A light rope runs through two frictionless pulleys of negligible mass. A mass, m, is hung from one of the pulleys and a force, F, is applied to one end of the rope so that the mass moves at a constant speed. What is the force needed to move the mass at a constant speed?
A) 0
B) mg
C) Mg
D) 2mg
E) 4mg

Question

A light rope runs through two frictionless pulleys of negligible mass. A mass, m, is hung from one of the pulleys and a force, F, is applied to one end of the rope so that the mass moves at a constant speed. What is the force needed to move the mass at a constant speed?
A) 0 
B) mg 
C) Mg 
D) 2mg 
E) 4mg

Quizplus · Accepted Answer

Since the mass is moving at a constant speed, that means the net force acting on the mass is zero. The only forces acting on the mass are its weight, mg, and the tension in the rope. However, since the pulleys are frictionless, the tension in the rope is the same at both ends. Therefore, the force applied, F, must be equal and opposite to the weight of the mass, mg. Thus, the force needed to move the mass at a constant speed is equal to its weight, which is B) mg.

A Light Rope Runs Through Two Frictionless Pulleys of Negligible