Question

A 0.0038 kg leaf falls 16.8 m to the ground, where it lands with a speed of 12.2 m/s. What was the average force of air resistance on the leaf while it was falling?

Answer 1

The energy required to push the air out of the way is proportional to the square of the velocity. As the object falls, its velocity increases, and so does the drag.

At some point, the force from the drag equals the force from gravity. That's terminal velocity. At that point, the forces balance, and the object won't increase in speed, but its momentum is constant. It continues to fall at that speed until it hits the ground.

The formula is:



and we're looking for the point at which the force of gravity (F=mg) is equal to the drag force:

g=12ρv2CDAm

For a random leaf, let's say that the area is 6 cm square and the mass is 1 gram. ρ will be 1.2 kg/m^3 for air. g is 9.8 m/s^2. Let's say for simplicity that CD (the coefficient of friction) is 1.

Solving for v, we get 2 meters per second, or about 4 miles per hour, at its top speed. The numbers here will vary a lot from leaf to leaf, but it gives the gist; actual numbers will be in the range of a slow walking pace.