# Potential Energy: Earth's Gravity Formula

Potential energy is energy that is stored in a system. There is the possibility, or potential, for it to be converted to kinetic energy. Gravitational potential energy exists when an object has been raised above the ground. If the object is released from its position it will fall, converting the potential energy to kinetic energy. Like all work and energy, the unit of potential energy is the Joule (J), where 1 J = 1 N∙m = 1 kg m^{2}/s^{2} .

*potential energy = (mass of the object)(acceleration due to gravity)(height)*

*U = mgh*

*U* = potential energy of an object due to Earth's gravity

*m* = the mass of the object

*g* = acceleration due to gravity (9.8 m/s^{2})

*h* = height above position with *U = 0 *(the ground, or floor typically)

Potential Energy: Earth's Gravity Formula Questions:

1) A 0.30 kg model airplane is hanging from the ceiling in a child's room. The airplane is hanging 2.50 m above the floor. If the floor is the position with *U* = 0, what is the potential energy of the model airplane?

Answer: The model airplane's mass is *m* = 0.30 kg, and it is at a position *h* = 2.50 m above the floor. The potential energy can be found using the formula:

*U = mgh *

*U* = (0.30 kg)(9.8 m/s^{2})(2.50 m)

*U* = 7.35 kg m^{2}/s^{2}

*U* = 7.35 J

The potential energy due to gravity of the model airplane is 7.35 Joules.

2) A 200.0 kg roller coaster car is at its highest point on its track, 50.0 m above the ground. The coaster car goes over the edge into its "first drop", and starts its trip around its track. At the end, the car comes to a stop beside an elevated deck, where riders are waiting. Here, it is 10.0 m above the ground. How much potential energy is lost between the top of the ramp and where the car stops?

Answer: The ground is taken to be the position where *U* = 0. So, both at the top of the ramp, and where the car came to a stop, the roller coaster car has potential energy. The question asks what the difference between these energies is. The mass of the car is *m* = 200.0 kg, and the acceleration due to gravity is *g* = 9.8 m/s^{2}. At the top of the ramp, the height of the car was *h _{1}* = 50.0 m, and where the car came to a stop the height of the car was

*h*= 10.0 m. With these, the potential energies at these heights can be found:

_{2}*U _{1} = mgh_{1}*

*U _{2} = mgh_{2}*

*U _{1}* = (200.0 kg)(9.8 m/s

^{2})(50.0 m)

*U _{2}* = (200.0 kg)(9.8 m/s

^{2})(10.0 m)

*U _{1}* = 98000 J

*U _{2}* = 19600 J

To find the lost potential energy, subtract one from the other:

*U = U _{2} - U_{1}*

*U* = 98000 J - 19600 J

*U* = 78400 J

The lost potential energy between the top of the ramp and where the car came to a stop was 78400 Joules.

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