Hello, and welcome to this lesson about efficiency and calculating efficiency from the physics unit, energy of moving objects.

My name is Mr. Fairhurst.

Okay, so here are the keywords that we're going to use in the lesson.

Dissipate is when energy spreads out into the surroundings and efficiency is about how effectively you can use energy to do the job that you want it to do.

The useful energy transferred by the device is the amount of energy that you use to do the job that you want it to do.

And the total energy supplied to the device is all of the energy that you put into the device in order to do that job in the first place.

Here are the definitions of those key terms. If at any point during the lesson you feel that you need to come back and have a look at these, just pause the video and come back and have a look at this slide again.

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

Then in the second part of the lesson, we're going to move on and calculate efficiency of different energy transfers.

Okay, so let's make a start.

Let's start by thinking about what happens when the 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 has been transferred into a thermal store.

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

But overall through the hole 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 look 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 whilst you think about it and start again once you're ready.

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

It is true that 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's 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 a 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 half the height, the efficiency's going to be a half or 50%, only half 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, it's 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 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 make sure the height of 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 bouncing, 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 going to put our eyes level with the mark and as the ball bounces up and stops momentarily at the top of its bounce, we can just quite easily whether it's bounced a little bit higher or a little bit lower than the mark, because we're ready at the right point and then we can get quite an accurate reading perhaps to the nearest 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 that it was the 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 underside 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 dropped on and the temperature of the ball.

So well done if you've 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 nervous 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 dropped 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 I had to 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 were 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.

As we've talked about before, efficiency is the fraction of the energy supplied to an object or a system that is usefully transferred by it.

And we can calculate efficiency by using this equation.

The useful energy transferred by the device divided by the total energy supplied to the device.

And both the useful energy transferred by the device and the total energy supplied to the device are measured in joules, because they're both amounts of energy.

And when we come to calculate efficiency, we're dividing the number of joules on top by the number of joules on the bottom.

So the number of joules cancel out each time and there's no units left for efficiency.

So efficiency has got no units.

And if you go back and think about our example of the bouncing ball, we know that the height the ball bounces to is proportional to the amount of energy in its gravitational store.

If the ball is higher up, it's got more energy in its gravitational store and we represent the gravitational store by this column here.

And as it bounces, it doesn't bounce that high, so its gravitational store won't have as much energy in it after the bounce, but all of that energy would've been transferred to the thermal store.

It would've been dissipated into the thermal store.

So the total energy supplied to the device is this amount of energy on the left and the useful energy transferred by the device is the amount of energy in the gravitational store 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.

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, 9000 divided by 12,000, but the joules have cancelled so there's no units there.

So efficiency is 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 if you're 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 books up, which is 400 joules and he used 1000 joules in total.

If we do the maths, 400 divided by 1000 0.

40.

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

So the efficiency is 0.

40.

I'd now like you to have a go at all of these calculations.

Don't forget to show all your workings out and just pause the video whilst you do them and start again once you're ready.

Okay, so how did you get on? In the first one, Izzy did 1200 of useful work putting books onto a high shelf and used 4000 joules of energy in total.

So it's 1200 joules divided by 4,000 gives an efficiency of 0.

3.

And don't forget, there are no units for efficiency.

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

So this time you've got to convert 10 kilojoules into 10,000 joules so you've got the same units for both measurements of useful work done.

And the efficiency this time is 0.

25.

For part C, you've got an electric motor using 50 kilojoules of energy and it transfers 32 kilojoules into the gravitational store.

So this time, the useful energy was 32 kilojoules divided by 50 joules of energy that was put in in the first place.

So the answer there is 0.

64.

And you'll notice that we haven't converted the kilojoules into joules, 'cause if we did so we'd have 32,000 divided by 50,000 joules and the thousands would simply cancel out, so there's no need because we're dividing the two energies by each other, there's no need to convert them into joules.

For part D, climbing the high mountain, Andeep transferred 500 kilojoules of energy into the gravitate store and did 1750 kilojoules of work in total.

So this time, his efficiency was 500 kilojoules divided by 1750, which is not 0.

2857.

You're asked to give the answer to two significant figures, so that is 0.

29.

The 0.

285 rounds up to 0.

29.

And then question two, explain why there is no unit for measuring efficiency.

Well, that's because we're calculating the number joules of energy divided by the number of joules of energy and the joules cancel each other out, so there's no joules left over, okay? So the answer if you calculate joules by joules is simply one.

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

So well done to make it to the end of the lesson.

This is a quick summary of the things you should have learned as you've gone through it.

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

And friction can cause energy to dissipate into the surroundings by heating to make something less efficient.

We can calculate efficiency using the equation, efficiency equals useful energy transferred by the device divided by the total energy supplied to the device.

In other words, the useful energy we get out is a fraction of the total energy we've put in to make the change happen.

The useful energy transferred to the device is measured in joules and so is the total energy supplied to the device, but efficiency itself has got no unit.

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

I do hope to see you next time.

Goodbye.