A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 *10^-³ kg . m² is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is: A) 2.0 J B) 4.0 J C) 14 J D) 22 J E) 28 J

Question

Quizplus · Accepted Answer

The total kinetic energy is the sum of the kinetic energy of the pulley and the kinetic energy of the blocks. The kinetic energy of the pulley is 1/2 * I * w^2, where I is the rotational inertia and w is the angular velocity. The angular velocity is v/r, where v is the linear velocity and r is the radius. The kinetic energy of the blocks is 1/2 * m * v^2, where m is the mass and v is the velocity. The total kinetic energy is:1/2 * I * (v/r)^2 + 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2= 1/2 * 4.5 * 10^-3 * (2/0.03)^2 + 1/2 * 2 * 2^2 + 1/2 * 4 * 2^2= 22 J

A Pulley with a Radius of 3