Question

A 1.5 kg mass and a 4.8 kg mass are connected by a massless string over a pulley that is in the shape of a solid wheel having a radius 0.54 m and mass 5.7 kg. The two blocks hang vertically down. The pulley has a constant friction torque 4 Nm. Determine the linear acceleration of the blocks.

Answer 1

here,

let the linear acceleration of the blocks is a

Using second law of motion

total force = (total effective mass) * a

4.8 * 9.8 - 1.5 * 9.8 - 4/0.54 = (1.5 + 4.8 + 0.50 * 5.7 * r^2/r^2) * a

4.8 * 9.8 - 1.5 * 9.8 - 4/0.54 = (1.5 + 4.8 + 0.50 * 5.7 ) * a

solving for a

a = 2.72 m/s^2

the linear acceleration of the blocks is 2.72 m/s^2