A hanging weight, with a mass
of m1 = 0.370 kg, is
attached by a string to a block with
mass m2 = 0.850 kg as
shown in the figure below. The string goes over a pulley with a
mass of M = 0.350 kg. The pulley can be
modeled as a hollow cylinder with an inner radius
of R1 = 0.0200 m, and an outer
radius of R2 = 0.0300 m; the
mass of the spokes is negligible. As the weight falls, the block
slides on the table, and the coefficient of kinetic friction
between the block and the table
is μk = 0.250. At the instant
shown, the block is moving with a velocity
of vi = 0.820
m/s toward the pulley. Assume that the pulley is free to spin
without friction, that the string does not stretch and does not
slip on the pulley, and that the mass of the string is
negligible.
A pulley of inner radius R1 and
outer radius R2 is attached to the
corner of a table such that the pulley is diagonal from the corner
and the center of the pulley is to the right of the edge. A hanging
weight of mass m1 hangs off the side
of the table and is suspended by a string that extends over the
pulley. The other end of the string is attached to a block of
mass m2, which is on the table. An arrow
between the block and the pulley points towards the pulley, and an
arrow between the pulley and the hanging mass points towards the
ground.
(a)
Using energy methods, find the speed of the block (in m/s) after
it has moved a distance of 0.700 m away from the initial position
shown.
m/s
(b)
What is the angular speed of the pulley (in rad/s) after the
block has moved this distance?
rad/s