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.

In this lesson, you're going to find out about efficiency and what we mean by efficiency, and how to calculate the efficiency of an energy change.

And you're also going to find out about what we mean when we say energy is dissipated into the surroundings.

These are the key words that we're going to use in the lesson.

Dissipate means when energy spreads out into the surroundings.

Efficiency is about how effectively you can use energy to do a job that you want it to do.

And useful output energy transfer is the amount of the energy that you use to do something useful, whereas total input energy transfer is all of the energy that you use in order to do that job in the first place.

These are the definitions of those keywords.

If at any point during the lesson, you feel that you need to come back and have a look at them, just pause the video and come back to this slide and have a look.

In this lesson, we're gonna start by investigating the efficiency of bouncing balls in order to understand clearly what we mean by efficiency.

And then we're going to move on to calculate the efficiency of different energy transfers, and then look at ways in which we can improve the efficiency of those transfers.

Okay, so let's make a start.

Let's start by thinking about what happens when a ball is dropped.

Energy is transferred from the gravitational store into other energy stores.

And some of that energy that's transferred is going to be into stores that are useful, and some of the energy is transferred into stores that are not useful.

We say that that energy is wasted.

And in this instance, we're gonna say that the useful energy is the energy that's transferred back into the gravitational store at the top of its bounce.

So as it falls, some energy is dissipated as it moves through the air and causes the air particles to move more quickly.

Some energy is dissipated when the ball hits the floor and squashes on impact.

And some energy is dissipated when the ball causes particles in the floor to vibrate more quickly.

So in each of these cases, the ball is causing particles somewhere else to vibrate more quickly, and their energy is spread out into the surroundings.

That's what we mean when we say energy is dissipated.

It is spread out into the surroundings.

And in all of those three ways in which energy is dissipated, causing the particles to vibrate more around the ball, the energy is being transferred into a thermal store.

So before the ball was bounced compared to after it was bounced, it starts with more gravitational energy, which was transferred into the thermal store.

But overall, through the whole of the bounce, the total amount of energy is conserved, which is that top bar on each of the bar graphs where we've added the gravitational store, the energy in the gravitational store to the amount of energy in the thermal store, and it stays the same.

Have a go at this question and see what you think.

The amount of energy in the ball remains the same as it bounces.

First of all, is that true or false? Pause the video as you think about it, and start again once you're ready.

Okay, what do you think? Did the amount of energy the ball has remain the same as it bounces? And the correct answer is no, it didn't.

The answer's false.

It is true, the total amount of energy stayed the same, but that's the energy that the ball has and the energy transferred to the surroundings as well.

So which of these two answers here justifies the reason why the answer is false? Just pause the video again, and start again once you're ready.

Okay, again, what do you think? What was the reason why the ball did not keep the same amount of energy all the way through? And the correct answer is that some of its energy is transferred to a thermal store.

It's easy to think that the energy is used up because it's got less, and that's what we can see.

But energy is always transferred somewhere else.

So the total amount of energy has remained the same.

We can measure the efficiency of our ball's bounce using this equation.

Efficiency is the height of the bounce divided by the height of the drop.

In other words, how high did it bounce compared to how high we dropped it from? If it dropped to 1/2 the height, the efficiency's going to be a 1/2 or 50%.

Only 1/2 of the energy is transferred to do something useful.

So in other words, efficiency is the fraction of the energy that the ball started with that was then used or transferred to make the ball bounce back up.

It's the fraction of the total energy that was useful.

And because it's a fraction, efficiency does not have any units.

Have a look at these equations and have a think which two of these equations could be used to calculate the efficiency of a bouncing ball.

Pause the video whilst you have a think, and start again once you're ready.

Okay, so which two equations do you think you can use to measure efficiency? The first one, the height of the bounce divided by the drop because that's the fraction of the height it bounced back to compared to what it was dropped from.

And it's this one at the bottom as well, D, is the energy it's got after the bounce divided by the total energy at the start.

If you think about it, it's the same thing.

It's got that fraction of the gravitational, of energy in the gravitational store, compared to what it had at the start.

So what we're going to do now is we're going to do an investigation to compare the bounce heights of several different balls.

And this is how we're going to do it.

We're going to start by measuring the height the ball bounces to using a ruler.

Now, you might want to use a metre ruler here rather than a 30 centimetre ruler.

And the issue we've got here with a 30 centimetre ruler is that zero is not at the end of the ruler, so to get zero onto the ground is quite challenging.

We're going to measure the height the ball bounces to the bottom of the ball, and that's because when the ball is on the floor, the bottom of the floor will be equal to the zero reading on the ruler.

So we measure the actual height the ball bounces up to.

And it's also easy to look at the ball from the bottom rather than trying, for example, to look at it in the centre, and to get an exact reading on the ruler from that part of the ball.

Now, when we're finishing the bounce of the ball, the ball's going to be moving.

It's going to slow down and stop momentarily at the top, but it's still going to be moving.

So when we're looking at the height the ball bounces to, it's going to be quite difficult.

Now, to improve accuracy, there's a number of things you can do.

And one way is to do a test drop and have a look to see roughly where the ball bounces to, and in that position make a mark.

What I've used here is a piece of masking tape or piece of tape that you can draw on and write on, and I've put a line on there which marks roughly where the ball bounced to.

When I say roughly, I mean to the nearest three or four millimetres perhaps.

And then what we're going to do is we're gonna drop the ball again, we're gonna put our eyes level with the mark.

And as the ball bounces up and stops momentarily at the top of its bounce, we can judge quite easily whether it's passed a little bit higher or a little bit lower than the mark because we're already at the right point.

And then we can get quite an accurate reading, perhaps to the nearest and millimetre if we're careful.

Now, that's okay, but we might still make a mistake.

So we're going to repeat our readings to check we've not made any silly mistakes on the way, we've not got any anomalous results that are wrong, caused by a mistake.

And what we're going to do then is we're going to compare the bounce height of different balls, keeping all of the different control variables the same.

And we're going to change, in other words, just the type of ball.

Everything else needs to be kept the same.

And that will give us a set of valid results that we can actually compare, so we can say it was the type of ball that made the difference, and not, for example, the temperature of the ball or the type of surface it bounced on, and so on.

What I want you to do now is have a think about those different control variables.

Which of these following are control variables that you're going to use in our investigation to compare the bounce height of different balls? Pause the video, and then have a look and tick off all of the ones that you think are control variables, and start the video again once you're ready.

Okay, which do you think the control variables were? The correct answers are the height of drop, the surface we've dropped on and the temperature of the ball.

So well done if you got those right.

Often, people choose option E and think that the same person needs to take the measurements every single time.

Whereas, if you've got the really good method to use, then it just shouldn't matter who takes the measurement.

You should always get the same height each time because the thing that's going to change is the type of ball, not the person measuring.

Okay, so here's your task.

What I'd like you to do is to do that investigation.

Use several different balls and investigate how efficiently each one bounces off the floor.

Control all those control variables that we were talking about just then.

Do a drop test, do a test drop for each measurement.

Repeat each measurement two or three times to check for any anomalous results.

And also calculate the efficiency of the bounce at the end.

And to do that, you can use this equation where the efficiency of the bounce is the height of the bounce divided by the height that you drop the ball from.

Okay, have a go at that investigation.

And when you've got all your results, come back and start the video again.

Right then, hopefully you've got a good set of results from that investigation using several different balls and seeing the height that each one bounces to.

Your results should look something similar to these ones.

The drop height that I used was 120 centimetres, and we've got the bounce heights for tennis ball, golf ball and a rubber ball.

The tennis ball, I've just crossed off one of the results there, which was 51 centimetres bounce height, and that's crossed off because I think it's an anomalous result.

It's very different from the other three.

And then to calculate its mean bounce height, I simply add those three other results together, ignoring the 51 centimetres, and divide the answer by the number of results, which is three.

So the average bounce height I got was 66 centimetres.

You'll also notice that I've rounded that up to the nearest centimetre to get the same accuracies I got for my measurements.

And then the efficiency of the bounce height is going to be 66 centimetres divided by the height I drop it from, 120, which gives me an efficiency of 0.

55.

So that is the fraction of the height I dropped it from that it actually bounced back to.

And now we do the same calculation for the golf ball to get the mean heights, and also the rubber ball, and then to work out the efficiency of each one in turn.

And the results I got was that the golf ball is the most efficient, followed by the rubber ball and the tennis ball, and that was because the golf ball had a higher fraction of the bounce height compared to the height it was dropped from.

More of the energy was transferred to make it bounce higher than was wasted and dissipated into the surroundings.

In this part of the lesson, we're going to look at how we can calculate efficiency in a range of different situations.

So as I've talked about, efficiency's a fraction of the energy supplied to an object or a system that is usefully transferred by it.

And we can calculate it using this equation.

Efficiency is equal to the useful output energy transfer divided by the total input energy transfer, which means, in simpler language, the useful energy we got out divided by all of the energy we put in.

What fraction of the energy we put in did we change into something useful? And the useful output energy transfer is measured in joules, and so is the total input energy transfer.

So when we're calculating efficiency, we've got one measurement, one's energy measured in joules divided by another energy in joules, so the joules, the units cancel out and efficiency itself has got no unit.

Going back to our example of the bouncing ball, we know that the height of the ball is proportional to the amount of energy in the gravitational store.

The higher the ball is, the more energy in the gravitational store.

So this is the amount, the blue columns here are the amount of energy represented in gravitational stores.

And when it bounces back up again, some of the energy has been transferred into the thermal store, but it's dissipated into the thermal store.

And what we've got here on the left is a total input energy transfer, the energy we put into the bouncing ball.

And here, we've got the useful output energy transfer, which is the gravitational energy that the ball has after it's bounced.

Let's have a look at an example.

Aisha does 12,000 joules of work cycling up a hill.

At the top of the hill, she's transferred 9,000 joules into a gravitational store of energy.

What is her efficiency? We start off by writing down the equation.

Now, I've just shortened it a little bit to fit onto the page.

So efficiency is the useful energy that we get out divided by the total energy that she's used.

Substitute the numbers in, 9,000 divided by 12,000, and the answer is 0.

75, 9,000 divided by 12,000, but the joules have cancelled, so there's no units there.

So efficiency's simply 0.

75.

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

Pause the video whilst you have a go, show all of you working out, and start the video again once you're ready.

Okay, how did you get on? Let's start with the equation again.

Efficiency is useful energy divided by total energy.

In this case, the useful energy is the energy of lifting the box up, which is 400 joules, and he used 1,000 joules in total.

If we do the maths, 400 divided by 1,000 is 0.

40.

And again, there's no units because the joules both cancelled out, top and bottom, that equation.

So the efficiency is 0.

40.

Power is the amount of energy transferred each second, which means we can use this equation to calculate efficiency, as well as the energy equation.

Efficiency is equals the useful power output divided by the total power input.

Thinking about this, the useful power output is the energy output each second, and the total power input is the energy input each second.

So we've got the same equation as before, but this time, in terms of power.

Power's measured in watts.

And because you've got power on top and underneath the equation, then they cancel each other out and we have efficiency again with no unit.

If you look at the example of that, in this case, a motor with a power five watts lifting a load, and as the load rises up, it gains three joules of energy each second.

What's the efficiency of the motor? Well, three joules of energy in a second is three watts, so it's got a power gain of three watts.

So in our efficiency equation with power, useful power output over total power input, we have three watts divided by five watts, which gives us 0.

6.

And the units cancel out, so we have no units.

Efficiency is simply equal to 0.

6.

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

Just pause the video whilst you have a go and start again once you've got your answer.

Okay, how did you get on? Let's start with the equation first.

Efficiency is equal to the useful power output divided by the total power input.

In this case, the useful power output is three kilowatts, and the total power input is eight kilowatts.

So we have three kilowatts divided by eight kilowatts.

Now, in this example, we did not convert kilowatts into watts because I knew we were going to be dividing one number by the other.

And as long as we're in the same units, the units will cancel out, we'll get the same answer.

So that works out at 0.

375.

Well done if you got that answer.

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

For each one, show all of your workings out.

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

Okay, how did you get on? Let's have a look at some answers.

In part A, Izzy did 1,200 joules of useful work.

So it's 1,200 joules divided by the total energy put in, which was 4,000 joules, and her efficiency was 0.

3, 1,200 divided by 4,000.

And you'll notice that there's no units for efficiency.

In part B, Jun did 2,500 joules of useful work and used 10,000 kilojoules of energy in total.

So we need to convert the 10 kilojoules into 10,000 joules so we've got the same units on top and bottom.

So 2,500 joules divided by 10,000 gives us an efficiency of 0.

25.

Part C, we've now got an electric motor with a power of 50 kilowatts, and it transfers energy to the gravitational storage at a rate of 32 kilowatts.

So that's 32,000 joules a second.

We can simply use the efficiency calculation, useful power output, which is 32 kilowatts, divided by the total power input, which is 50 kilowatts, and that gives us 0.

64.

Don't forget that you don't need to convert kilowatts into watts because we're dividing, all we need is the same units on the top and the bottom, so we can leave them as kilowatts.

For part D, this time, we've got 500 kilojoules of useful energy in the gravitational store divided by 1,750 kilojoules of work done in total.

So that gives us 0.

2857 for the efficiency.

You're answering to two significant figures.

So the 0.

2857 rounds up to 0.

29.

So well done if you got that right.

And the final question, explain why there's no units for measuring efficiency.

It's because we've got the number of joules on the top or the number of watts on the top, and we're dividing by the number of joules or watts on the bottom as well.

And the units simply cancel out and the units are equal to one.

So there's no units for efficiency.

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

In this part of the lesson, we're going to consider ways in which we can improve efficiency.

And we're going to do that by thinking about ways we can improve the efficiency of pulling this block along the ground.

Just by dragging it is very inefficient because there's a huge amount of friction adding, and all the rubbing of the friction is causing the bottom of the block and the ground to heat up, and energy is being dissipated into the surroundings all the while.

If we add a lubricant, it makes the surface more slippery, and the block slides with less force needed to pull it across the surface.

And that means we need to do less work to drag it a certain distance.

And because we do less work to do the same amount of work on the block, it becomes more efficient.

Another way to improve the efficiency by reducing the force needed to drag it is to add wheels.

Because wheels don't drag along the surface or rub along the surface, they simply roll over the top of it.

And that means that less work is done to move the load up the same distance, and it is, again, more efficient.

However, there is some rubbing between the wheels, the axles of the wheels and the bearings.

And if we were to grease the wheels, that again would reduce the friction and make it even easier to pull the block, and it would make it even more efficient so that less energy would be dissipated into the thermal store.

So just pause for a moment and have a think of this question.

Which of these changes is unlikely, not likely to improve the efficiency for a bicycle going up a hill? Pause the video whilst you think about this, and start again once you're ready.

Okay, how did you get on? Which of these is not likely to improve the efficiency for a bicycle going up a hill? The correct answer is cycling off-road up a steeper track.

All of the other ones are about reducing the amount of friction and making it more efficiency to go up the hill.

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

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

I'd like you to annotate the picture for the few comments around each of the different ways that you can see to improve the efficiency of the moped.

See how many you can find.

Just pause the video as you do that, and start again once you're ready.

Okay, so how did you get on? Let's have a look at some of the answers you might have found.

The first one I've put down here is to add the windshield to reduce the drag to make the moped more streamlined so the air slips around it rather than has to be pushed out of the way.

We could pump the tyres so they roll more easily over the ground.

You could oil the chain so that it slides more easily over the cogs and it makes it easier to turn that back wheel.

And in a similar way, you could put clean oil into the engine.

The engine is full of all sorts of gears which are bathed in oil, and the oil is there to reduce the friction and to enable them to move around more freely.

And finally, we could clean and grease the bearings on the wheels to make the wheels spin around more easily.

So well done if you got most of those, and congratulations if you found any extra ones that I've missed off.

So well done for making it to the end of the lesson.

This is a quick summary of what you should have learned during it.

Efficiency is the fraction of energy supplied to an object or a system that is usefully transferred by it.

And friction can cause energy to dissipate into the surroundings by heating, and that means that the system becomes less efficient.

We can reduce friction by using lubrication, by using bearings or wheels to increase the efficiency.

And we can calculate efficiency in two ways.

We can calculate efficiency as being equal to the useful output energy transfer divided by the total input energy transfer.

The useful energy we get divided by the total energy we've used.

And the energy transfers are both measured in joules, and the efficiency itself has got no unit.

We can also use efficiency is useful power output divided by the total power input where power is measured in watts and efficiency, again, has got no units.

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

I do hope to see you next time, goodbye.