Work done by gravitational force in a freely falling body

When a body is in free fall under the influence of gravitational force only, the work done by gravity on the body is zero.

This can be derived as follows:

Work is defined as:

Work = Force x Displacement

W = F x d

Where:

W = Work done by the force (in Joules)
F = Force (in Newtons)
d = Displacement (in meters)

For a freely falling body, the only force acting on it is gravitational force (Fg). This force acts vertically downward.

The displacement (d) of the freely falling body is also vertically downward, in the same direction as Fg.

Therefore, the angle between Fg and d is 0 degrees.

Substituting this into the work equation:

W = Fg x d x cos(0)
W = Fg x d

But Fg is constant for a freely falling body. So the work done is:

W = 0

Intuitively, this makes sense – gravity does no “work” on a freely falling body, since the body is already accelerating downward at g due to gravity. The gravitational force does not speed up or slow down the motion.

In summary:

• Gravitational force (Fg) and displacement (d) are parallel for a freely falling body
• This results in a 0 degree angle between them
• Therefore, the work done by gravity on a freely falling body is zero.