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Understand Gravitational Energy

Worksheet Overview

QUESTION 1 of 10

You need to have a good understanding of kinetic energy before you try this activity. If you haven't already, it's definitely worth taking a look!

Imagine ...

 

You're slowly climbing to the very top of the rollercoaster track in one of the cars.  You feel the rush of adrenaline.  You're nearly there and then suddenly, there's nothing.   You look out over the park for a split second and then you plummet, fast, towards the ground.    

 

Rollercoaster

 

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 understand the science behind this all too familiar feeling? In this activity, we'll be looking at gravitational energy, its equation and how it is linked to kinetic energy.

 

Hopefully, you know that gravitational energy is the store of energy that things gain as they do work against gravity. In simple terms, 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 do you need to use to get an object 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 starting point!

 

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's 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

 

You will always be told the gravitational field strength in the question.

 

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

 

A roller coaster car has a mass of 15,000 kg and falls a distance of 10 m. How much gravitational energy would it lose during this fall?

Gravitational field strength on Earth = 9.8 N/kg

 

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

A roller coaster car has a mass of 15,000 kg and falls a distance of 10 m. How much gravitational energy would it lose during this fall?

Gravitational field strength on Earth = 9.8 N/kg

 

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

m = 15,000 kg

g = 9.8 N/kg

h = 10 m

 

Step 3  Put the numbers into the equation:

Energy = mass x gravitational field strength x height

E = 15,000 x 9.8 x 10

 

Step 4  Calculate the equation with a calculator. Write out your answer and don’t forget the unit.

 

1,470,000 J

 

All done?  Let’s try out some questions!

Can you match the correct values to their units?

Column A

Column B

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

The Empire State Building is 443 m tall. If you drop a penny that has a mass of 0.025 kg from the top of the Empire State Building, how much energy will it have when it hits the ground? 

 

Gravitational field strength = 9.8 N/kg

Column A

Column B

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

An elephant falls off a step.

 

Calculate the amount of 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 A

Column B

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

You pick up a box from Amazon and put it on the shelf for when your parents get home (aren't you nice).

 

Calculate the amount of energy it took for you to lift that package.

 

The mass of the package is 2 kg and the shelf is 1.5 m from the ground.

 

Gravitational field strength on Earth = 9.8 N/kg

Column A

Column B

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

A skateboarder travels down a 3 m high ramp. He reaches his maximum speed at the bottom of the ramp. The mass of the skateboarder is 55 kg.

 

Calculate the kinetic energy of the skateboarder at the bottom of the ramp.

 

Assume there is no energy lost to friction. 

 

Skateboarder

 

Gravitational field strength on Earth = 9.8 N/kg

In the last question, the energy the skateboarder had at the bottom of the ramp was not the same as the amount you calculated.

 

Choose the correct explanation for this from the list below: 

Energy is gained from the skateboarder's speed as he travels down the ramp

Energy is lost as the skateboarder travels up the ramp on the other side

Energy is lost through friction heating up the moving parts of the skateboard

A cat jumps from a two storey window 11.5 m from the ground.

 

Calculate the amount of energy that the cat loses when it jumps.

 

Give your answer to 3 significant figures.

Mass of cat  = 2.3 kg

Gravitational field strength = 9.8 N/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 mouth.

 

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

 

 Give your answer to one decimal place.

 

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.

 

Use 2 significant figures in your answer. 

 

Gravitational field strength = 9.8 N/kg

  • Question 1

Can you match the correct values to their units?

CORRECT ANSWER

Column A

Column B

Mass (m)
kg
Energy (E)
J
Gravitational field strength (g)
N/kg
Height (h)
m
EDDIE SAYS
How did you get on with this first one? If you know the units in these questions, then you are halfway there! You will be given the equation (most of the time) and then all you have to do is match the numbers to their correct place in the equation.
  • Question 2

The Empire State Building is 443 m tall. If you drop a penny that has a mass of 0.025 kg from the top of the Empire State Building, how much energy will it have when it hits the ground? 

 

Gravitational field strength = 9.8 N/kg

CORRECT ANSWER
EDDIE SAYS
A nice simple one to start off with. Find the correct numbers and multiply them together to get the answer. m = 0.025 kg g = 9.8 N/kg h = 443 m E = mgh E = 0.025 x 9.8 x 443 E = 108.535 J
  • Question 3

An elephant falls off a step.

 

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

 

Elephant mass = 6000 kg

Gravitational field strength = 9.8 N/kg

Height = 0.5 m 

CORRECT ANSWER
EDDIE SAYS
Again, find the correct numbers and plug them into the equation: E = mgh m = 6000 kg g = 9.8 N/kg h = 0.5 m E = 6000 x 9.8 x 0.5 E = 29 400 J
  • Question 4

You pick up a box from Amazon and put it on the shelf for when your parents get home (aren't you nice).

 

Calculate the amount of energy it took for you to lift that package.

 

The mass of the package is 2 kg and the shelf is 1.5 m from the ground.

 

Gravitational field strength on Earth = 9.8 N/kg

CORRECT ANSWER
EDDIE SAYS
Find the correct numbers and put them into the equation! E = mgh m = 2 kg g = 9.8 N/kg h = 1.5 m E = 2 x 9.8 x 1.5 E = 29.4
  • Question 5

A skateboarder travels down a 3 m high ramp. He reaches his maximum speed at the bottom of the ramp. The mass of the skateboarder is 55 kg.

 

Calculate the kinetic energy of the skateboarder at the bottom of the ramp.

 

Assume there is no energy lost to friction. 

 

Skateboarder

 

Gravitational field strength on Earth = 9.8 N/kg

CORRECT ANSWER
1617 J
1 617 J
1,617 J
1617
1 617
1,617
EDDIE SAYS
This one relies on you remembering the special relationship between gravitational energy and kinetic energy. If there is no energy lost to friction, then all of the lost gravitational energy will be converted into kinetic energy. So, all you need to do is to work out the gravitational energy! Aren't we sneaky! E = mgh m = 55 kg g = 9.8 N/kg h = 3 m E = 55 x 9.8 x 3 E = 1617 J Did you remember to include the unit?
  • Question 6

In the last question, the energy the skateboarder had at the bottom of the ramp was not the same as the amount you calculated.

 

Choose the correct explanation for this from the list below: 

CORRECT ANSWER
Energy is lost through friction heating up the moving parts of the skateboard
EDDIE SAYS
Energy is always lost when you have it changing from one store to another. This happens 99% of the time as heat. If you are ever given a question like this, then choose the answer that has heat in it. We guarantee it will be the correct answer.
  • Question 7

A cat jumps from a two storey window 11.5 m from the ground.

 

Calculate the amount of energy that the cat loses when it jumps.

 

Give your answer to 3 significant figures.

Mass of cat  = 2.3 kg

Gravitational field strength = 9.8 N/kg

CORRECT ANSWER
259 J
259
EDDIE SAYS
Just a simple equation, right? WRONG! Did you see the words in bold. It's our age-old adage - words in bold get you marks, look out for them. You must put your answer to 3 significant figures. Let's look at how we would do it. E = mgh m = 2.3 kg g = 9.8 N/kg h = 11.5 m E = 2.3 x 9.8 x 11.5 E = 259.21 J But then you need to round it! E = 259 J to three significant figures! Boom!
  • Question 8

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 might have been able to work out that there was something wrong with it because some information was missing - the gravitational field strength was not included! 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 9

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

 

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

 

 Give your answer to one decimal place.

 

Gravitational field strength 9.8 N/kg

CORRECT ANSWER
2.6 J
2.6
EDDIE SAYS
Hopefully, by this point, you are looking out for things in bold in the question. In this one, there are two 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 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 Now round this to 1 dp: E = 2.6 J
  • Question 10

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.

 

Use 2 significant figures in your answer. 

 

Gravitational field strength = 9.8 N/kg

CORRECT ANSWER
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 this up and get 0.24 J. That's another activity completed and hopefully, you are feeling really confident with this equation by now.
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