Solved: A motor supplies a constant torque M = 6 kN # m to

Problem 18-16

A motor supplies a constant torque M = 6 kNm to the winding drum that operates the elevator. If the elevator has a mass of 900 kg, the counterweight C has a mass of 200 kg, and the winding drum has a mass of 600 kg and radius of gyration about its axis of k = 0.6 m, determine the speed of the elevator after it rises 5 m starting from rest. Neglect the mass of the pulleys.

                                                              Step by Step Solution

Step  1 of 4

First we will find out the Kinetic Energy

Since the system starts from rest, the kinetic energy at position 1 is zero, and the rotational kinetic energy at position 2 is

Where  is the winding drum mass,

 is the elevator mass,

  is the counterweight mass

  are the velocities of elevator and counterweight respectively and they are equal but in opposite directions

 is the radius of gyration of the winding drum.