Question

Two bodies, one of mass 4 slugs and the other of mass m is fastened to the two ends of a string. The string passes over a smooth pulley so that the two bodies hang vertically and the 4 slug mass is 4 𝑓𝑡 from the floor. One second after the bodies are released, the 4 slug mass reaches the floor. Find the mass of the other body. 

Answer 1

First, find the acceleration of both bodies (it is the acceleration of the M=4-slug-body):

$$a=\frac{2d}{t^2}.$$

By Newton's second law:

$$-Ma=T-Mg,\\ ma=T-mg.\\\space\\ m=\frac{T}{a+g}=\frac{M(g-a)}{g+a}=M\frac{g-2d/t^2}{g+2d/t^2},\\\space\\ m=2.4\text{ slugs}.$$