Rain drops falling

A raindrop with mass kg falls from a cloud at a height of h=1000 m.

• How much work is done by the force of gravity?
• What would the velocity be if there was no drag force?
• The terminal velocity is 8 m/s. How much work is done by the drag force?

According to our expression for work we have

Note that even though this is a small energy it would cause damage to living animals because the impact is over a small area!

We get the final velocity in the absence of drag force by using the Work-energy equation 3

We then use the expression for the kinetic energy to solve for the final velocity:

If the terminal velocity was actually only 8 m/s due to air drag then our work energy equation reads:

I can add up work from different sources like this because forces add to produce the net force which controls the change in kinetic energy. Solving for we have

Putting in numbers we get

the work performed is negative because the drag force opposes the direction of motion. The magnitude is almost as large as the magnitude of the work performed by gravity because the drag force is as large as the force of gravity for most of the fall of the rain-drop.