Question

A block of mass 2. 0 kg is hanging from a massless cord that is wrapped around a pulley (i =1. 1 x10-3 kg. M2), as the drawing shows. Initially, the pulley is prevented from rotating, and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0. 040 m during the block's descent.

Answer 1

To find the acceleration, tension, and speed in this system, Newton's second law and equations for free fall can be used.

Step-by-step explanation:

To determine the acceleration of the system, we need to apply Newton's second law for both blocks. Let's assume the direction of motion for the hanging mass is downward and the block on the table is moving to the right.

(a) The net force on the hanging mass is the tension in the rope minus the weight of the mass:

T - m_2g = m_2a

The net force on the block on the table is the force of tension minus the force of kinetic friction:

m_1a = T - μ_k m_1g

(b) To find the tension in the rope, we can substitute the acceleration from part (a) into one of the equations and solve for T.

(c) The speed with which the hanging mass hits the floor can be found using the equation for final velocity of an object in free fall:

v_f² = v_i² + 2gh