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.

(mouse clicking) 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 the ball is dropped.

Energy is transferred from the gravitational store into other energy stores, and some of that energy that is 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 starts with more gravitational energy which it 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 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 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 have remained 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 transfer 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 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 is 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 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, a 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 at 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 bounced 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 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 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 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'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 then investigate how efficiently each one bounces off the floor.

Control all those control variables that we were talking about just then, 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 height 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 asset by a 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 means the fraction of the height I dropped it from, that it actually bounced back to.

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

And the results I got with 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 we've talked about, efficiency is 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 the gravitational stores, and when it bounces back up again some of that energy has been transferred into the thermal store, but is 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 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 12000, and the answers 0.

75, 9,000 divided by 12,000, but the jewels have cancelled so there's no units there, so efficiency 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 your workings 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 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 of that equation, so the efficiency is not 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? And the first one is he did 12,000 joules of for work putting books onto a high shelf, and used 4,000 joules of energy in total.

So it's 1,200 joules divided by 4,000, gives an efficiency of no 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 not 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 the first place.

So the answer there is nor 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 1,000s was 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 a high mountain, Andeep transferred 500 kilojoules of energy into the gravitational store and did 1,750 kilojoules of working total.

So this time his efficiency was 500 kilojoules divided by 1,750, which is 0.

2857.

You are asked to give us two significant figures so that is 0.

29, and 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 a number of joules of energy divided by the number of joules of energy, and the joules cancel each other out so there's no jewels 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.

In this part of this I'm 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 and rub along the surface, they simply roll over the top of it.

And that means that less work is done to move the load of 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 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 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 the hill? And 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 efficient 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 undertake the picture, so add a few comments around for 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 while 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 up the tyres so they roll more easily over the ground, you could oil the chain so that it slides more easily over the cox 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 route more freely.

And, finally, we could clean and grease the bearings on the wheels to make the wheel spin round 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 reaching 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 useful transferred by it, and friction within that system can cause energy to dissipate into the surroundings by heating, making it less efficient.

We can reduce friction by using lubrication, bearings, or wheels, all of which increase efficiency.

And we can calculate efficiency by using the equation; efficiency is equal to the useful output energy transfer divided by the total input energy transfer.

In other words, the useful energy we get out is a fraction of all the energy we put in.

The useful output energy transfer is measured in joules and so is the total input energy transfer, and that means that efficiency itself has got no unit.

So once again, well done for reaching the end of the lesson, I do hope to see you next time.

Goodbye.