In the figure below, the hanging object has a mass of m1 = 0.450 kg; the sliding
ID: 2166123 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.450 kg; the sliding block has a mass of m2 = 0.865 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is ?k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table.(a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away.
. m/s
(b) Find the angular speed of the pulley at the same moment.
rad/s
Explanation / Answer
The total energy in the system is given by T = 1/2 m2 Vo^2 + 1/2 m1 Vo^2 + 1/2 I wo^2 = 1/2 m2 Vf^2 + 1/2 m1 Vf^2 + 1/2 I wf^2 - m1gd + uk m2g d where Vo,Vf are the initial and final velocity of the blocks, wo/wf are the initial and final angular velocity of the pulley, I is the moment of inertia of the pulley. w is related to V as Vo = R2 wo and Vf = R2 wf. Also, the moment of inertia is given by I = 1/2 m (R2^2 + R1^2) You have all the data now, you can go ahead and solve for Vf in the energy equation above. After that, you can calculate wf.