In the figure below, the hanging object has a mass of m 1 = 0.380 kg; the slidin
ID: 1265326 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.380 kg; the sliding block has a mass of m2 = 0.845 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
Using work-energy method,
work done by gravity + work done by friction = change in K.E.
0.380 *9.81 *0.700 + ( -0.250 * 0.845*9.81*0.700) = (0.380 + 0.845) ( v^2 - 0.820^2) /2 + I(wf^2 - wi^2 ) / 2
wi = vi / r = 0.820 / 0.03 = 27.33 rad/s
2.32 = 1.225v^2 + I ( wf - 27.33^2)
I = 0.350 * ( 0.030^2 - 0.020^2) /2 = 8.75 x 10^-5 kg.m^2
wf = v / r = v / 0.03 = 33.33v
2.32 = (1.225v^2 ) + ( 8.75 x 10^-5 ( (33.33v)^2 - 27.33^2) )
2.32 = 1.225v^2 + 0.0972v^2 - 0.0654
v = 1.34 m/s
b) angular speed = 33.33v = 44.77 rad/s