Two masses, m1 = 17.7 kg andm2 = 26.5 kg are connected by a rope that hangs over

Question

Two masses, m1 = 17.7 kg andm2 = 26.5 kg are connected by a rope that hangs overa pulley (as in the figure ). The pulley is a uniform cylinder ofradius 0.260 m and mass 7.60 kg. Initially, m1 is on theground and m2 rests 2.70 m above the ground. If the system is now released, useconservation of energy to determine the speed of m2 just before itstrikes the ground. Assume the pulley is frictionless. Two masses, m1 = 17.7 kg andm2 = 26.5 kg are connected by a rope that hangs overa pulley (as in the figure ). The pulley is a uniform cylinder ofradius 0.260 m and mass 7.60 kg. Initially, m1 is on theground and m2 rests 2.70 m above the ground. If the system is now released, useconservation of energy to determine the speed of m2 just before itstrikes the ground. Assume the pulley is frictionless. If the system is now released, useconservation of energy to determine the speed of m2 just before itstrikes the ground. Assume the pulley is frictionless.

Explanation / Answer

m1 = 17.7 kg, m2 = 26.5 kg, r =0.260 m, M = 7.60 kg. moment of inertia I =Mr2/2
h = 2.70 m
Find the speed v of m2 just before it strikesthe ground.

initial energy = m2*gh
final energy = m1*gh + (m1 + m2)*v2/2 +I2/2 = m1*gh + (m1 + m2)*v2/2 +(Mr2/2)(v/r)2/2 = m1*gh + (m1 + m2 +M/2)*v2/2
energy conservation:
m2*gh = m1*gh + (m1 + m2 + M/2)*v2/2
v = [2(m2 - m1)gh/(m1 + m2 + M/2)] = 3.11m/s

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