The two masses in the Atwood\'s machine shown in Figure 8-23 are initially at re
ID: 1601195 • Letter: T
Question
The two masses in the Atwood's machine shown in Figure 8-23 are initially at rest at the same height. After they are released, the large mass, m_2, falls through a height h and hits the floor, and the small mass, m_1, rises through a height h. (a) Find the speed of the masses just before m_2 lands, giving your answer in terms of m_1, m_2, g, and h. Assume the ropes and pulley have negligible mass and that friction can be ignored. (b) Evaluate your answer to part (a) for the case h = 1.2 m, m_1 = 3.7 kg, and m_2 = 4.1 kg.Explanation / Answer
36. (A) Applying work - energy theorem ,
for two block system, Tension will be internal force and only external force will be force due to gravity.
net work done by external force = change in KE
m2 g h - m1 g h = m1 v^2 /2 + m2 v^2 /2 - 0 - 0
v^2 (m1 + m2) / 2 = g h (m2 - m1)
v = sqrt[ 2 g h (m2 - m1 ) / (m1 + m2) ]
(B) putting values,
v = sqrt[ 2 x 9.8 x 1.2 (4.1 - 3.7) / (4.1 + 3.7)]
v = 1.10 m/s
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