# Apply Kinetic Energy

In this worksheet, students will develop their knowledge of how to use the kinetic energy equation in more complex problems.

### 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'll be looking at kinetic energy in this activity and by the end of it, you should be able to remember and use the equation for kinetic energy to solve complex problems.  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? Is it because it's light? 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 (∝), is called the proportional sign. When something is proportional it means that if one thing goes up, then the other must go up as well. Here, this means 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:

Energy (E) ∝ mass (m) x velocity (v)

All we are saying here is that if we change either the mass or the velocity, then it will affect how much energy there is. If either of them goes up, then the energy will also go up and vice-versa, if they go down.

Unfortunately, it isn’t as simple as all that… scientists have conducted experiments and found that one of these things has a much more significant effect on energy than the other. When we draw graphs of energy against mass and velocity, we find that the mass graph forms a line of about y = ½ x and the velocity graph looks like a y = x2 graph!

This leads us to the equation - we have to halve the mass and square the velocity so the equation looks like this:

Fun fact time! You have to remember this equation - you will not be given in the exam!

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

Jim has a kit bag that has a mass of 5 kg and has just done a sprint at the gym burning 18 calories. He is now walking home from the gym at a speed of 2.3 m/s with his kit bag. What is his kinetic energy? Jim has a mass of 80 kg.

Step 1  Find the values that matter to you in this question and highlight them:

Jim has a kit bag that has a mass of 5 kg and has just done a sprint at the gym burning 18 calories. He is now walking home from the gym at a speed of 2.3 m/s with his kit bag. What is his kinetic energy? Jim has a mass of 80 kg.

Step 2  Write out the values next to their symbols. Remember if there is more than one number, then you might have to add them together. Think of the situation in real life and apply that to the equation:

mass = 80 kg + 5 kg = 85 kg

velocity = 2.3 m/s

Step 3   Halve the mass and square the speed:

m = 42.5 kg

v = 5.29 m/s

Step 4   Put these into the equation:

E = 42.5 x 5.29

Step 5   Put these into your calculator and press =

E = 224.825 J

Step 6   Round the answer to one decimal place or 2 significant figures unless the question specifies otherwise!

E = 224.8 J

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

Now let's have a go at some questions.

What unit is used for energy?

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

Calculate its kinetic energy.

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 3.2m/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?

A London tube carriage has a mass of 200,000 kg and a full train is made of eight carriages. The train will travel at an average speed of 18 m/s on the line.

What is the average kinetic energy if the train does not have any people on it?

A round is shot from a gun at 120 m/s at a target. This target has a break energy of 500 J. Each round has a mass of 0.032 kg.

Calculate the number of rounds needed to break the target.

A lift has a maximum capacity of 12 people and can travel at 14 m/s.

The lift has a mass of 250 kg, and a person has a mass of approximately 75 kg.

If the lift is half full, what is its kinetic energy?

A car's brakes when fully depressed can take 12,000 J of energy out of the car for every metre of breaking distance.

A car on the motorway has a mass of 1,500 kg and is travelling at 30 m/s.

Calculate the distance it takes it to stop once the brakes are depressed.

When driving on the motorway, what will have the bigger impact on your braking distance?

Use what you've learned from the last question to answer this one and assume that all brakes will take out the same amount of energy.

Mass

Velocity

• 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 have said 'joule' or just simply 'J' as they are both used to represent the unit of energy. In equations, however, we tend to use J instead of writing the whole thing out.
• Question 2

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

Calculate its kinetic energy.

EDDIE SAYS
How did you get on? Let's take the process one step at a time: 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
• Question 3

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
1.9 J
EDDIE SAYS
When we say round your answer to 2 significant figures, what we mean is 2 numbers that are not a 0. So 1.9044 rounded to 2 numbers is 1.9, but 0.0026 is 0.0026 (because we ignore the 0's). 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 it: 1.9 J Remember - words in bold get you marks in an exam.
• Question 4

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 3.2m/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 5

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
When we say mega, we mean millions - 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. You should always leave a space between numbers and their unit when writing answers, so you should have written the number, a space and then MJ, for megajoules. 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 one million from this (6 zeros) to turn it into megajoules, you are left with 17,500 or 1.7 x 104 You should have come across this idea in maths - it's known as standard form.
• Question 6

A London tube carriage has a mass of 200,000 kg and a full train is made of eight carriages. The train will travel at an average speed of 18 m/s on the line.

What is the average kinetic energy if the train does not have any people on it?

259.2 MJ
259.2
EDDIE SAYS
There are two things to consider here. The first is that there are eight train carriages and each carriage has a mass of 200,000. The first thing you should have done is: 200,000 x 8 = 1,600,000 kg. This is the mass. Then you put this into the equation as usual: m = 1,600,000 kg v = 18 m/s E = (0.5 x 1,600,000) x 182 E = 800,000 x 324 E = 259,200,000 J This is now the second part - we must convert this into MJ. Remember, just take away six zeros (for one million) but this presents us with a problem. Here, we only have five zeros. A better way to think about this is to move the decimal point six places to the left (in other words, divide the number by one million). This is how we end up with 259.2.
• Question 7

A round is shot from a gun at 120 m/s at a target. This target has a break energy of 500 J. Each round has a mass of 0.032 kg.

Calculate the number of rounds needed to break the target.

3
EDDIE SAYS
So, for this question, you have to work out the energy each round has. Once you have done this, you can divide 500 by the energy you calculated and this will give you the number of rounds. You will ALWAYS have to round up in this sort of question. Hopefully, you halved the mass to get 0.016 kg and squared the speed to get 14400 m/s. Once you multiplied these together, you should have got the energy to be 230.4 J. If you divide 500 by 230.4, you get the answer of 2.17 rounds. That means that the answer you wrote should have been 3.
• Question 8

A lift has a maximum capacity of 12 people and can travel at 14 m/s.

The lift has a mass of 250 kg, and a person has a mass of approximately 75 kg.

If the lift is half full, what is its kinetic energy?

EDDIE SAYS
Are you getting the hang of these now? The key to it is remembering that all-important equation! A number of things have to be done here to the mass before we start our calculations: 1 The lift is half full, so 12 ÷ 2 = 6. 2 Each person weighs 75 kg, so 75 x 6 = 450 kg. 3 The mass of the car is 250 kg, so we need to add that on. That makes the final mass 700 kg. Once we have done that, it is time to put it into the equation: E = (0.5 x 700) x 142 E = 68,600 J
• Question 9

A car's brakes when fully depressed can take 12,000 J of energy out of the car for every metre of breaking distance.

A car on the motorway has a mass of 1,500 kg and is travelling at 30 m/s.

Calculate the distance it takes it to stop once the brakes are depressed.

EDDIE SAYS
There's a lot to do with this one! When you are confronted with a complicated question like this, don't panic but just take it steadily, one step at a time. First of all, you need to work out the amount of energy in the car to begin with. m = 1500 kg v = 30 m/s E = 700 x 900 E = 675,000 J Ok, now we need to work out how far something is going to travel if 12,000 J of energy are taken out every metre. This is simple: you just divide 675,000 by 12,000 and you get your answer: 56.25 m. That wasn't so bad, was it?
• Question 10

When driving on the motorway, what will have the bigger impact on your braking distance?

Use what you've learned from the last question to answer this one and assume that all brakes will take out the same amount of energy.

Velocity
EDDIE SAYS
Hopefully, you found this one easy! You've just completed nine questions where you have squared the velocity and halved the mass. This means that velocity has a much bigger effect on the kinetic energy of an object than the mass does. Therefore, it will have a greater impact on the breaking distance of a car. How do you feel about kinetic energy now? You've had a lot of practice at using the equation but make sure you remember it!! E = ½m x v²
---- OR ----