Blocks of mass m1 and m2 are connected by a massless string that passes over the

Question

Blocks of mass m1 and m2 are connected by a massless string that passes over the pulley in figure. The pulley turns on frictionless bearings. Mass m1 slides on a horizontal, frictionless surface. Mass m2 is released while the blocks are at rest. Assume the pulley is massless. Find the acceleration of m1 and the tension in the string. ( Use any variable or symbol stated above along with the following as necessary: g.) a = T = Suppose the pulley has mass mp and radius R. Find the acceleration of m1 and the tensions in the upper and lower portion of the string. Verify that your answers agree with part a if you set mrho = 0. ( Use any variable or symbol stated above along with the following as necessary: g.) A = Tupper = Tlower =

Explanation / Answer

a.m2g - T = m2a T = m1a ==>a = m2g/(m1+m2) T = m1m2g/(m1 + m2) b.T1 = m1a m2g - T2 = m2a (T2-T1)R = 1/2 mp * R^2 w = 0.5 mp a ==>m2g - m2a - m1a = 0.5 mpa/R ==>a = m2g/(m1 + m2 +0.5mp/R) T1 = m1m2g/(m1 + m2 +0.5mp/R) --- T upper T2 = m2g - m2m2g/(m1 + m2 +0.5mp/R) ----T lower

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