Lecture 9, #4 – Rotational and Translational Motion

PROBLEM DESCRIPTION

The Carnegie Museum of Natural History has hired you to move a baby grand piano (m = 240 kg) into the Dinosaur Hall for a wedding party. One part of the job requires you to move the piano up an incline that is 30° above the horizontal. You rig up a system to move the piano up the incline by releasing a block (same mass as the piano) that is attached to the piano by a rope over a pulley. The system is shown below. The pulley has radius 1.5 m, and moment of inertia 22.5  kg-m². The mass of your rope is negligible compared to the mass of the piano and the pulley. You have put non-stick sliders on the feet of the piano, so you can neglect friction between the piano and the ramp. Assume that the rope slides over the pulley without slipping.

The rope will break if the tension in the rope is larger than some threshold value. What should the minimum threshold value for the rope be?

Note: This is a very long video example, mostly because of the Algebra.

ANSWER:
Tension in rope on side attached to piano = 1752 N
Tension in rope on side attached to block = 1776 N