Gravitational potential energy is stored when work is done against the force of gravity. Kinetic energy is stored when there is movement. Through mechanical work, the two energy stores can transfer.
Equation
You will be learning about the following equations in this lesson.
These are the symbols and units for the equations above.
QUANTITY NAME
SYMBOL
UNIT NAME
UNIT
gravitationalpotentialenergy
Ep
joule
J
mass
m
kilogram
kg
gravitationalfieldstrength
g
newtonperkilogram
N/kg
height
h
metre
m
kineticenergy
Ek
joule
J
velocity
v
metrepersecond
m/s
Gravitational potential energy (Ep)
Gravitational potential energy (Ep) is stored when when work is done against the force of gravity. Work done is the energy transferred when a force is applied to an object.
Gravitational potential energy increases with increasing height.
Example
Fox number two has more gravitational potential energy than fox number one as it is higher on the stairs.
1.
Fox at the bottom of the stairs
2.
Fox at the top of the stars
To calculate gravitational potential energy, you will need to use the following equation
Gravitational field strength is used to represent how much force acts upon one kg of mass. For example, Earth's gravitational field strength is 10N/kg. For every one kg of mass on Earth, a force of 10N from the Earth pulls down on the mass.
Gravitational field strength varies depending on the mass of the object. Jupiter's gravitational field strength is about 2.5 times bigger than Earths, because Jupiter has a much larger mass.
Example
A ball is thrown into the air, and reaches a height of 4m. The ball has a mass of 500g. What is the gravitational potential energy of the ball?
Firstly, write down the quantities and make sure they are in the correct units:
mgh=500g=0.5kg=10N/kg=4m
Next, write down the equation you need to use:
Ep=m×g×h
Then, substitute the values into the equation:
Ep=0.5×10×4
Don't forget to include your units:
20J
At a height of 4m, the ball has 20J of gravitational potential energy.
Kinetic energy (Ek)
Kinetic energy (Ek) is stored when an object is moving.
The faster something is going, the more kinetic energy there is.
Example
Fox number two is a running fox and is moving faster than fox number one. Therefore, fox number two has more kinetic energy.
1.
Stationary fox
2.
Running fox
To calculate kinetic energy, you will need to use the following equation.
kineticenergyEk=21×mass×velocity2=21×m×v2
Hint: When gravitational potential energy has completely transferred into kinetic energy, they are the same value!
Example
Assume all gravitational potential energy from the previous example is converted into kinetic energy. What is the velocity of the ball when it hits the ground? Give your answer to two significant figures.
Firstly, write down the quantities and make sure they are in the correct units:
Ekm=20J=0.5kg
Secondly, write down the equation you need to use:
Ek=21×m×v2
Next, start rearranging the formula. Divide Ek by half and mass:
21×mEk=v2
Now, you need to square root both sides in order to get v, rather than v2:
21×mEk=v
Then, you should substitute the values into the equation:
21×0.520=v
Don't forget to include your units and to round your answer to two significant figures:
8.9m/s
The ball hits the ground at a velocity of 8.9m/s.
Energy transfer between Ep and Ek
Kinetic and gravitational potential stores are often transferred to each other. When there is a gravitational potential energy store, work has been done against gravity which will be transferred from a kinetic energy store. This is because movement must have happened.