# Understand Kinetic Energy

In this worksheet, students will learn how to use the kinetic energy equation as well as deepen their understanding of kinetic energy.

### QUESTION 1 of 10

What would you rather be hit by - a speeding feather or a speeding train?

It’s the feather, right? But why?  We will be looking at kinetic energy in this activity and by the end of it, you should be able to use the equation for kinetic energy. Let’s get stuck in!

As you should already know, kinetic energy is how moving things store their energy. There are a few things that affect this and we will be using the idea of the feather and the train to try and understand the factors that affect kinetic energy.

Why would you rather be hit by a feather? Most of you will say because it’s light, right? This is true, the mass of the object will affect how much kinetic energy it has. The more massive an object, the more energy it will have.  Let’s make a note of this:

Energy (E) ∝ mass (m)

That fancy sign in the above equation (∝)  literally means 'will affect' (we call it ‘proportional’). So, all we are saying is that if we change the mass, we also change the energy.

Let’s change the situation a little bit now. The train is moving at 0.01 m/s and the feather is moving at 1,000 m/s. Which one would you rather be hit by now? Did you say the train? That’s because speed (or velocity) also has an effect on the kinetic energy. Let’s add this to our proportionality equation:

Energy (E) ∝ mass (m) x velocity (v)

However, it isn’t as simple that…scientists found that the mass doesn’t make as much difference as the velocity. In fact, the mass needs to be halved. They also found that the velocity makes a big difference to the amount of energy. They found that the velocity squared gives us energy.

So how do you use this equation? Simple! Let’s go through an example together.

Jim runs at 3 m/s and has a mass of 60 kg. What is Jim’s kinetic energy?

Step 1  Find the values in the question and highlight them:

Jim runs at 3 m/s and has a mass of 60 kg. What is Jim’s kinetic energy?

Step 2  Write out the values next to their symbols:

mass = 60 kg

velocity = 3 m/s

Step 3  Halve the mass and square the speed:

m = 30 kg

v = 9 m/s

Step 4  Put these into the equation:

E = 30 x 9

Step 5  Put these into your calculator and press =

E = 270 J

Don’t forget the unit of energy is the joule (J).

Now it's time to have a go at some questions.

What unit is used for energy?

A frog has a mass of 0.5 kg and is able to jump at a speed of 2.5 m/s.

Calculate the kinetic energy of the frog.

Amy is riding a motorbike on the motorway at 30 m/s. Both her mass and the motorbike's mass combined come to 300 kg.

Calculate her kinetic energy.

A cricket ball has a mass of 0.1 kg and can travel at a speed of 30 m/s. It takes 40 joules of energy to break the windows of a nearby house.

Does the cricket ball have enough energy to break these windows?

Yes

No

A train has a mass of 1000 kg and can travel at a speed of up to 55 m/s.

Calculate the kinetic energy of the train.

Yes

No

When driving his Mercedes on the Silverstone circuit, Lewis Hamilton reached speeds of up to 90 m/s in a car that weighs only 733 kg.

Calculate his kinetic energy at top speed.

Yes

No

A car has a mass of 1200 kg and is travelling at 20 m/s.

Calculate its kinetic energy.

Yes

No

A tennis ball hit by Andy Murray can travel at 46 m/s. A tennis ball has a mass of 0.06 kg.

Calculate the kinetic energy of the tennis ball when served by Andy Murray.

Which of these has more kinetic energy?

A dog running at 1.2 m/s with a mass of 3.2 kg.

A dog running at 3.2 m/s with a mass of 1.2 kg.

Dog one

Dog two

An airplane has a cruising altitude of 13 km and a speed of 250 m/s. A fully laden Airbus A380 has a maximum mass of 560,000 kg.

What is its kinetic energy just after takeoff?

• Question 1

What unit is used for energy?

joule
joules
J
EDDIE SAYS
Named after the scientist who first defined it, the unit of energy is called the joule. You could also have written it simply as a 'J' as they are both used to represent the unit of energy. In equations, we tend to use the J instead of writing the whole thing out.
• Question 2

A frog has a mass of 0.5 kg and is able to jump at a speed of 2.5 m/s.

Calculate the kinetic energy of the frog.

EDDIE SAYS
Here we go again! Step 1 Highlight all of the numbers. Step 2 Write out the numbers next to their symbols: m = 0.5 kg v = 2.5 m/s Step 3 Do the maths using your calculator: E = (0.5 x 0.5) x 2.5² E = 0.25 x 6.25 E = 1.5625 J E = 1.6 J Here we round the answer to the same number of significant figures as in the question - and there you have it!
• Question 3

Amy is riding a motorbike on the motorway at 30 m/s. Both her mass and the motorbike's mass combined come to 300 kg.

Calculate her kinetic energy.

EDDIE SAYS
How did you get on with this one? Did you remember the all-important equation?! E = ½mv² Step 1 Highlight all of the numbers. Step 2 Write out the numbers next to their symbols: m = 300 kg v = 30 m/s Step 3 Do the maths using your calculator (we have done it in steps here - first of all halve the mass and then square the velocity). E = (0.5 x 300) x 30² (Then we just multiply those two together) E = 150 x 900 E = 135,000 J
• Question 4

A cricket ball has a mass of 0.1 kg and can travel at a speed of 30 m/s. It takes 40 joules of energy to break the windows of a nearby house.

Does the cricket ball have enough energy to break these windows?

Yes
EDDIE SAYS
So, for this question, we just need to work out the total amount of energy and see if it is higher than the threshold energy needed to break the windows. Step 1 Highlight all the numbers. Step 2 Write out the numbers next to their symbols: m = 0.1 kg v = 30 m/s Step 3 Do the maths using your calculator: E = (0.5 x 0.1) x 30² E = 0.05 x 900 E = 45 J 45 is above 40, so it has enough energy to break the windows.
• Question 5

A train has a mass of 1000 kg and can travel at a speed of up to 55 m/s.

Calculate the kinetic energy of the train.

EDDIE SAYS
Are you getting the hang of these yet? The key is to remember the equation: E = ½mv² Step 1 Highlight all of the numbers. Step 2 Write out the numbers next to their symbols: m = 1000 kg v = 55 m/s Step 3 Do the maths using your calculator: E=(0.5 x 1000) x 55² E = 500 x 3025 E = 1,512,500 J
• Question 6

When driving his Mercedes on the Silverstone circuit, Lewis Hamilton reached speeds of up to 90 m/s in a car that weighs only 733 kg.

Calculate his kinetic energy at top speed.

EDDIE SAYS
Step 1 Highlight all of the numbers. Step 2 Write out the numbers next to their symbols: m = 733 kg v = 90 m/s Step 3 Do the maths using your calculator: E = (0.5 x 733) x 90² E = 366.5 x 8100 E = 2,968,650 J
• Question 7

A car has a mass of 1200 kg and is travelling at 20 m/s.

Calculate its kinetic energy.

EDDIE SAYS
Step 1 Highlight all of the numbers. Step 2 Write out the numbers next to their symbols: m = 1200 kg v = 20 m/s Step 3 Do the maths using your calculator: E = (0.5 x 1200) x 20² E = 600 x 400 E = 240,000 J Remember the units - they can gain or lose you the marks!
• Question 8

A tennis ball hit by Andy Murray can travel at 46 m/s. A tennis ball has a mass of 0.06 kg.

Calculate the kinetic energy of the tennis ball when served by Andy Murray.

1.9 J
1.9
EDDIE SAYS
When we say round your answer to 2 significant figures, what we mean is 2 numbers. So 1.9044 rounded to 2 numbers is 1.9. Let's look at it one step at a time: Step 1 Highlight all of the numbers. Step 2 Write out the numbers next to their symbols: m = 0.06 kg v = 46 m/s Step 3 Do the maths using your calculator: E = (0.5 x 0.06) x 46² E = 0.03 x 2116 E = 1.9044 J Rounded to 2 significant figures makes the answer: 1.9 J Remember - words in bold will get you the marks in the exam.
• Question 9

Which of these has more kinetic energy?

A dog running at 1.2 m/s with a mass of 3.2 kg.

A dog running at 3.2 m/s with a mass of 1.2 kg.

Dog two
EDDIE SAYS
For this question, there are two ways you could answer it: 1 Do the maths, work it all out and be confident of your answer. The issue is that in an exam, you might not have the time to do this. 2 Look at the numbers and see which ones will affect the total more. We know that mass is halved, so this will not have very much of an effect on the final number. We also know that velocity is squared, so this will have a huge effect on the final number. So the one with the bigger velocity must be the answer. Simple comparisons like this can get you out of a tight spot in an exam and save you valuable time.
• Question 10

An airplane has a cruising altitude of 13 km and a speed of 250 m/s. A fully laden Airbus A380 has a maximum mass of 560,000 kg.

What is its kinetic energy just after takeoff?

17,500 MJ
17 500 MJ
17500 MJ
EDDIE SAYS
Were you fooled by the red herring here? The cruising altitude was not relevant in any way to this question, so you could ignore it. When we say mega, we mean millions of - it's a scientist's way of writing millions. For example, you could say "he won 17 mega pounds on the lottery" - this just means 17 million pounds. The shorthand way of writing mega is with a capital M so megajoules is written MJ. So, if you have worked out the answer, you should have got 17,500,000,000 or 1.75 x 1010 If you then take away 1 million from this (6 zeros) you are left with 17,500 or 1.7 x 104 Well done for completing this activity. Are you feeling more confident with using this important equation now?
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