Question

A 6 kg block is attached to a massless rope that passes over a frictionless pulley. The pulley can be modeled as a uniformly dense solid cylinder with a mass of 4 kg that rotates around an axis passing through its center. The other end of the rope is wound around a uniformly dense solid sphere with a mass of 10 kg and a radius of 6 cm. When released from rest the block will fall and the sphere will rotate as the rope unwinds from it. The rope will pass over the surface of the pulley without slipping. What is the effective mass of this system (in kg)?

Answer 1

The effective mass of the system is 12 kg.

Explanation:

• The effective mass of the system is given by the expression,

                    = mₓ + 1/2 m₁ + 2/5 m₂

• In the above equations the subscript x denotes block B and the subscript 2 denotes the mass of the solid sphere and the subscript 1 denotes the pulley.

• Expressing the above functions with the data given below. we have,

           = 6 kg + 1/2 (4 kg) + 2/5 (10 kg)

           =  12 kg.

with the findings above we can conclude that the effective mass of the system is 12 kg