In the figure below, the hanging object has a mass of m1 = 0.415 kg; the sliding
ID: 1906286 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.415 kg; the sliding block has a mass of m2 = 0.885 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
(a)
I(cylinder) = 0.5*0.35*(0.02^2+0.03^2) =2.275*10^-4
By conservation of energy:
initial KE = 0.5*0.415*0.82^2+0.5*0.885*0.82^2-0.25*0.885*9.8*0.7+0.5*2.275*10^-4*(0.82/0.03)^2
= -0.99573
Final KE = 0.5*0.415*V^2+0.5*0.885*V^2-0.415*9.8*0.7+0.5*2.275*10^-4*(V/0.03)^2
=0.7764V^2-2.8469
Thus:
0.7764V^2-2.8469 = -0.99573
V=1.54412 m/s
(b)
w = 1.54412/ sqrt(.02^2 + .03^2)
=42.826 rad/s