Three objects of known mass m1,m2, and m3 are connected by a system of light(mas

Question

Three objects of known mass m1,m2, and m3 are connected by a system of light(massless) strings over frictionless, massess pulleys as shown and are accelerating. The tabletop is fictionless. Use Newtons Second Law to: 1) Find the magnitude of the systems acceleration in terms of known quantities. NOTE: the direction of acceleration is ambiguous here 2) What is the tension in each of the strings? 3) Evaluate your answer and tell me under what conditions would the acceleration switch directions. 4)Evaluate your answer and tell me under what conditions would acceleration=0?

Explanation / Answer

let the string between m1 and m2 be named 1, and that between m1 and m3 be 2; assume the direction of accelerations as shown in diagram to start with, T2-m3g = m3a ----(eq.1); T1-T2 = m1a ----(eq.2); m2g-T1 = m2a -----(eq.3); (1) adding all three equations we get, m2g-m3g=(m1+m2+m3)a which implies a=(m2-m3)*g/(m1+m2+m3); (2) T2 = m3g ( 1+ (m2-m3)/(m1+m2+m3)) = m3*g*(m1+2*m2)/(m1+m2+m3); similarly T1 = m2g(1- (m2-m3)/(m1+m2+m3)) = m2*g*(m1+2*m3)/(m1+m2+m3); (3) aceeleration will switch directions according to the values of m2 and m3; if m2>m3, acc. as shown in the fig. , if m2

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