# Analyse Gravitational Energy

In this worksheet, students will use the gravitational energy and kinetic energy equation to solve complex problems. They will also analyse systems where these models can be used.

Key stage:  KS 4

GCSE Boards:   AQA, AQA Trilogy, AQA Synergy, OCR 21st Century, OCR Gateway, Pearson Edexcel

Difficulty level:

### QUESTION 1 of 10

You should have a good understanding of Kinetic energy before you try this worksheet. If you haven't already, take a look at our worksheet on it here (LINK TO WORKSHEET)

Word of warning - to complete this activity, you will need to be confident rearranging complex equations.

A small gust of wind hits your face as you slowly start to ascend the lift hill 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 are stopped suddenly – nothing in front of you but thin air and excitement. The car you are riding is suspended above the trees and you can see the rest of the theme park extending outwards from 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 do you know a decent way to sap the fun out of everything? Looking at 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. This will involve looking at multi-staged equations and solving for multiple unknowns.

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.

For a second, I want you to think about how you would move something to do work against gravity, what types of energies would you give to put into it to get it to move upwards?

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 wherever 2 objects touch through friction. This is a favourite question of examiners – they love asking where the energy went – it was 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 right? RIGHT! 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, right? So, the higher the object travels, the more energy you need to use to lift that object. Let’s put that in our proportionality.

Energy (E) ∝ mass (m) x height (h)

3 – This is the strange one. But 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, right? 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:

(INSERT IMAGE OF EQUATION HERE)

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

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

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 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.

E = 200 J <- 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. We can then use this to work out multiple things about that object, including its velocity.

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 mass and gravitational field strength, leaving you with an equation that looks like this.

(IMAGE OF EQUATION HERE)

Step 4 – Put the numbers into the calculator.

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 value to its units.

## Column B

m
J
g
gk
h
N/kg
E
m

You throw a ball up into the air 2.4 m and catch it again. The ball has a mass of 0.03kg. 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 0.45m from your lips. Calculate the energy it takes to lift the coffee cup to your lips. Include units in your answer. Give your answer to one decimal place

Gravitational field strength 9.8 N/kg

A child is on a swing that is no longer being pushed. The swing speeds up as it reaches the bottom of the swing and then slows down again as it reaches the top until it stops and reverses its direction. The height of the swing decreases with every repetition until it is not swinging anymore. Using the idea of energy, describe and explain these observations. (4 marks)

A child on a swing has a mass of 35 kg. They are swung 1.2m vertically on each swing. Calculate their maximum kinetic energy.

Gravitational field strength = 9.8 N/kg

A ski jumper reaches the bottom of the slope after falling 70m. Calculate their speed at the bottom of the slope if they have a mass of 70 kg. Give your answer to 1 decimal place.

Gravitational field strength = 9.8 N/kg

(5 marks)

A leaf falls from a tree that is 30 m high. The leaf has a mass of 0.02 kg.

a) Calculate the velocity the leaf should achieve when it hits the ground. Give your answer to 1 decimal place (4 marks)

(We will consider part b in the next question.)

Gravitational field strength = 9.81 N/kg

Part b)

The actual speed that the leaf reaches is considerably lower than your answer you calculated in part a. Using ideas of energy, describe and explain why the leaf does not reach your calculated top speed (2 marks)

A roller coaster travels around a loop. The roller coaster needs a minimum kinetic energy as it enters the loop to allow it to travel all the way around. The roller coaster cars with passengers are 1250 kg and they enter into the loop with a speed of 26 m/s. Calculate the maximum theoretical height of the loop and explain why the real height of the roller coaster needs to be less.

(6 marks)

A bird dives from the top of a tree building up speed as it is falling down. It then uses this speed to gain height again, but it needs to flap its wings to achieve the same height as the top of the tree. Using the idea of energy, explain why. (4 marks)

• Question 1

Match the correct value to its units.

## Column B

m
gk
g
N/kg
h
m
E
J
EDDIE SAYS
If you know the units then you will never fail in these questions, then all you have to do is match the numbers to their correct place in the equation. Learn the equation and these and you'll be quid’s in when it comes to these 2 mark questions in the exam.
• Question 2

You throw a ball up into the air 2.4 m and catch it again. The ball has a mass of 0.03kg. 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 0 as it has lost the same amount of energy that it has gained. A mean question - but you could have worked out that there was something wrong with this question because some information 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 3

A full coffee cup has a mass of 0.6 kg and is 0.45m from your lips. Calculate the energy it takes to lift the coffee cup to your lips. Include units in your answer. Give your answer to one decimal place

Gravitational field strength 9.8 N/kg

2.6J
2.6 J
EDDIE SAYS
Hopefully, you are looking out for things in bold in the questions. In this one, there are 2 things in bold, the units and the rounding. Don't let either of them catch you out! Also, did you notice that it said round to 1 decimal place, and not 1 significant figure? They can and will you both of these terms in the exam - so know them both and how tehy are different. E = mgh E = 0.6 x 9.8 x 0.45 E = 2.646 J E = 2.6 J
• Question 4

A child is on a swing that is no longer being pushed. The swing speeds up as it reaches the bottom of the swing and then slows down again as it reaches the top until it stops and reverses its direction. The height of the swing decreases with every repetition until it is not swinging anymore. Using the idea of energy, describe and explain these observations. (4 marks)

EDDIE SAYS
This can be considered in 2 parts: Part 1 - looking for the energy transfers: You need to spot that kinetic is going into gravitational and gravitational is going into kinetic. You also need to describe each of these independently - that is HOW is the kinetic energy is transferred into kinetic. Think about what you are actually seeing when you see someone on a swing. draw a picture if you need to. Part 2 - This is about describing the energy loss. The child does not get as high each time, so they are losing energy. Where is that energy lost? As heat - we should all know that by now! So we need to describe this energy loss and the effects that it will be having on the system.
• Question 5

A child on a swing has a mass of 35 kg. They are swung 1.2m vertically on each swing. Calculate their maximum kinetic energy.

Gravitational field strength = 9.8 N/kg

411.6
EDDIE SAYS
Look at the words in bold. The maximum kinetic energy will be when the gravitational energy is at 0. When you realise this, the question becomes a simple calculate the change in gravitational energy question. Let's go though it: E = mgh E = 35 x 9.8 x 1.2 E = 411.6J
• Question 6

A ski jumper reaches the bottom of the slope after falling 70m. Calculate their speed at the bottom of the slope if they have a mass of 70 kg. Give your answer to 1 decimal place.

Gravitational field strength = 9.8 N/kg

(5 marks)

37.0
EDDIE SAYS
This is about as hard as the questions get in GCSE energy (maybe even in GCSE science!) but it can be worked out simply if you have understood everything that we have guided you though so far - let's break it down (Lucio style) Always make this your first step when you look at a question and get a bit stuck: Write down what you have been given: m = 70 kg g = 9.8 N/kg h = 70 m Looking at the above numbers, we know we can work out the gravitational energy, right? Because we remember that the equation is E = mgh. So let's do that! E = 70 x 9.8 x 70 E = 48020J okay - now we have an energy, we need to get to a speed. What equation uses both energy and speed? The kinetic energy equation. We also know that a loss of gravitational energy leads into kinetic energy - another piece of evidence that this is our next move. Let's see if that works. (INSERT EQUATION) Looks like there is some rearranging to do! (INSERT REANGANED EQUATION) okay - now lets put the numbers in and see what speed we get out. v = 37.0 m/s Finally - does this look right? 30 m/s is about 60 mph. do you think they would travel that fast at the bottom of a ski jump? You do? Good - because tehy do travel that fast. equation DONE! 5 marks in the bag!
• Question 7

A leaf falls from a tree that is 30 m high. The leaf has a mass of 0.02 kg.

a) Calculate the velocity the leaf should achieve when it hits the ground. Give your answer to 1 decimal place (4 marks)

(We will consider part b in the next question.)

Gravitational field strength = 9.81 N/kg

24.2
EDDIE SAYS
First of all, as we have done before, calculate the energy of the leaf. We know this because there is not enough information to work out the answer, so we need to take several steps on our journey towards the answer. E = mgh m = 0.02 kg g = 9.81 N/kg h = 30 m E = 0.02 x 9.81 x 30 E = 5.886 J Now put this into kinetic energy and work out the velocity. I would always rearrange first, but you might like to put the numbers in first and then rearrange. (INSERT REARRANGED EQUATION HERE) v = 24.2 m/s
• Question 8

Part b)

The actual speed that the leaf reaches is considerably lower than your answer you calculated in part a. Using ideas of energy, describe and explain why the leaf does not reach your calculated top speed (2 marks)

EDDIE SAYS
There must be something taking away the energy to stop it from reaching this top speed. All you need to do is think about where that energy is going. Again, picture what a leaf falling looks like in real life and use this to try and work out where the energy has gone.
• Question 9

A roller coaster travels around a loop. The roller coaster needs a minimum kinetic energy as it enters the loop to allow it to travel all the way around. The roller coaster cars with passengers are 1250 kg and they enter into the loop with a speed of 26 m/s. Calculate the maximum theoretical height of the loop and explain why the real height of the roller coaster needs to be less.

(6 marks)

EDDIE SAYS
This is a lovely 2 part question - do the calculation and then do some writing about the calculation you have just done. You have answered 2 very similar questions to this already, so you should be quite well versed in doing questions like this. Part 1 is about working out the kinetic energy to start off with and then putting that back into the equation for gravitational energy to work out the height. Part 2 is all about looking at energy loss and describing energy transfers. You need to talk about why the car needs a set amount of kinetic energy going in (i.e. it will use this to convert into gravitational) and then you need to talk about energy losses in the track to explain why it will never really reach that maximum height.
• Question 10

A bird dives from the top of a tree building up speed as it is falling down. It then uses this speed to gain height again, but it needs to flap its wings to achieve the same height as the top of the tree. Using the idea of energy, explain why. (4 marks)

EDDIE SAYS
This is a question about describing the energy changes and where there are energy losses. We want you to think about where the energy losses are and how they affect any system. In this case, we are not only looking at where the energy losses are, but also how energy is put back into the system. Energy losses - this is only from the air resistance. There are not any other connected parts, so no friction. This is the only place that energy losses can happen. Energy gained - the bird files to the top of the tree height again. That means that energy needs to be put back into the system, so in this case, it is the flapping of the wings. Look out for stuff in the question that might give you clues, we had a throw-away line about flapping wings, and that was the clue you needed to answer this question.