7. +-10 points My Notes Ask Your Teacher A m1 16.5 kg object and a m2 11.5 kg ob

Question

7. +-10 points My Notes Ask Your Teacher A m1 16.5 kg object and a m2 11.5 kg object are suspended, joined by a cord that passes over a pulley with a radius of 10.0 cm and a mass of 3.00 kg (Fig. P10.46) The cord has a negligible mass and does not slip on the pulley. The pulley rotates on its axis without friction. The objects start from rest 3.00 m apart. Treating the pulley as a uniform disk,determine the speeds of the two objects as they pass each other. (Hint: There are two ways to do this problem: (1) The easy method is with conservation of energy; (2) The hard method is with torque and angular acceleration. If you choose this more challenging method, note that the tensions on either side of the pulley are NOT the same.) A-3.00 kg R = 10,0 cm 3.00 m Figure P10.46

Explanation / Answer

Applying energy conservation,

PEi + KEi = PEf + KEf

m1 g (3) + m2 g (0) + 0 = m1 g (0) + m2 g (3) + ( (m1 + m2) v^2 /2 + I w^2 /2 )

3 m1 g = 3 m2 g + ((m1 + m2) v^2 /2 + (M r^2 /2)(v/r)^2 / 2)

3 g (16.5 - 11.5) = (16.5 + 11.5) v^2 /2 + 1.5 v^2 /2

3x 9.8 x 5 = 14.75 v^2

v = 3.16 m/s

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