Part A Two masses, m A = 33.0kg and m B = 42.0kg are connected by a rope that ha

Question

Part A

Two masses, m A   = 33.0kg and m B   = 42.0kg are connected by a rope that hangs over a pulley (as in the figure(Figure 1) ). The pulley is a uniform cylinder of radius R = 0.312m and mass 3.2kg . Initially, m A   is on the ground and m B   rests 2.5m above the ground.

Part A

If the system is now released, use conservation of energy to determine the speed of m B   just before it strikes the ground. Assume the pulley is frictionless.

Two masses, m A m_A = 33.0kg kg and m B m_B = 42.0kg kg are connected by a rope that hangs over a pulley (as in the figure(Figure 1) ). The pulley is a uniform cylinder of radius R R = 0.312m m and mass 3.2kg kg . Initially, m A m_A is on the ground and m B m_B rests 2.5m m above the ground. Part A If the system is now released, use conservation of energy to determine the speed of m B m_B just before it strikes the ground. Assume the pulley is frictionless.

Explanation / Answer

since the pulley is frictionless,no energy is spent on it

from conservation of energy,

(0.5)mAVA12+(0.5)mBVB12+mAghA1+mBghB1=(0.5)mAVA22+(0.5)mBVB22+mAghA2+mBghB2

VA1=VB1=0

VA2=-VB2=V

hA1=0=hB2

hB1=2.5m=hA2=h

mBghB=(0.5)(mA+mB)V2+mAghA

V2=2(mB-mA)gh/(mA+mB)

V=2.425 m/s

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