In the figure below, the hanging object has a mass of m1 = 0.470 kg; the sliding
ID: 1443718 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.470 kg; the sliding block has a mass of m2 = 0.810 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.
Explanation / Answer
The change in kinetic energy of the system {block m1+block m2+pulley} is
equal to the net work done on the system. Only friction on the block m2 and
gravitation force on block m1 have non-zero work. On the other hand, angular
speed of the pulley is related to the sped of the objects =v/R2
and a pulley
of a hollow cylinder shape has a moment of inertia of : 1/2M(R1^2 + R2^2)
1/2(m1 + m2)(v^2f v^2i) + 1/2I(^2f ^2i) = m1gh µkm2g
1/2(m1 + m2)(v^2f v^2i) + 1/2 1/2M(R1^2 + R2^2)v^2f v^2iR2^2= m1gh µkm2g
Rearranging should give :
vf = sqrt v2i +m1gh µkm2g/1/2*(m1 + m2) + 1/2M(1 + R1^2/R2^2)
With the given numerical values we get :
vf = 1.48 m/s
The angular speed of the pulley :
f =vf/R2
=1.48/0.030
= 49.33 rad/s