An Atwood\'s machine consists of blocks of masses m1 = 9.0 kg and m2 = 24.0 kg a

Question

An Atwood's machine consists of blocks of masses m1 = 9.0 kg and m2 = 24.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 8.90 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping.

(a) Why must the tension T2 be greater than the tension T1?


(b) What is the acceleration of the system, assuming the pulley axis is frictionless?
m/s2

(c) Find the tensions T1 and T2.
T1 = N
T2 = N

Explanation / Answer

m1 = 9.0 kg, m2 = 24.0 kg, M = 8.90 kg, r = 0.200 m. (a) Why must the tension T2 be greater than the tension T1? If T2 were not greater than T1, the pulley could not rotate, so m2 could not move down. (b) What is the acceleration of the system, assuming the pulley axis is frictionless? For m2: m2*g - T2 = m2*a For pulley: (T2 - T1)*r = I*a = (Mr2/2)*(a/r), so T2 - T1 = Ma/2 For m1: T1 - m1*g = m1*a add them together, (m2 - m1)g = (m1 + M/2 + m2)a a = (m2 - m1)g/(m1 + M/2 + m2) = 3.93 m/s2 (c) Find the tensions T1 and T2. T1 = m1(g + a) = 124 N T2 = m2(g - a) = 141 N

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