 # Applying Kinetic Energy

In this worksheet, students will develop their knowledge of how to use the kinetic energy equation in more complex problems. Key stage:  KS 4

Curriculum topic:   Energy, Movement and Interactions, Explaining Motion, Conservation of Energy

Difficulty level:   ### QUESTION 1 of 10

What would you rather be hit with, 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 what the factors that affect kinetic energy are.

Why would you rather be hit by a feather? Is it 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. This seems simple, right? 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. This means in our example if we change the mass, we also change the energy.

Let’s change up 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 to get our equation - the equation must look 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 underline 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 mas 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)!

What is the unit of energy?

A car has a mass of 1200 kg and is traveling at 20 m/s. Calculate its kinetic energy and include the units in your answer. A tennis ball when hit by Andy Murray can travel at 46 m/s. Calculate the kinetic energy of the tennis ball when served by Andy Murray. A tennis ball has a mass of 0.06 kg. Round your answer to 2 significant figures Which of these objects 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 1

Dog 2

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's its kinetic energy just after takeoff? Give your answer in megajoules.

A London tube car has a mass of 200,000 kg and a full train is made of 8 cars. The train will travel at an average of 18 m/s on the line. What is the average kinetic energy if the train does not have any people on it? Give your answer in MJ

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

A lift says it has a maximum capacity of 12 persons and can travel at 14 m/s. If the lift is half full, what is the kinetic energy of the lift?

A person has a mass of approximately 75 kg.

The lift has a mass of 250 kg.

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.

When driving on the motorway, what will have a bigger impact on your braking distance? Use your knowledge 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 is the unit of energy?

Joule
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 the J instead of writing the whole thing out.
• Question 2

A car has a mass of 1200 kg and is traveling at 20 m/s. Calculate its kinetic energy and include the units in your answer. 240000J
240000 J
240,000J
240,000 J
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 (302) E = 600 x 400 E = 120,000 J Remember - look for the words in BOLD, they will get you marks!
• Question 3

A tennis ball when hit by Andy Murray can travel at 46 m/s. Calculate the kinetic energy of the tennis ball when served by Andy Murray. A tennis ball has a mass of 0.06 kg. Round your answer to 2 significant figures 1.9
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 objects 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 2
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's its kinetic energy just after takeoff? Give your answer in megajoules.

17500
17,500
EDDIE SAYS
When we say mega, we mean millions of, 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 if you have worked out the answer, you should have got 17,500,000,000 or 1.75 x 108. If you then take away 1 million from this (6 zeros) you are left with 17,500 or 1.7 x 103 You should have come across this idea in maths.
• Question 6

A London tube car has a mass of 200,000 kg and a full train is made of 8 cars. The train will travel at an average of 18 m/s on the line. What is the average kinetic energy if the train does not have any people on it? Give your answer in MJ

259.2
EDDIE SAYS
There are two things to consider here. The first is that there are 8 train cars and each car has a mass of 200,000. The first thing you should have done in 200,000 x 8 = 1,600,000 kg. This is the mass. Then you put this into the equation like normal: 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 6 0's, but this presents us with a problem. Here, we only have 5 0's. A better way to think about this is to move the decimal point 6 places to the right. This is how we end up with 259.2 with the .2 at the end.
• 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. Calculate the number of rounds needed to break the target. Each round has a mass of 0.032 kg.

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 these sort of questions. You should have got your energy to be 230.4 J This should have given you a number of rounds to be 2.17. That means that the answer you wrote should have been 3.
• Question 8

A lift says it has a maximum capacity of 12 persons and can travel at 14 m/s. If the lift is half full, what is the kinetic energy of the lift?

A person has a mass of approximately 75 kg.

The lift has a mass of 250 kg.

68,600
68600
EDDIE SAYS
A number of things you have to do 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 put it into the equation time: 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.

56.25
EDDIE SAYS
For this question, 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 12,00 and you get your answer: 56.25 m.
• Question 10

When driving on the motorway, what will have a bigger impact on your braking distance? Use your knowledge from the last question to answer this one and assume that all brakes will take out the same amount of energy.

Velocity
EDDIE SAYS
This one should be obvious by this point. We've spent 9 questions squaring the velocity and halving the mass. This means that velocity has a much bigger effect on the kinetic energy of an object, and, therefore, how long it takes a car to brake on the motorway.
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