# (Near the Earth)

## The Problem:

Suppose we have an object with weight = mg. How much will its gravitational potential energy change if we raise it to a height h?

## The Solution:

 As the object (here, a book) is raised a distance h from the floor, gravity does work = -(Force)(distance) = -mgh. Therefore, the energy stored by gravity - the gravitational potential energy = mgh

Following the steps for calculating potential energy:

1. Pick GPE = 0: Let's say that the object has GPE = 0 J at its current location. This choice is arbitrary, but convenient. We are free to pick any other location for the GPE = 0 J location.
2. GPEh = -(work gravity does when object is moved from GPE = 0 to height h): As the object moves upward a distance h, gravity exerts a downward force = mg, so the work done by gravity = -(mg)(h) = -mgh. Therefore, GPEh = mgh.

## Examples:

Example 1: A block of mass 2.0 kg rests on a table. If its gravitational potential energy is 0 Joules now, what will its gravitational potential energy be when it is raised 1.0 meter above the table?

Solution: m = 2.0 kg, h = 1.0 m, g = 10 m/s2

GPE = mgh = (2.0 kg)(10 m/s2)(1.0 m) = 20 Joules

Example 2: A book weighing 8.0 Newtons is on a table 75 cm high. What is its GPE relative to the floor?

Solution: If GPE = 0 J at floor level, then mg = 8.0 N and h = 75 cm = 0.75 m

GPE = mgh = (8.0 N)(0.75 m) = 6.0 J

last update February 25, 2003 by JL Stanbrough