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Analyse Gravitational Energy

Worksheet Overview

QUESTION 1 of 10

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

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, 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 – there is 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 this 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 them for multiple unknowns. Are you up for the challenge?

 

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 to do work against gravity - what types of energy would you have 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 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 trickier).

 

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 given 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 1   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 mass and 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 A

Column B

m
J
g
N/kg
h
kg
E
m

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

 

 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 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]

A child on a swing has a mass of 35 kg. He swings 1.2 m vertically each time.

 

Calculate the maximum kinetic energy.

 

Gravitational field strength = 9.8 N/kg

A ski jumper reaches the bottom of a slope after falling 70 m.

 

Calculate the speed at the bottom of the slope if the skier has a mass of 70 kg.

 

Give your answer to 1 decimal place.

 

Gravitational field strength = 9.8 N/kg

 

[5]

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

 

 Calculate the velocity the leaf will achieve when it hits the ground.

 

Give your answer to 1 decimal place.

 

Gravitational field strength = 9.81 N/kg

 

[4]

The actual speed that the leaf in question 7 reaches, will be considerably lower than the answer you calculated.

 

Using ideas of energy, describe and explain why the leaf does not reach your calculated top speed.  

 

[2]

A roller coaster travels around a loop. It needs a minimum amount of 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 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]

A bird dives from the top of a tree, building up speed as it is flies 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]

  • Question 1

Match the correct values to their units. 

CORRECT ANSWER

Column A

Column B

m
kg
g
N/kg
h
m
E
J
EDDIE SAYS
If you know the units, then you are halfway there with these questions. All you have to do then is to match the numbers to their correct places in the equation. Learn the equation and these units and you'll be all set when it comes to these two 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 0.03 kg.

 

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

CORRECT ANSWER
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 this question because some information was missing (there was no gravitational field strength given!) 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 0.45 m from your lips.

 

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

 

 Give your answer to one decimal place.

 

Gravitational field strength 9.8 N/kg

CORRECT ANSWER
2.6 J
2.6
EDDIE SAYS
Hopefully, you are looking out for things in bold in the questions. Did you notice that it said round to 1 decimal place, and not 1 significant figure? They can, and will, ask you 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 4

A child is on a swing that is no longer being pushed. The swing speeds up as it reaches the bottom 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]

CORRECT ANSWER
EDDIE SAYS
This can be considered in two 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 the kinetic energy is transferred into gravitational. Think about what you are actually seeing when you watch 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. He swings 1.2 m vertically each time.

 

Calculate the maximum kinetic energy.

 

Gravitational field strength = 9.8 N/kg

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

A ski jumper reaches the bottom of a slope after falling 70 m.

 

Calculate the speed at the bottom of the slope if the skier has a mass of 70 kg.

 

Give your answer to 1 decimal place.

 

Gravitational field strength = 9.8 N/kg

 

[5]

CORRECT ANSWER
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 through so far - let's break it down. Always make this your first step when you look at a question and get a bit stuck: Write down the numbers 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 because we remember that the equation is E = mgh So let's do that! E = 70 x 9.8 x 70 E = 48020 J Okay, now we have the energy, we need to get the speed. What equation uses both energy and speed? The kinetic energy equation! We also know that a loss of gravitational energy leads to kinetic energy - another piece of evidence that this is our next move. Let's see if that works. Kinetic energy = ½mass x velocity² E = ½mv² Looks like there is some rearranging to do! v = √(2E ÷ m) Okay - now let's put the numbers in and see what speed we get out. v = √((2 x 48020) ÷ 70) v =√1372 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 they do travel that fast! Equation done and five marks in the bag! Well done!
  • Question 7

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

 

 Calculate the velocity the leaf will achieve when it hits the ground.

 

Give your answer to 1 decimal place.

 

Gravitational field strength = 9.81 N/kg

 

[4]

CORRECT ANSWER
EDDIE SAYS
There is not enough information to work out the answer at present, so we need to take several steps on our journey towards solving this problem. First of all, we need to find the energy of the leaf. 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 the kinetic energy equation and work out the velocity. You will need to rearrange the equation to make velocity the subject: v = √(2E ÷ m) v = √ 588.6 v = 24.2 m/s Phew - that's a lot to do!
  • Question 8

The actual speed that the leaf in question 7 reaches, will be considerably lower than the answer you calculated.

 

Using ideas of energy, describe and explain why the leaf does not reach your calculated top speed.  

 

[2]

CORRECT ANSWER
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. It needs a minimum amount of 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 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]

CORRECT ANSWER
EDDIE SAYS
This is a lovely two part question - do the calculation and then do some writing about the calculation you have just done. You have answered two very similar questions to this already, so you should be quite well versed in how to do it. 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 flies 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]

CORRECT ANSWER
EDDIE SAYS
This is a question about describing energy changes and where there are energy losses. You need 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 air resistance. This is the only place that energy losses can happen because there are no connected parts - so there is no friction. Energy gained - the bird flies to the top of the tree 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. Well done for completing this really challenging activity. Don't worry if you found some of it too tricky, you'd be unlucky to get more than one question of this level of difficulty in the exam.
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