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 F_A and F_B,while the power supplied is respectively P_A and P_B.Which statement is correct? A)F_B = F_A;P_B = P_A. B)F_B = F_A;P_B = 2 P_A. C)F_B = 2 F_A;P_B = P_A. D)F_B = 2 F_A;P_B = 2 P_A. E)P_A = F_A;P_B = F_B.

Question

Quizplus · Accepted Answer

Since mass B is raised twice as fast as mass A, the velocity of mass B is twice that of mass A. Therefore, the force required to lift mass B must also be twice that of mass A (Newton's second law). As the work being done (lifting the masses at a constant velocity) is the same for both masses, the power supplied must be proportional to the force required. Hence, P_B = 2 P_A. The forces must be equal to keep the masses at the same velocity, so F_B = F_A. Therefore, the correct statement is B.

Two Equal Masses Are Raised at Constant Velocity by Ropes