In the figure below, the hanging object has a mass of m 1 = 0.350 kg; the slidin
ID: 1284726 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.350 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
Ei + W friction = Ef
1/2 m2 v^2 + 1/2 m1 v^2 + 1/2 I w^2 + m1 g d - u m2 g d = 1/2 m2 v^2 + 1/2 m1 v^2 + 1/2 I w^2
I = 1/2 M (R2^2 +R1^2)
w = v/R2
0.5*0.86*0.82^2 + 0.5*0.35*0.82^2 + 0.5*(0.5*0.35*(0.03^2+0.02^2))*(0.82/0.03)^2 + 0.35*9.81*0.7 - 0.25*0.86*9.81*0.7 = 0.5*0.86*v^2 + 0.5*0.35*v^2 + 0.5*(0.5*0.35*(0.03^2+0.02^2))*(v/0.03)^2
solve for v
v= 1.39 m/s
b) w = v/r = 1.39/0.03= 46.3 rad/s