Question

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 2.6 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?

Answer 1

Diameter d = 1.2 m

Radius r = d/2

             = 0.6m

Circumference of the circular cylinder for one revolution S = d

     S = (22/7) 1.2 m

        = 3.77 m

Initial angular speed of the cylinder = v/ r

                                                       = 2.6 / 0.6

                                                       = 4.333 rad/s

Final angular speed ' = 0

Angular displacment for one revolution = 2 rad

From the relation ' ² - ² = 2

Angular accleration = [ ' ² - ² ] / 2

                                = (0-18.77)/(2 x2)

                                = - 1.494 rad/s ²

Required time t = ( ' - ) /

                        = (0-4.3333) / (-1.494)

                        = 2.9 s