The cable lifting an elevator is wrapped around a 1.2-m-diameter cylinder that is turned by the...

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?

Solutions

Expert Solution

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

genius_generous answered 1 year ago

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