Question

The cable lifting an elevator is wrapped around a 1.1m diameter cylinder that is turned by the elevator's motor. The elevator is moving upward at a speed of 2.6 ms. It then slows to a stop, while the cylinder turns one complete revolution. How long does it take for the elevator to stop? Express your answer to two significant figures and include the appropriate units.

Answer 1

t = 2.7 s

Step-by-step explanation:

This is a kinematics problem.

How the elevator reduces its speed to zero by a distance equal to the length of the cylinder

y = 2π r = 2 π d / 2

y = π d

y = π 1.1

y = 3,456 m

now we can look for the acceleration of the system

v² = v₀² - 2 a y

0 = v₀² - 2 a y

a = v₀² / 2y

a = 2.6² / 2 3.456

a = 0.978 m / s²

now let's calculate the time

v = v₀ - a t

0 = v₀ - at

t = v₀ / a

t = 2.6 /0.978

t = 2.658 s

ask for the result with two significant figures

t = 2.7 s