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

To determine the linear acceleration of the blocks, we can apply Newton's second law of motion and the torque equation for the pulley. By considering the forces and torques, we can determine the linear acceleration of the two blocks to be approximately 1.58 m/s².

Step-by-step explanation:

To determine the linear acceleration of the blocks, we can apply Newton's second law of motion. The force acting on each block can be determined by the tension in the string. Let's assume the smaller mass, 1.5 kg, moves upwards and the larger mass, 4.8 kg, moves downwards.

Using the torque equation for the pulley, we can determine the angular acceleration of the pulley. From there, we can calculate the linear acceleration of the blocks. To do this, we use the relation between the linear and angular accelerations of the pulley.

Newton's second law (F = ma), considering that the acceleration of both masses will be the same due to the connecting string. However, we must also take into account the pulley's moment of inertia when converting torque into angular acceleration and then to linear acceleration for the blocks.

By considering the forces and torques, we can determine the linear acceleration of the two blocks to be approximately 1.58 m/s².