Mass m1 = 11.3 kg is on a horizontal surface. Mass m2 = 7.43 kg hangs freely on

Question

Mass m1 = 11.3 kg is on a horizontal surface. Mass m2 = 7.43 kg hangs freely on a rope which is attached to the first mass. The coefficient of static friction between m1 and the horizontal surface is ?s = 0.480, while the coefficient of kinetic friction is ?k = 0.152.

1. If the system is in motion with m1 moving to the left, then what will be the magnitude of the system's acceleration? Consider the pulley to be massless and frictionless.

2. If the system is in motion with m1 moving to the right, then what will be the magnitude of the system's acceleration?

Explanation / Answer

(a.) mass m1 is moving to the left with acceleration let a . let the tension in the rope=T then friction on m1 is to the right. hence force balance equation for m1:- T+m1*g*0.152=m1*a....(1) for m2:- T-m2*g=m2*a...(2) solving we get, a=23.164 m/s^2 T=244.925 N (b.)mass m1 is moving to the right with acceleration let a . let the tension in the rope=T then friction on m1 is to the left hence force balance equation for m1:- T-m1*g*0.152=m1*a....(1) for m2:- m2*g-T=m2*a...(2) solving we get, a=-22.835 m/s^2 T=241.2 N

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