Classical Mechanics - Fluid

A sphere of mass m is released from rest in a stationary viscous medium. In addition to the gravitational force of magnitude mg, the sphere experiences a retarding force of magnitude bv, where v is the speed of the sphere and b is a constant. Assume that the buoyant force is negligible. Which of the following statements about the sphere is correct?

1. Its kinetic energy decreases due to the retarding force.
2. Its kinetic energy increases to a maximum, then decreases to zero due to the retarding force.
3. Its speed increases to a maximum, then decreases back to a final terminal speed.
4. Its speed increases monotonically, approaching a terminal speed that depends on b but not on m.
5. Its speed increases monotonically, approaching a terminal speed that depends on b and m.

(GR9677 #31)

Solution:

ma = mg − bv

Terminal speed, a = 0

mg = bv
v = mg/b → (E) TRUE

(A) FALSE.
m is released from rest v_i = 0 → KE_i = 0

(B) FALSE.
Terminal speed released from rest v_f  = mg/b ≠ 0 → KE_f  ≠ 0

(C) FALSE.
v_i = 0 to v_f  = mg/b, no v_max

(D) FALSE.
 v_f  = mg/b, depend on both m and b

Answer: E