Question

A hanging weight, with a mass of m₁ = 0.365 kg, is attached by a cord to a block with mass m₂ = 0.815 kg as shown in the figure below. The cord 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 μ_k = 0.250. At the instant shown, the block is moving with a velocity of v_i = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the cord does not stretch and does not slip on the pulley, and that the mass of the cord 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

Answer 1