# Apply Ideas of Gravitational Energy

In this worksheet, students will study how gravitational energy interacts with kinetic energy and how to calculate gravitational energy.

### QUESTION 1 of 10

You need to have a good understanding of kinetic energy before you try this worksheet. If you haven't already, take a look at one of our activities on the subject.

A small gust of wind hits your face as you slowly start to ascend the lift vertically, adrenaline rushing through your veins at the prospect of falling down the drop on the other side of the roller coaster. After what feels like an age of going up, you suddenly stop – nothing in front of you but thin air, and excitement. The car you are riding in is suspended above the trees and you can see the rest of the theme park stretching out below you. You feel powerful, and then suddenly all of that power is drained from you as you plummet towards the ground – gravity pulling you harder and harder. Just in time, the track hurtles you upwards and through the rest of the roller coaster.

This is the best example of kinetic and gravitational energy there is. Roller coasters are all about just falling, and the best way to do that is to put you up high and let you fall. But have you ever thought about it from a scientific point of view? That’s what we are going to do here. We will be looking at gravitational energy, its equation and how it is linked to kinetic energy.

As you should know by now, gravitational energy is the name we give to the store of energy things gain as they do work against gravity. This means that something will gain energy when you move it upwards and lose energy when it falls back down.

Think about how you would move something up -what types of energy would you need to put into it to get it to move up?

If you said kinetic energy, you would be correct! Kinetic energy and gravitational energy have a ‘special relationship’ where kinetic energy needs to be used to give something gravitational energy. The reverse is also true -if something loses gravitational energy, then it will gain kinetic! Now, because the world isn’t perfect, some of the energy lost from gravitational energy becomes wasted as heat from friction – but it’s a pretty good estimate! All you need to remember is that there is no such thing as a perfect system and some energy will be lost through friction wherever two objects touch. This is a favourite question of examiners – they love asking where the energy went – it is always lost as heat through friction.

So, what things will affect how much gravitational energy there is? Well, think of the things that will make it harder to lift an object up, there are three of them (two are obvious and one is a bit stranger).

1  The mass of the object. Okay – so this should make sense, the more massive the object, the harder it is to lift it up. So, that means that energy is proportional to the mass of the object.

Energy (E) ∝ mass (m)

2  The height you lift the object to. You have to use more energy to lift an object higher, so the higher the object travels, the more energy you need to use to lift that object. Let’s put that into our proportionality.

Energy (E) ∝ mass (m) x height (h)

3   Gravity - this is the tricky one. What if you were to lift that object up on the moon? Would it be easier or harder (assuming you have a spacesuit)? It would be easier because gravity is weaker on the moon than it is on Earth. So, the strength of gravity also affects the gravitational energy. If we put this into our equation, we get something that looks like this:

Gravitational energy = mass x gravitational field strength x height

E = mgh

Gravitational field strength will always be told to you in the question.

Now we have the equation, let's go through an example of how to use it:

An object falls a distance and gains 200 J of kinetic energy. Calculate the height the object fell from.

Mass of the object = 5 kg

Gravitational field strength on Earth = 9.8 N/kg

Step one  Find all of the numbers you need and highlight them:

An object falls a distance and gains 200 J of kinetic energy. Calculate the height the object fell from.

Mass of the object = 5 kg

Gravitational field strength on Earth = 9.8 N/kg

Step 2   Write out the symbols with their numbers next to them:

REMEMBER, we said that kinetic energy and gravitational energy are linked, and if you lose one then you will gain the other. So, if we say that we gain kinetic, it has come from gravitational energy - that is 200 J.

E = 200 J

m = 5 kg

g = 9.8 N/kg

h = ?

Step 3  Rearrange the equation to make height the subject:

You do this by dividing by the mass and the gravitational field strength, leaving you with an equation that looks like this:

height = energy ÷ (mass x gravitational field strength)

Step 4  Put the numbers into the equation:

h = 200 ÷ (5 x 9.8)

Step 5  Put the numbers into the calculator and press = Don’t forget the units.

h = 4.08 m

All done, let’s try out some questions!

Match the correct values to their units.

## Column B

Mass (m)
N/kg
Gravitational field strength (g)
J
Height (h)
m
Energy (E)
kg

An elephant falls off a step.

Calculate the energy the elephant has when it hits the ground.

Elephant mass = 6000 kg

Gravitational field strength = 9.8 N/kg

Height = 0.5 m

## Column B

Mass (m)
N/kg
Gravitational field strength (g)
J
Height (h)
m
Energy (E)
kg

You throw a ball up into the air 2.4 m and catch it again. The ball has a mass of 0.03 kg.

What is the total change in gravitational energy the ball has when you catch it again?

A full coffee cup has a mass of 0.6 kg and is 0.45 m from your lips.

Calculate the energy it takes to lift the coffee cup to your lips.

Gravitational field strength 9.8 N/kg

A pen has a mass of 0.02 kg and is placed on a table 1.2 m from the ground.

Calculate the energy the pen is storing.

Gravitational Field strength = 9.8 N/kg

During a ski jump, a skier loses 4,200 J of energy as she falls. This is then converted into 4,152 J of kinetic energy.

Describe what happened to the lost energy.

[2]

A person hits the ground after falling over with an energy of 205 J.

Calculate the mass of the person.

Gravitational field strength = 9.8 N/kg

Height of the person 1.6 m

A person has a mass of 50 kg and is travelling downwards at 8 m/s.

Assuming there is no energy lost to the environment, calculate the height they dropped from.

Gravitational field strength = 9.8 N/kg

A roller coaster drops a height of 10 m and has a mass of 2,000 kg.

If the track gains a total of 1,000 J of energy as heat, how much kinetic energy does the car have at the bottom of the track?

Gravitational field strength = 9.8 N/kg

An object falls a distance of 2.3 m and gains kinetic energy of 328 J.

Calculate the mass of the object.

Gravitational field strength = 9.81 N/kg

• Question 1

Match the correct values to their units.

## Column B

Mass (m)
kg
Gravitational field strength (g)
N/kg
Height (h)
m
Energy (E)
J
EDDIE SAYS
It is really important to know your units - whether in maths or science. The equation will be given (most of the time) and then all you have to do is match the numbers to their correct place in the equation. Learn these and you'll be halfway there when it comes to these two mark questions in the exam.
• Question 2

An elephant falls off a step.

Calculate the energy the elephant has when it hits the ground.

Elephant mass = 6000 kg

Gravitational field strength = 9.8 N/kg

Height = 0.5 m

EDDIE SAYS
A simple question to start off with. You just need to find the numbers and put them into the equation correctly. Find m, g and h and you should just be able to multiply them together. E = mgh m = 6000 kg g = 9.8 N/kg h = 0.5 m E = 6000 x 9.8 x 0.5 E = 29400 J
• Question 3

You throw a ball up into the air 2.4 m and catch it again. The ball has a mass of 0.03 kg.

What is the total change in gravitational energy the ball has when you catch it again?

0
EDDIE SAYS
This is a mean trick question. The ball gains energy when you throw it up, but (assuming your hands are in the same position as when you threw it) the ball will lose the same amount of energy when you catch it again. This means that the total change in energy is going to be zero, as it has lost the same amount of energy as it has gained. A mean question - but you could have worked out that there was something wrong with it because some information was missing - the gravitational field strength was missing! This is the same in an exam, if there is information missing, then you need to look out for the trick in the question.
• Question 4

A full coffee cup has a mass of 0.6 kg and is 0.45 m from your lips.

Calculate the energy it takes to lift the coffee cup to your lips.

Gravitational field strength 9.8 N/kg

2.6 J
2.6
EDDIE SAYS
Hopefully, by this point, you are looking out for things in bold in the question. Did you notice that it said round to 1 decimal place, and not 1 significant figure? They can and will use both of these terms in the exam - so know them both and how they are different. E = mgh E = 0.6 x 9.8 x 0.45 E = 2.646 J E = 2.6 J
• Question 5

A pen has a mass of 0.02 kg and is placed on a table 1.2 m from the ground.

Calculate the energy the pen is storing.

Gravitational Field strength = 9.8 N/kg

0.24 J
0.24
EDDIE SAYS
In this question, it was all about the rounding. Firstly, solve the equation: 0.02 x 9.8 x 1.2 = 0.2352 Remember, 2 significant figures means two numbers that are not 0. In this case, the answer was 0.2352 but because the third number is on or above 5, we round it up and get 0.24 J.
• Question 6

During a ski jump, a skier loses 4,200 J of energy as she falls. This is then converted into 4,152 J of kinetic energy.

Describe what happened to the lost energy.

[2]

EDDIE SAYS
As we all know by now, whenever you have energy transfers, there will be energy loss if you have a system that involves a moving object. The energy loss is always as heat. This would have got you the first mark. The second mark then comes from saying where that energy loss comes from. This is friction (or contact) between the skis and the snow, or even air resistance. Any of these would be acceptable. Yes, that right, as you move the air out of the way, you are heating it up - just not very much!
• Question 7

A person hits the ground after falling over with an energy of 205 J.

Calculate the mass of the person.

Gravitational field strength = 9.8 N/kg

Height of the person 1.6 m

13.07 kg
13.07
EDDIE SAYS
Did you remember the equation? Step 1 Rearrange the equation to get m as the subject: m = E ÷ (g x h) Step 2 Put in the numbers: m = 205 ÷ (9.8 x 1.6) m = 13.07 kg Normally you would round to 2 decimal places if there is nothing specifically said in the question.
• Question 8

A person has a mass of 50 kg and is travelling downwards at 8 m/s.

Assuming there is no energy lost to the environment, calculate the height they dropped from.

Gravitational field strength = 9.8 N/kg

EDDIE SAYS
At first glance, this question might look as though it doesn't have enough information for you to be able to answer it. That is because the information is hiding - all you need to do is find it. Step 1 Take a look at what you have been given: E = ? m = 50 kg g = 9.8 N/kg h = ? v = 8 m/s Because we don't have the figure for energy, we can't work out the height - this means we need to work out energy to start off with. Do we have enough data to work out kinetic energy? Yes, yes we do. Step 2 Work out kinetic energy - do you remember the equation: E = ½m x v² E = (0.5 x 50) x (82) E = 1600 Step 3 Now we have energy, let's put that back into our gravitational energy question. 1600 (E) = 50(m) x 9.8 (g) x h Step 4 Rearrange for height: h = E ÷ (m x g) h = 1600 ÷ (50 x 9.8) h = 3.27 m This would be a 4 mark question - if you are sitting the higher paper, then expect to see questions like this. It is less likely to be in the foundation tier, but it might be there!
• Question 9

A roller coaster drops a height of 10 m and has a mass of 2,000 kg.

If the track gains a total of 1,000 J of energy as heat, how much kinetic energy does the car have at the bottom of the track?

Gravitational field strength = 9.8 N/kg

EDDIE SAYS
In this question, you must work out the gravitational energy in the normal way - find the numbers and plug them into the equation. But that's not all! Then you have to do the extra step of taking away the energy lost as heat! So, let's give it a go. E = mgh E = 2000 x 9.8 x 10 E = 196,000 Now take away the energy lost to heat: 196000 - 1000 = 195,000 J
• Question 10

An object falls a distance of 2.3 m and gains kinetic energy of 328 J.

Calculate the mass of the object.

Gravitational field strength = 9.81 N/kg

14.6 kg
14.6
EDDIE SAYS
In this question, you need to rearrange the equation first to make mass the subject. This is fairly simple, you just need to divide by both g and h, giving you an equation that looks like this: m = E ÷ (g x h) Then it's just a case of plugging in the numbers as usual: m = 328 ÷ (9.81 x 2.3) m = 14.55449059 kg Okay, did you notice the part in bold? 2 significant figures, so we need to round our answer. You will notice that the third number is a 5 so we round up. Our answer should be 14.6 kg. Did you remember to include the unit? Another activity completed - great work with all those complicated equations!