In the figure below, the hanging object has a mass of m 1 = 0.445 kg; the slidin
ID: 1444596 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.445 kg; the sliding block has a mass of m2 = 0.895 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.
(b) Find the angular speed of the pulley at the same moment.
Explanation / Answer
from the conservation of energy
1/2(m1+m2)(vf^2-vi^2)+1/2I(wf^2-wi^2) = m1gh-mue*m2g
1/2(m1+m2)(vf^2-vi^2)+1/2*1/2M(R1^2+R2^2)(vf^2-vi^2)/R2^2 = m1gh-mue*m2g
from this vf = 1.27 m/sec
b) wf = vf/R2 = 1.27/0.03 = 42.33 rad/sec