Answer to Question #246110 in Physics for Kristine

Question #246110

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 𝑓𝑑 from the floor. One second after the bodies are released, the 4 slug mass reaches the floor. Find the mass of the other body. 


1
Expert's answer
2021-10-06T08:13:00-0400

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


a=2dt2.a=\frac{2d}{t^2}.

By Newton's second law:


βˆ’Ma=Tβˆ’Mg,ma=Tβˆ’mg. m=Ta+g=M(gβˆ’a)g+a=Mgβˆ’2d/t2g+2d/t2, m=2.4 slugs.-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}.


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