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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 would you calculate what power is equal to.

So these are the key words 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 in watts or in kilowatts, with one kilowatt being equal to 1,000 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 easily calculate values for power.

So let's make a start with that.

So let's start with an example, and in this example Sophie'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 is 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, and this time Sophie'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 her 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 pushing more force and effort into that movement, and it's true that when you are running you do push off with a bigger force.

But when you are 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 Sophie'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 it three metres.

Does the more powerful crane do more work? Does the more powerful crane lift the heavier load? Or does the more powerful crane do work in less time? Pause the video as 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 because it's lifting exactly the same load of bricks by the same distance, but it's doing it more quickly.

(mouse clicks) 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 uses 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 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 we're gonna 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 three, for example, is five times five times five.

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

In other words, it's the amount of work done per second or the amount or 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 a 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 while 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.

And now, I'd 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 has 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 we've got four times the amount of power; we then need to halve 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 the lesson I'm going to put those ideas together into a simple equation that we can use to calculate power.

So we now know that power is directly proportional to the amount of work done and is inversely proportional to the amount of time taken to do that work.

And we can put those ideas together into this equation, power is work done divided by the time taken.

And if we take a few moments to think about that, if we double the amount of work on the right hand side, then we double the amount of power.

And because it's divided by time, if we double the amount of time, then we halve the amount of power.

So that equation gives us the relationships that we've seen work.

In symbols power is P, work done is W, divided by t for time, lowercase t.

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

Let's have a look at an example.

When Lucas drives his wheelchair up a ramp, 400 joules of work is done in two seconds.

What's the power of his chair? So start with the equation, power is work divided by time.

He does, well, his wheelchair does 400 joules of work in two seconds.

So 400 divided by two, that gives us a power of 200 watts, so that's the right answer.

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

Just pause the video whilst you have a go, and then start again once you've got your answer, and don't forget to show your working out.

Okay, how did you get on? So, Izzy runs a race, she did 20,000 joules of work in eight seconds.

What was her power during the race? So power is work divided by time, always start with the equation.

That is equal to 20,000 joules of work divided by eight seconds.

You can do that on your calculator if you wish, and the correct answer will be 2,500 watts.

So well done if you got 2,500 watts for your answer.

Here's another example.

Sam drives a go-cart round the racetrack in 50 seconds.

The go-cart's got a power of 3,000 watts.

How many kilojoules of work does the go-cart do? Well, as for work done, we've got a power and a time, and the equation that's got those three in is power is work divided by time.

Now, what we can do first of all is to put in the values that we already know.

And when we do that, we've got power is 3,000 watts is work divided by 50.

But we want to calculate what the work is so we want that on its own.

So to get rid of the divide by 50, we multiply both sides by 50 and we end up with 3,000 times 50 equals the work done.

If we do the calculation we get 150,000 joules.

But if you remember, we were asked to give our answer in kilojoules, so 150,000 joules is simply 150 kilojoules, so that's the right answer.

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

Just pause the video whilst you do that, and then turn back on once you're ready.

Okay, so how did you get on? Sophia drives her go-cart around the track in 45 seconds, and her go-cart's got a power of 3,200 watts.

Again, how many kilojoules of work does the go-cart do? Well, start with the equation power is work divided by time, put in the values that you know, and then this time we've gotta divide by 45 on the right hand side.

So if we multiply both sides by 45 we can get rid of that, and then do the sums, we end up with work done is 144,000 joules or 144 kilojoules.

If you've got the right answer with all the working out, very well done.

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 1,000 watts in each kilowatt, and in 4,300 watts we have 43 kilowatts.

So, essentially, we've replaced the word 1,000 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 are ready.

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

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

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

Okay, how did you get on? Here are the answers.

The first few questions are fairly straightforward.

Question one is six watts, question two is 20 watts.

In question three you've got to remember to change 500 kilojoules into 500,000 joules before you put it into the equation, and then the answer is 40 watts.

For question four, it's a little bit more challenging because you've got to find the work done, and that is 19,200 joules.

Adding kilojoules for question five, that is 19.

2 kilojoules.

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

And if you've got any that you weren't sure about, perhaps have a look back at the previous examples that we showed you, and then have another go at these ones.

Well, that's the end of the lesson.

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 work it out using the equation power equals work done divided by time, where power is measured in watts, work done is measured in joules, and time is measured in seconds.

And then, sometimes, to get simpler numbers, we use kilowatts instead of watts to measure power, and one kilowatt is equal to 1,000 watts.

So that's it, that's the end of the lesson.

Well done for getting this far.

See you next time, bye-bye.