Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively PA and PB. Which statement is correct?
A)FB = FA; PB = PA.
B)FB = FA; PB = 2 PA.
C)FB = 2 FA; PB = PA.
D)FB = 2 FA; PB = 2 PA.
E)PA = FA; PB = FB.

Question

Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively PA and PB. Which statement is correct? 
A)FB = FA; PB = PA. 
B)FB = FA; PB = 2 PA. 
C)FB = 2 FA; PB = PA. 
D)FB = 2 FA; PB = 2 PA. 
E)PA = FA; PB = FB.

Quizplus · Accepted Answer

Since the masses are raised at constant velocity, the net force on each mass must be zero. Therefore, FA = mgA and FB = mgB, where g is the acceleration due to gravity. Since mass B is raised twice as fast as mass A, we have vB = 2vA. Using the work-energy principle, we have PB = FBy2vB and PA = FAyvA. Substituting FB = FA and vB = 2vA, we get PB = 2PA. Therefore, the correct statement is FB = FA; PB = 2 PA.

Two Equal Masses Are Raised at Constant Velocity by Ropes