Question

A hanging weight, with a mass of m₁ = 0.355 kg, is attached by a rope to a block with mass m₂ = 0.845 kg as shown in the figure below. The rope 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 rope does not stretch and does not slip on the pulley, and that the mass of the rope 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.

Use conservation of energy, treating the universe as the system of interest. What types of energy are changing? How do you relate the kinetic energy of the pulley to its moment of inertia and angular speed? What is the moment of inertia of a hollow cylinder? How is the angular speed related to the linear speed of the block? What is the internal energy change of the system, and how is it related to friction? 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

Solution in the uploaded images