# Gravitational Potential Energy Formula

The gravitational potential energy of an object is the 'stored energy' that the object has by being at that height. This is equivalent to its mass times the force of gravity, g (a defined constant of 9.8 m/s^{2}) times the height of the object.

Potential energy = mass x gravity x height.

E_{grav} = PE = mgh

PE = potential energy, J or kg.m^{}2/s^{2}

m = mass, kg

g = gravity = 9.8 m/s^{2}

h = height, m

Gravitational Potential Energy Formula Questions:

1) A basketball, with a mass of 2.2 kg, falls off a window ledge, to the ground 50 m below. What is the gravitational potential energy of the ball when it arrives below?

Answer: The mass, m = 2.2 kg; the height, h = 50 m; the force of gravity, g =9.8 m/s^{2}.

PE = mgh

PE = (2.2 kg)(9.8 m/s^{2})(50 m)

E = 1078 kg m^{2 }/ s^{2 } = 1078 J

2) You move to a different floor in the building and drop the same ball. It now hits the sidewalk with a PE of 925 kg m^{2}/s^{2}, what is the height from which the ball fell?

Answer: The mass, m = 2.2 kg; the force of gravity, g = 9.8 m/s^{2}; and the

PE = 925 kg m^{2}/s^{2}.

PE = mgh

h = (PE) /mg

h = (925 kg m^{2}/s^{2})/ (2.2 kg)(9.8 m/s^{2})

h = 42.9 m

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