In the figure below, the hanging object has a mass of m1 = 0.500 kg; the sliding
ID: 1449747 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.500 kg; the sliding block has a mass of m2 = 0.860 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
friction force = uk N = uk m2 g = 0.25 x 0.865 x 9.8 = 2.12 N
moment of inertia, I = M (R1^2 + R2^2)/2 = 0.350 x (0.02^2 + 0.03^2) /2 = 2.275 x 10^-4 kg m^2
using work -energy theorem.,
work done by grvaity + work done by friction = change in KE
m1ghd - fd = [(m1 + m2) vf^2 /2 + Iwf^2 /2 ] - [(m1+m2)v^2 /2 + I w^2 /2 ]
(0.47 x 9.8 x 0.7) - (2.12 x 0.7) = [(0.47 + 0.865) x v^2 /2) + (2.275 x 10^-4 x (v/0.03)^2 / 2)] -
[(0.47 + 0.865) x 0.82^2 /2) + (2.275 x 10^-4 x (0.82/0.03)^2 / 2)]
1.7402 = 0.794v^2 - 0.534
v = 1.69 m/s
b) w = v / r = 1.69 / 0.03 = 56.4 rad/s