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Understand Gravitational Energy

In this worksheet, students will understand gravitational energy and how to apply it to solve problems. They will also be introduced to the gravitational energy equation.

Worksheet Overview

QUESTION 1 of 10

You should 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 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.  For a second, I want you to think about how you would move something up. What types of energies do you need to put in 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 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:

 

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 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 number into the calculator.

E = 15,000 x 9.8 x 10

 

Step 4 – Write out your answer and don’t forget the unit.

 

1,470,000 J

 

All done?  Let’s try out some questions!

Unit match up!  Can you match the correct value to its unit?

Column A

Column B

Mass (m)
m
Energy (E)
N/kg
Gravitational Field Strength (g)
kg
Height (h)
J

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 = 10 N/kg

An elephant falls off a cliff. Calculate the energy the elephant has when it hits the ground. 

Elephant mass = 6000 kg

Gravitational Field Strength = 10 N/kg

Height = 0.5 m

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 mas 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

A skateboarder travels down a 3 m high ramp. When they reach the bottom of the ramp, they reach their maximum speed. 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 = 10 N/kg

In the last question, the energy the skateboarder had at the bottom of the ramp was not the same as what you calculated. Chose the correct explanation for this from this list. 

Energy is gained from the scateboaders speed as he travels down the ramp.

Energy is lost as the scateboader 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-story 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.

Cat mass = 2.3 kg

Gravitational field strength = 9.8 m/s

 

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 mouth. Calculate the energy it takes to lift the coffee cup to your mouth. Include units in your answer. 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. Give the units and use 2 significant figures in your answer. 

Gravitational Field strength = 9.8 N/kg

  • Question 1

Unit match up!  Can you match the correct value to its unit?

CORRECT ANSWER

Column A

Column B

Mass (m)
kg
Energy (E)
J
Gravitational Field Strength (g)
N/kg
Height (h)
m
EDDIE SAYS
If you know the units then you will never fail in these questions. They will give you the equation (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 quid’s in when it comes to these 2 mark questions in the exam.
  • 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 = 10 N/kg

CORRECT ANSWER
110.75
EDDIE SAYS
A nice simple one to start off with. Find the correct numbers and times them together to get the answer. m = 0.025 kg g = 10 N/kg h = 443 m E = mgh E = 0.025 x 10 x 443 E = 110.75J Simples!
  • Question 3

An elephant falls off a cliff. Calculate the energy the elephant has when it hits the ground. 

Elephant mass = 6000 kg

Gravitational Field Strength = 10 N/kg

Height = 0.5 m

CORRECT ANSWER
30,000
30000
EDDIE SAYS
Again, find the correct numbers and plug them into the equation. E = mgh m = 6000 kg g = 10 N/kg h = 0.5 m E = 6000 x 10 x 0.5 E = 30,000 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 mas 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
29.4
EDDIE SAYS
Find the correct numbers and put them into the equation! E = mgh m = 2 g = 9.8 h = 1.5 E = 2 x 9.8 x 1.5 E = 29.4 J
  • Question 5

A skateboarder travels down a 3 m high ramp. When they reach the bottom of the ramp, they reach their maximum speed. 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 = 10 N/kg

CORRECT ANSWER
559.83
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 = 559.83 J
  • Question 6

In the last question, the energy the skateboarder had at the bottom of the ramp was not the same as what you calculated. Chose the correct explanation for this from this list. 

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

A cat jumps from a two-story 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.

Cat mass = 2.3 kg

Gravitational field strength = 9.8 m/s

 

CORRECT ANSWER
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 = 259.21J But then you need to round it! E = 259 <- 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 0.03kg. 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 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 9

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

 

Gravitational field strength 9.8 N/kg

CORRECT ANSWER
2.6 J
2.6J
EDDIE SAYS
Hopefully, by this point, you are looking out for things in bold in the question. 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 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 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. Give the units and use 2 significant figures in your answer. 

Gravitational Field strength = 9.8 N/kg

CORRECT ANSWER
0.24J
0.24 J
EDDIE SAYS
In this question, it was all about the units and the rounding. Remember, 2 significant figures means two numbers that are not 0. In this case, the un-rounded answer would have been 0.2352 but because the third number is on or above 5, we round our answers up and get 0.24 J.
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