The barbell possesses gravitational potential energy.

The book possesses gravitational potential energy.

The hammer possesses gravitational potential energy.

Gravitational potential energy (E_{g})

Is the energy stored as the result of the vertical position (height) of an object.

Relative to the position where the ball leaves the hand …

The ball leaving the hand has 100% kinetic energy, E_{k}.

As the height of the ball increases, E_{k} is being reduced and E_{g} is gaining.

At maximum height, the ball has no kinetic energy and 100% potential energy.

When the ball is moving downward the potential energy is being converted to E_{k}.

This position may be relative to

ground level (the surface of the earth or the floor of any room)
or

a base level (some arbitrary reference point).

For our juggler, the value of E_{p} will be larger if the position of the object was compared to the floor and not the base level of the hand.

It may be calculated using
E_{g} = mgh where

E_{g} = gravitational potential energy (J)
m = mass of the object (kg)
g = acceleration due to gravity = 9.80 m/s^{2}
h = change in height relative to the reference point (m)

Sample Problem

A 25.0 kg box is lifted from the floor to a desk 1.87 m above the floor.

What is the gravitational potential energy relative to the floor?

What is the gravitational potential energy relative to a shelf 0.57 m high?

Solution:
m= 25.0 kg
g = 9.80 m/s^{2}
E_{g} = mgh

h = 1.87 m - 0 m = 1.87 m
E_{g} = mgh
= (25.0 kg)( 9.80 m/s^{2})(1.87 m)
= 458 J

h = 1.87 m - 0.57 m = 1.30 m
E_{g} = mgh
= (25.0 kg)( 9.80 m/s^{2})(1.30 m)
= 319 J

The work done on an object results in an equivalent increase in gravitational potential energy.

Crane lifting an object.

A juggling juggler.

When an object is raised, kinetic energy and gravitational potential energy is constantly being interchanged.

The sum of kinetic and gravitational potential energy (total mechanical energy) remains constant in any system.

E_{T} = E_{g} + E_{k}

A moving golf ball possesses mechanical energy due to its speed (kinetic energy) and its vertical position above the ground (gravitational potential energy).

Sample Problem
1. a) Determine the total mechanical energy of a 48 g golf ball if it has a velocity of 25 m/s when it leaves the golf club.

The total mechanical energy is 30 J.

b) If the golf ball goes in an arc and has a speed of 15 m/s at its maximum height, what will the maximum height be?