## 7.4 Work Done by a Gravitational Force

To calculate the work done by the gravitational force is given by:

where q is the angle between the gravitational force, and the displacement of the object.

We can see that we have two situations:

If the object is falling vertically , the work (done by gravity force) is positive (q = 0°)and energy is transferred to the object and its kinetic energy increases.

Ball (m = 0.1 kg) falling down from rest

Ball (m = 0.1 kg) projected vertically up with initial speed 14 m/s

 Script by Dr. Mohamed S. Kariapper using Physlets from

If the object is thrown vertically , the work (done by gravity force) is negative (q = 180°)and energy is transferred from the object and its kinetic energy decreases.

Work Done in Lifting and Lowering an Object

In the case where the object is lifted (upward displacement) by a person without acceleration, the work energy theorem tells us that

However, in this case q = 180° and the work done by the person (  ) is positive on the object.

In the case where the object is lowered (downward displacement) by a person without acceleration, the applied force does negative work on the object (  ).

Demos/Animations Examples/Checkpoints Interactive Problems
am = animation ,dm = demo, cp = checkpoint, ex = example, ip = interactive problem