Answer to Question #239494 in Physics for rshiii

Question

16. 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

Find the acceleration from time and displacement:

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

Find the acceleration from equations by NSL for both bodies:

$$-m_1a=-m_1g+T,\\ m_2a=-m_2g+T.\\\space\\ a(m_1+m_2)=(m_1-m_2)g,\\\space\\ m_2=m_1\frac{g-a}{g+a}.$$

Substitute acceleration (the first eqn above):

$$m_2=m_1\frac{g-2d/t^2}{g+2d/t^2}=2.4\text{ slug}.$$