Question

Two masses, mA = 29.0 kg and mg = 42.0 kg are connected by a rope that hangs over a pulley (as in the figure). The pulley is a uniform cylinder of radius R. 0.311 m and mass 3.4 kg. Initially, mis on the ground and mp rests 2.5 m above the ground. MA 25 m Part A If the system is now released, use conservation of energy to determine the speed of me just before it strikes the ground. Assume the pulley is frictionless and that the rope does not slip. The moment of intertia of the pulley is .5MR, where is the mass of the pulley. Express your answer using three significant figures and include the appropriate units.

Answer 1

Part A

For the work-energy principle we have

W = change in K.E + change in potential energy

1/2 * m1 * v² + 1/2 * m2 * v²+ 1/2 * I * w² = gh ( m2 - m1)

1/2 * m1 * v² + 1/2 * m2 * v²+ 1/2 * 1/2 * m * r²* v² / r² = gh ( m2 - m1)

1/2 * m1 * v² + 1/2 * m2 * v²+ 1/4 m * v² = gh ( m2 - m1)

Put in the values, we have

1/2 * 29 * v² + 1/2 * 42 * v² + 1/4 * 3.4 * v² = 9.8 * 2.5 ( 42 - 29)

36.35 v² = 318.5

so,

v = 2.96 m/s

_________________________

Part B

w = v / r

w = 2.96 / 0.311

w = 9.517 rad/sec

so,

K.E = 1/2 * 1/2 * 3.4 * 0.311² * 9.517²

K.E = 7.45 J