In: Physics
The cable lifting an elevator is wrapped around a 1.2-m-diameter cylinder that is turned by the elevator's motor. The elevator is moving upward at a speed of 1.3 m/s . It then slows to a stop, while the cylinder turns one complete revolution.
How long does it take for the elevator to stop?
Diameter of the cylinder = D = 1.2 m
Radius of the cylinder = R = D/2 = 0.6 m
Speed of the elevator = V = 1.3 m/s
Initial angular speed of the cylinder = 1
V = 1R
1.3 = 1(0.6)
1 = 2.167 rad/s
Final angular speed of the cylinder = 2 = 0 rad/s (Comes to rest)
The cylinder makes 1 revolution before coming to rest.
Angle traveled by the cylinder = = 2 = 6.283 rad
Angular acceleration of the cylinder =
Time taken to come to a stop = T
22 = 12 + 2
(0)2 = (2.167)2 + 2(6.283)
= -0.373 rad/s2
2 = 1 + T
0 = 2.167 + (-0.373)T
T = 5.81 sec
Time taken by the elevator to come to a stop = 5.81 sec