Two objects, each of weight W, hang vertically by spring scales as shown in the figure. The pulleys and the strings attached to the objects have negligible weight, and there is no appreciable friction in the pulleys. The reading in each scale is
A) W.
B) more than W, but not quite twice as much.
C) less than W.
D) 2W.
E) more than 2W.

Question

Two objects, each of weight W, hang vertically by spring scales as shown in the figure. The pulleys and the strings attached to the objects have negligible weight, and there is no appreciable friction in the pulleys. The reading in each scale is 
A) W. 
B) more than W, but not quite twice as much. 
C) less than W. 
D) 2W. 
E) more than 2W.

Quizplus · Accepted Answer

Since the two objects are connected by the same string and pulley system, their accelerations must be equal and opposite. Therefore, the tension in the string must be equal for both objects. By Newton's Third Law, this tension is equal to the force the two objects exert on the pulley. Since the pulley is weightless, this force must be equal to the weight of the two objects combined, which is 2W.

However, this force is distributed equally between the two scales, so each scale reads half of this force, which is W. Therefore, the answer is A) W.

Two Objects, Each of Weight W, Hang Vertically by Spring