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The calculations for determining the number of revolutions a pulley makes, the acceleration of an elevator, and the tension in the cable when an elevator falls from a height of 15 meters with a solid disc pulley. The calculations are based on the given information and the principles of physics.

Typology: Exams

2012/2013

1 / 1

Download Calculation of Revolutions, Acceleration, and Tension in a Falling Elevator and more Exams Physics in PDF only on Docsity! 4. (30 pts) An elevator is at the top of a building. Suddenly the drive shaft attached to the large pulley snaps. The pulley begins to rotate as the elevator falls. a) (10 pts) How many revolutions does the pulley make by the time the elevator has fallen a distance of 15 m? θ = s r = 15 0.625 = 24 rad 24 rad× 1 rev 2π rad = 3.82 rev 1.25 m 100 kg 2000 kg b) (15 pts) Determine the acceleration of the elevator and the tension in the cable if the pulley is a solid disc (I = MR2/2). You can neglect friction at the pulley bearings. I = 1 2 mr2 = 1 2 (100)(0.625)2 = 19.53 kg m2 Pulley Elevator 0.625T = 19.53α = 19.53 0.625 a (2000)(9.8)− T = 2000a 0.625T = 31.248a 19600− T = 2000a T = 49.99a Then, combining the last two equations and solving for T and a, 19600− 49.99a = 2000a 19600 = 2049.99a a = 9.56 m/s2 and finally, T = 478 N c) (5 pts) Is your computed acceleration correctly larger (or smaller) than gravitational acceleration g? Give a brief physical justification of your answer. Since there is an upwards force on the elevator from the rope, it is not in free-fall and should accelerate more slowly than when in free-fall. Our answer is smaller than g as expected.