Question

A block is attached to a light string that is wrapped around a cylindrical spool.

A) the spool consists of a uniform solid disk of radius r= 0.500m and a rim along the outside edge of the disk at a radius of r = 0.500m. The mass of the solid disk is mdisk= 4.00 kg and the mass of the rim is also mrm= 4.00 kg. What is the moment of inertia of the entire spool?

B) the block is released from rest and travels a distance of mdisk = 4.00 kg before hitting the ground. While traveling, it unwinds the spool. What is the velocity of the block before it hits the ground?

C) how long does it take the block to drop h = 5.0 m after it is released from rest?

Answer 1

A)   the moment of inertia of the entire spool = 1/2 * 4.00 * 0.5² + 4 * 0.5²

                                                                     = 1.5 kg.m²

B)   Applying conservation of energy -

=> 4 * 9.8 * 5 = 1/2 * 4 * v² + 1/2 * 1.5 * (v/0.5)²

=> v = 6.26 m/s

Thus,   velocity of the block before it hits the ground =   6.26 m/s

C)   long does it take the block to drop = 6.26/3.918

                                                             = 1.597 sec