Hello and welcome to this lesson about efficiency and calculating efficiency from the physics unit 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 keywords that we're going to come across in the lesson.

Dissipate is about when energy spreads out and moves into the surroundings.

These are the keywords 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, I'm gonna start off by investigating the efficiency of bouncing balls in order to understand what we mean by efficiency.

And 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's 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's dissipated as it moves through the air and causes the air particles to move more quickly.

Some energy's dissipated when the ball hits the floor and squashes on impact and some energy's 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 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 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's 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 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 a metre ruler here rather than a 30-centimeter ruler.

And the issue we've got here with a 30-centimeter 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 measuring 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 passes 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 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 that 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 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 a 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 test drop for each measurement.

Repeat each measurement two or three times to check for any anonymous 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 or 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 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 can 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.

So as we've talked about, efficiency's the 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've 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 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 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 the 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.

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 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 of your 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 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 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 equal to 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 is measured in watts.

And because we'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 of 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 they're in the same units, the units will cancel out and 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 whilst 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, John 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 store 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.

We 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 kilowatt joules 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 asked for the answer 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 got most of those right? Well done for making it to the end of the lesson.

Here's a quick summary of the things you should have learned during it.

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

And friction can cause energy to dissipate into the surroundings by heating, so it can make things less efficient.

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

The useful energy we get out divided by the total energy we've put in or how much of that total energy is useful.

Energy transfers are measured in joules and efficiency has got no unit.

Now, because power is the amount of energy transferred each second, efficiency is also equal to the useful power output divided by the total power input where power is measured in watts and again, efficiency has got no unit.

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

I do hope to see you next time.

Goodbye.