers in.

We've got 1/2 times the mass which is 800 kilogrammes times 100 squared.

And that comes out as 1/2 times 800 times 10,000, which is 100 squared.

Do that in the calculator and we have 4 million joules.

Have a go at this question yourself, pause the video whilst you do so and start again once you've got your answer and don't forget to show you are working out.

Okay, so how did you get on with that? Let's start with the equation for kinetic energy again, 1/2 times mass times speed squared and we put the numbers in from the question.

The family car had a mass of 1400 kilogrammes and it had a speed on the motorway of 32 metres per second So we need to do 32 squared, which is 1,024 and if we multiply that out on the calculators we get we get 716,800 joules.

So well done if you got that answer.

Here's another example to look at.

A sky diver is formed a steady speed of 30 metres per second and has got a kinetic energy of 315 kilojoules.

What's the mass of the sky diver? Well we've got a mass, we've got a speed and we've got a kinetic energy.

So the equation that has got all those three terms in is the kinetic energy is 1/2 mv squared equation.

Now to start with kinetic energy, we've got 31.

5 kilojoules, but in this equation we need that into joules.

So 31,500 joules when we convert it.

Put the terms into the equation, we've got 31,500 joules.

It's 1/2 times the mass times 30 squared, which is the speed squared.

Multiply it.

That's how we get 900 for the speed squared.

And then multiply those two terms on the right hand side we get 31,500 equals 450 times the mass, so we then have to divide both sides by 450 to get the mass, which is 70 kilogrammes.

Have a go at this example yourself, don't forget to show you are working out and just pause the video whilst you do that.

Start again once you're ready.

Okay, how did you get on? We'll start again with the kinetic energy equation and we'll put in the terms that we know from the question.

So we get 192 joules equals 1/2 times the mass times 16 squared for the speed squared.

That gives us 256, multiply the terms on the right hand side and then divide both sides by 128 to get the mass, which comes in at 1.

5 kilogrammes.

So well done.

If you've got that answer and showed all you're working out.

What I'd like you to do now is to have a go at these questions, show all of your workings out and give all of your answers to two significant figures.

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

Okay, how did you get on? Let's start with question one.

Which of the following has got the most kinetic energy? Well, we've got to show all of our working out.

So let's start with the car.

We've got the kinetic energy equation put in the values and calculate them out step by step.

And we get an ounce of 228,150 joules to two significant figures.

That is 230,000 joules or 230 kilo joules.

If we do the same thing for the van, we end up with 202,500 joules, which rounds up to two significant places to 200 kilo joules.

That means that the one with the most kinetic energy is the car.

So well done if you've got that answer.

For question two, we've got to calculate the kinetic energy of a cricket ball hit up in the air with a speed of 36 metres per second.

And calculating that out, we get an ounce of 103.

68 joules, which rounds up to, or rounds down to 100 joules.

For part B, state the kinetic energy of the same ball falling down with the speed of 35 metres per second.

We get exactly the same answer.

Now because it said state in the question, it means we don't have to show any working out and we should be able to find the answer in an earlier part of the question.

And because it's got a speed of 36 metres per second and the same matters before, it's gonna have the same kinetic energy.

Question three, what is the mass of a bus that's got a kinetic of 1 million joules and the speed of 14 metres per second? Well, the kinetic energy is 1/2 times mass times speed squared.

Put the values in, we've got, a million is 1/2 times mass times 14 squared.

That gives us 1/2 times the mass times 196, which is 98 times the mass divide both sides by 98 and we get an ounce of masses, 10,204 kilogrammes, which rounds off to 10,000 kilogrammes to two significant figures, which is 10 metric tonnes.

So well done if you've got those answers correct, Congratulations on reaching the end of the lesson.

This is just a short summary of the key points from the lesson and the main point really is that the energy an object has because it's moving, is energy in the kinetic store is often referred to as that object's kinetic energy and it can be calculated using the equation.

Kinetic energy equals 1/2 times the mass, times the speed squared.

Remembering on the right hand side of the equation, it's just the speed term that is squared.

Kinetic energy is measured in joules, mass is measured in kilogrammes, and speed is measured metres per second.

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

I do hope to see you next time.

Goodbye.

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