Lesson video

Hello and welcome to this lesson about power and about calculating power from the physics unit The Energy of Moving Objects.

My name is Mr. Fairhurst.

So in this lesson, you're going to learn how to describe power, and how to calculate the rate at which energy is transferred by a force, which is just another way of saying, how do you calculate what power is equal to? So these are the keywords that we're going to come across in the lesson.

Work or work done is the amount of energy transferred when you push or pull with a force.

And rate or the rate of change is how quickly that energy is transferred, and how quickly the energy is transferred is what we call power.

And power is measured watts or in kilowatts, with one kilowatt being equal to 1000 watts.

Here are the definitions of those key terms, and if at any point in the lesson you feel that you need to return to these, just pause the video and come back to this slide.

We're gonna start off by thinking about work done by a push or a pull, and what it's like to do that work more quickly or less quickly.

And then we're going to combine those ideas of work done and how quickly work's done with a definition of power in that middle section of the lesson.

And then finally, we're going to combine all of those ideas into an equation that allows us to simply and easy calculate values for power.

So let's make a start with that.

So let's start with an example, and in this example, Sofia's walked to the top of the hill, and she's doing some physical work to get herself there.

And what she's actually doing, she's transferring energy from her chemical store to her gravitational store, and to the thermal store of the surroundings.

In other words, the chemical reactions in her body are enabling her muscles to do some work to lift her up the hill, and she's getting a little bit warm and passing that onto her surroundings as she does so.

Now, we can calculate the amount of work she does climbing the hill, and we can use the equation work done is force times distance in the direction of the force.

Now, she's lifting herself up, so the force that she's lifting is her weight, and the distance she's moving in the direction of that force is the height of the hill.

So her work done is her weight times the height of the hill.

Now let's think about a similar situation but slightly different.

This time, Sofia's running up the hill, and she does exactly the same amount of work, because her work's calculated in the same way.

Her work done is the force times the distance she moves, which is her weight, times by the distance, which is the height of the hill.

So she does exactly the same amount of work running as she does walking.

Now, you might think that if she's running, she's gonna do more work.

Well, let's have a think about that in a little bit more detail.

It might be that you think that when she's running, she's putting more force and effort into that movement.

And it's true that when you're running, you do push off with a bigger force.

But when you're running compared to walking, for a lot of the times when you're between strides, you're not actually in contact with the ground, so you're putting no force into the movement whatsoever.

So on average when you're running or walking, the average force is roughly the same, so the work done will be the same amount.

So here's a quick check for you.

When Sofia's running up the hill compared to when she's walking up the same hill, how much work does she do? Less work when she runs, the same amount of work, whether she's running or walking, or more work when she's running? Pause the video, have a think of your answer, and start again when you're ready.

Okay, how did you get on? The correct answer is that she does the same amount of work whether she's running or walking, because she's climbed the same height, and on average, she's used the same size force to move herself there.

So if work done is force times distance, it will be the same.

Okay, let's take that idea a little bit further.

What's the difference when she's running? When she runs up the hill, she does the same amount of work as walking, but when she gets to the top, she might be more tired, she might be out of breath, she might be a little bit sweaty.

She clearly feels differently when she's run, so what's the difference? The difference is she's done the same amount of work in less time.

She's done it more quickly, so her body has had to do all those chemical reactions a lot faster than before.

She's transferred the energy at a faster rate, and when she gets to the top of a hill, her body is recovering from that exertion that it made in order that she could cope with doing that.

So let's move on to a different example.

This one is a mechanical crane that's lifting a heavy load 10 metres up into the air.

Again, we can calculate the work that it does, which is the force times the distance it moves that load, and the more powerful crane would lift that same load up, do the same amount of work, but it would lift it more quickly.

In both cases, the pulling force and the distance are exactly the same, so the same work done.

Which statement about those cranes is correct? They're lifting 500 newton pallet of bricks to a height of three metres.

So the weight of the bricks is 500 newtons, they're lifting at three metres.

Does the more powerful crane do more work? Does the more powerful crane lift a heavier load? Or does the more powerful crane do work in less time? Pause the video whilst you think about it and then start again once you're ready.

Okay, how did you get on? The correct answer is that the more powerful crane does the same amount of work but in less time.

Does the same amount of work, 'cause it's lifting exactly the same load of bricks by the same distance, but it's doing it more quickly.

Right, here's a task for you to have a go at.

Andeep, Sam and Jacob each carry a 50 newton bag of potatoes up the same three flights of stairs.

And it's got a list of the different times that they took to do that.

What I'd like you to do is to state who you think does the most work on the potatoes and explain your answer.

And then secondly, state who used the most power to carry the potatoes up the stairs and explain your answer.

Which of those three boys was the most powerful in this instance? Pause the video as you do that, and then start again once you're ready.

Okay, so let's have a look at some answers.

The first part of that question was to state who you think does the most work out of these three boys on lifting a sack of potatoes up the same flight of stairs? Now the answer, correct answer is they all did exactly the same amount of work, because they all lifted the same weight of potatoes the same distance.

So work done in each case was the weight of the potatoes, the force times by the height of the stairs, which was the distance they've moved it in the direction of the force.

Who the most powerful person was in this instance is different.

Power is a measure of how quickly the work is done.

So the person who did the work the most quickly in this case was Andeep, and he was the most powerful because he did the same amount of work as the others, but he did it much, much more quickly.

So well done if you got those answers.

In this part of the lesson, I'm going to put those ideas together and come up with a very clear definition of what we mean when we're talking about power in physics.

The word power can mean a lot of different things in everyday speech, for example, we often say that somebody who is very strong is powerful, and the government in charge is in power.

And if somebody's got a special ability, we often say they've got the power to do something, for example, the power to fly.

And in maths when we talk about powers, we talk about how many times you multiply a number by itself.

So five to the power of three, for example, is five times five times five.

Now in physics, power's also got a very particular meaning, and it's defined as the rate at which we do work.

In other words, it's the amount of work done per second, or the amount of the number of joules of work done each second.

And it's measured in units called watts.

So what we're talking about here is that one watt is one joule of work done in one second.

And if we've got a power of eight watts, we're doing eight joules of work each second.

And if we've got a power of 27.

2 watts, we're doing 27.

2 joules per second and so on.

Have a look at this question.

Which of these three choices is not a correct unit for power? Just pause the video whilst you think about that, and start again when you're ready.

Okay, how did you get on? The correct answer is joules, because joules per second and watts are both units for power.

So well done if you chose joules as the odd one out.

In this example, 20 joules of work is done picking a heavy book off the floor and putting it onto a shelf.

Now, if that work is done in two seconds, what's the power needed to lift it? Well, we've got 20 joules in two seconds, so that comes out as 10 joules each second for two seconds, adding up to 20 joules in total.

So we've got the power of 10 joules per second or 10 watts.

What happens if we do twice the amount of work in the same amount of time? Now, if we're doing twice the amount of work in the same time, we're doing twice as much work each second, so the power is going to be twice as big.

And if we were to do three times the work in the same time, we do three times the work each second, the power would be three times bigger.

In other words, the power is directly proportional to the amount of work done.

Okay, have a look at this question.

How much power is needed to lift a 300 newton sack of potatoes 1.

2 metres in two seconds compared to the power needed to lift 100 newton sack of potatoes the same distance in the same time? Just pause the video whilst you think about your answer and start again once you're ready.

Okay, so how did you get on? The only difference between the potatoes was the weight.

The first bag was three times the weight of the second, so three times the amount of work was done lifting it, and the time was the same, so it needed three times the power.

So the correct answer was C.

Well done if you got that.

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

It takes four times as much work to move two identical crates twice as far as one crate is moved.

If it takes twice as long to move them that distance, how much more power is needed? You're gonna need to think carefully about your answer, and once you've got your answer, I'd like you to explain it.

Just pause the video whilst you're doing that and start again once you've got your answer and your explanation ready.

Okay, so how did you get on? The correct answer was twice the power, but why is it twice the power? It takes a little bit of careful reading of the question in order to explain your thinking.

Let's start with the first part.

It takes four times as much work to move the two identical crates twice as far as one crate.

So four times the work means four times the amount of power.

But it takes twice as long to move them, so though we've got four times the amount of power, we then need to half that because it took twice as long to move them.

So half of four times longer is just twice the power.

So well done if you've got that answer.

In this part of lesson, I'm going to put those ideas together into a simple equation that we can use to calculate power.

What we've already found out is that power is directly proportional to the amount of work done, and it's inversely proportional to the amount of time taken to do the work.

And we can put that together into this equation, power equals work done divided by time.

Now, if we just take a few moments to think about that, if we double the amount of work on the right hand side, then we also double the amount of power, which is right.

And because you've got to divide by time on the right hand side, if we double the amount of time, we would half the amount of power, which again is correct with our relationships.

So that equation seems to work.

Power is given the symbol capital P, work done is measured in joules.

It's a type of energy, so we give it symbol capital E for energy, and we divide that by lowercase t for time.

Power is measured in watts, work done in joules, and time as always is measured in seconds.

Let's look at an example.

When Lucas drives his wheelchair up a ramp, 800 joules of work is done in five seconds.

What's the power of his chair? Give your answer to two significant figures.

So let's start with the equation that links power, work done and time, and that's this one.

Then we put in the values that we know, so the work done was 800 joules, divided by five seconds, and then the answer is 160 watts, and that's already to two significant figures, so we can leave it as it is.

Okay, here's a second example for you to have a go at.

Just pause the video whilst you do that, and don't forget to write all your working out.

Start the video again once you're ready.

Okay, so how did you get on? Let's start with the equation again, power is work divided by time.

Izzy did 15,000 joules of work in eight seconds, so put those values in.

Then we can do the maths.

The answer's 1,875, but we were asked for that up to two significant figures.

So Izzy's power was 1,900 watts, 1,900 watts to two significant figures.

Here's another example.

Sam drives a go-cart round a racetrack in 47 seconds, and the go-carts got a power of 3,200 watts.

How much work to two significant figures does the go-cart do, measured kilojoules? Well, we've got a power, we've got work done that we need, and we've got a time, but they're not in the right order.

So let's just pop down the equation first, then we can pop in the values that we know.

So we've got the power and we've got the time.

If we multiply both sides by 47, we can get rid of the divide by 47 on the right and we get this.

We can do the maths and we get 150,400 joules.

But we were asked that in kilojoules, so that would in kilojoules be 150.

4 kilojoules, but that rounds down to two significant figures to 150 kilojoules.

Okay, so here's an example for you to have a go at.

See how you get on.

Pause the video whilst you try this one, and then turn it on again once you've finished.

So how did you get on? Let's start with the equation power is work divided by time again, and then pop in what we know.

Now, this time the unknown is time, and it's a divide by time and that's a bit awkward.

So let's get rid of that first of all by timesing both sides by the time, and we get time is 2,900 watts equals 135,000 joules.

Notice we've changed the 135 kilojoules to 135,000 joules because the units need to be in joules for this equation.

Next step is to divide both sides by 2,900, and we get time on its own this time.

We can do the maths, and the answer to two significant figures is 47 seconds.

So very well done if you got the right answer there.

When there's a lot of power, it's often simpler to use kilowatts rather than watts.

It's simply because we get smaller numbers.

There's 1000 watts in each kilowatt, and in 43,000 watts, we have 43 kilowatts.

So essentially we've replaced the word a thousand for kilo, and got rid of all the zeros.

So 262,300 watts would be equal to 262.

3 kilowatts.

I've got this question.

How many kilowatts in 370,000 watts? Just pause the video whilst you have a go, and start again once you're ready.

Okay, how did you get on? 370,000 watts is 370 kilowatts, so well done if you've got that answer.

I'd now like you to have a go at these calculations to practise what you've just been learning, and don't forget to show all of your working out.

Just pause the video whilst you do that, and start again once you've got all of your answers.

Okay, how did you get on? Here's all the answers.

The first one's fairly straightforward, it's 20 watts.

In the second one, again, just putting the values into the equation.

Power is work done divided by time, but this time we've got to change the 500 kilojoules into 500,000 joules to get the correct answer, which is 40 watts.

The other questions are a little bit more awkward.

Question three, the work needs 19,200 joules.

And in question four, the work needs 72,000 joules or 72 kilo joules.

And the final question and the last answer is just 20 seconds.

So well done if you got all of those right, and if there's any you weren't sure about, perhaps go back and look at some of the examples from earlier in the lesson and then try them again.

Well, that's the end of the lesson, and here's a quick summary of the main points that we've covered.

Power is the rate at which work is done.

It's equal to the amount of work done each second.

And we can calculate it using the equation power is work done divided by time.

And power is measured in watts, work done is measured in joules, and time is measured in seconds.

And sometimes if we need to, have got very large numbers for power, we measure it in kilowatts rather than watts, and one kilowatt is equal to 1000 watts.

So well done for reaching the end of the lesson.

I hope to see you next time.

Bye-bye.