Question

a ball is falling at terminal velocity. terminal velocity occurs when the ball is in equilibrium and the forces are balanced. which free body diagram shows the ball falling at terminal velocity?

Explanation:

To determine the correct free - body diagram for a ball falling at terminal velocity, we use the concept of balanced forces. When an object is at terminal velocity, the gravitational force ($F_g$) pulling it downwards and the drag force ($F_d$) (air resistance) pushing it upwards are equal in magnitude and opposite in direction.

1. Analyze the first diagram: The upward force and the downward force have different magnitudes (e.g., if $F_d = 5N$ and $F_g=20N$), so the forces are not balanced.
2. Analyze the second diagram: The upward force ($F_d = 20N$) and the downward force ($F_g = 20N$) have the same magnitude and are opposite in direction. This means the net force on the ball is zero, which is the condition for terminal velocity (equilibrium).
3. Analyze the third diagram: There is only one force (downward), so the forces are not balanced.
4. Analyze the fourth diagram: The upward force and the downward force have different magnitudes (e.g., $F_d = 20N$ and $F_g = 30N$), so the forces are not balanced.

Answer:

The second free - body diagram (where the upward force and the downward force both have a magnitude of 20N) shows the ball falling at terminal velocity.