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

Let us assume that the masses of A and B are m each. Since mass B is raised twice as fast as mass A, the velocities of masses A and B are v and 2v, respectively. Therefore, the power supplied P is given by P = Fv = mghv/t, where h is the height through which the masses are raised, and t is the time taken to raise the masses. As the masses are raised at constant velocity, t is proportional to h. Therefore, P is proportional to mghv/h = mghv/t, which is the same for both masses. Therefore, P_B = P_A. Since the two masses are equal, the forces on the ropes supporting them are also equal, neglecting the mass of the ropes. Therefore, F_A = mg, and F_B = 2mg. Therefore, F_B = F_A. Thus, the correct answer is B: F_B = F_A;P_B = 2 P_A.

Two Equal Masses Are Raised at Constant Velocity by Ropes