Gravitational Potential Energy
Brook Edgar & Hannah Shuter
Teachers
Contents
Explainer Video
Gravitational Potential Energy
Gravitational potential energy is the energy an object has due to its position above the ground.
The higher an object is above the ground, the more gravitational potential energy it has.
Formula:
The value of is always given to you in exams unless you are given all other terms of the equation and asked to calculate it. On Earth, the value of is . It tells us how much force acts on each kilogram of mass. It gives us information on the size of the planet as a larger planet will exert a bigger downwards force on a mass than a smaller planet. For example, the value of on Mars, a smaller planet than the Earth, is .
To calculate the gravitational potential energy of an apple, mass kilograms, in a tree metres above the ground on Earth, where we just need to multiply all of the numbers together as the equation tells us to do.
Worked Example:
Find the gravitational potential energy of an apple of mass , above the Earth’s surface, where is .
Answer:
The first step is to figure out which equation to use. The question asks us to calculate gravitational potential energy, so we write the equation for gravitational potential energy.
Next, we need to figure out where the numbers go.
, represents mass in the equation, and we know that mass is measured in kilograms, , so the number we use for mass is .
We know that represents height. Distances are measured in metres, , in physics so the number we use for height/distance is .
We then fill the numbers into the correct places in the equation to calculate gravitational potential energy.
*Don't forget to include the final unit for gravitational potential energy, joules, .
Worked Example:
An astronaut visits the Moon where . He decides to play golf, hitting a golf ball, mass , to a height of above the Moon’s surface. How much gravitational potential energy did the golf ball gain?
Answer:
As the question asks us to calculate gravitational potential energy, again, we are using the equation .
As , represents mass in the equation and mass is measured in the unit of kilograms () we need to convert from grams into kilograms.
Remember -> of cash = pounds, so .
We know that represents height. Distances are measured in metres, , in physics so the number we use for height/distance is .
We then fill the numbers into the correct places into the equation to calculate the gravitational potential energy.
*Don't forget to include the final unit for gravitational potential energy, joules, .
Rearranging Equations
Sometimes we need to calculate the height of an object above the ground or the mass of an object, so we need to rearrange the equation.
Always follow the same steps:
1. Write the equation.
2. Fill the numbers into their correct places using their units.
3. Calculate the final answer, remembering to include the final unit.
For example, lets say humpty dumpty falls to the ground losing of gravitational potential energy and we want to calculate his mass.
Gravitational field strength on Earth .
The question tells us the gravitational potential energy in joules, , the height that he fell from in metres , and the value of . We know that the only physics equation with all of these variables is , so we fill the numbers into the correct places into the equation.
First we should simplify the equation by multiplying by .
Now we want to calculate the unknown term, mass.
To do this, we need to get the letter , by itself on the RHS of the equation. So we need to get rid of the '' from the RHS. To get rid of something from an equation, we do its opposite. The opposite of multiplying by is dividing by , and what we do to one side, we must do to the other.
The mass of humpty dumpty is kilograms -> .
This is the answer in standard form, .
If the question asked us to give our answer to 2 significant figures.
This means that we only want an answer with two digits.
The final answer would then be .
Remember: When rounding, if the number after is five or above, you round the previous number up, e.g 1.28 -> 1.3, but 1.22 -> 1.2.
Worked Example:
A firework rocket has a mass of . It is launched and, in an explosion, releases of energy. Calculate the maximum height it reaches to 2 significant figures.
Use
Answer:
The question tells us the gravitational potential energy in joules, , the value of and the mass , but we know that mass is measured in kilograms, .
Remember,of cash pounds so .
The only physics equation with all of these variables that allows us to calculate the height is , so we fill the numbers into the correct places in the equation.
Now we want to calculate the unknown term, -> height.
To do this, we need to get the letter , by itself on the RHS of the equation.
First, we can simplify the equation by multiplying by .
We then need to get rid of the '' from the RHS. To get rid of something from an equation, we do its opposite. The opposite of multiplying by is dividing by , and what we do to one side, we must do to the other.
The maximum height reached by the firework is metres -> .
The question asked us to give our answer to significant figures, so there will be a mark available for this in the exam.
This means that we only want an answer with two digits.
The final answer would then be .
Teacher Tip: This is the maximum height reached by the rocket as we assumed that no energy was lost to the environment -> that no energy was dissipated.
Practice Questions
Find the mass of a man who is about to jump into the ocean. He has of energy at a height of above the ocean floor. Use
-> Check out Brook's video explanation for more help.
Answer:
Calculate the gravitational potential energy of a apple that is above the surface of the Earth. Use
-> Check out Brook's video explanation for more help.
Answer: