A cue ball of weight W is falling with an acceleration downward of g/3 and speed v.What is the magnitude of the drag force on the ball at this moment?
A) 0.33W
B) 0.67W
C) 0.11W
D) There is insufficient information to solve this problem.

Question

Quizplus · Accepted Answer

The drag force can be found using the formula Fdrag = (1/2)ρAv^2Cdrag, where ρ is the density of the fluid, A is the cross-sectional area of the object, v is the velocity of the object relative to the fluid, and Cdrag is the coefficient of drag. We do not have information about ρ, A, or Cdrag, so we cannot solve for Fdrag directly. However, we do know that the acceleration of the cue ball is g/3, which is less than the acceleration due to gravity (g). This suggests that there is some upward force acting on the ball, which would be the drag force. Because the cue ball is falling, we can assume that the drag force is acting in the upward direction. Therefore, the magnitude of the drag force must be less than the weight of the ball (W), but greater than if the ball were falling freely under the influence of gravity (i.e. Fdrag = 0). That leaves us with choices B and C. We can eliminate C because 0.11W is too small of a force to counteract the weight of the ball, even with a reduced acceleration. Therefore, the best choice is B, which is 0.67W.

A Cue Ball of Weight W Is Falling with an Acceleration