Question

which free body diagram shows the ball falling at terminal velocity?

Explanation:

To determine the free - body diagram of a ball falling at terminal velocity, we need to recall the concept of terminal velocity. When an object reaches terminal velocity, the net force acting on it is zero (since it moves at a constant velocity, according to Newton's first law). This means that the upward force (air resistance, \(F_{air}\)) and the downward force (gravitational force, \(F_g\)) must be equal in magnitude and opposite in direction.

Let's analyze each diagram:

1. In the first diagram, there is only a downward gravitational force (\(F_g = 20\ N\)) and no upward air - resistance force shown. So, the net force is non - zero (\(F_{net}=F_g = 20\ N\) downward), and the ball is not at terminal velocity.
2. In the second diagram, the upward air - resistance force (\(F_{air}=20\ N\)) and the downward gravitational force (\(F_g = 20\ N\)) have the same magnitude. So, the net force \(F_{net}=F_g - F_{air}=20\ N- 20\ N = 0\ N\). When the net force is zero, the object moves at a constant velocity, which is terminal velocity for a falling object.
3. In the third diagram, the upward air - resistance force (\(F_{air}=5\ N\)) is less than the downward gravitational force (\(F_g = 20\ N\)). The net force \(F_{net}=F_g - F_{air}=20\ N - 5\ N=15\ N\) downward, so the ball is accelerating downward and not at terminal velocity.
4. In the fourth diagram, the upward air - resistance force (\(F_{air}=30\ N\)) is greater than the downward gravitational force (\(F_g = 20\ N\)). The net force \(F_{net}=F_{air}-F_g = 30\ N-20\ N = 10\ N\) upward, so the ball would be accelerating upward, which is not the case for a falling ball at terminal velocity.

Answer:

The free - body diagram with \(F_{air}=20\ N\) (upward) and \(F_g = 20\ N\) (downward) (the second diagram among the given ones).