Question

A skyscraper in Manhattan has an elevator that weighs 1000 kg when loaded. The elevator is lifted at a constant rate to 480m above the ground by an electric winch motor. The drum of the winch motor is a solid uniform cylindrical drum in which a steel cable can wrap around it. The mass of the drum is 500 kg and has a diameter of 1 m. It takes the elevator a total of 120 s to get to the top. For simplicity sake assume the steel cable is mass-less.

Note: give all answers as positive values, you may have to consider direction for your calculations but if you get a negative value I just want the positive alternative.

Part 1. What is the Tension in the cable attached to the drum? Give your answer to the nearest Newton.

N

Part 2. What is the Rotation Speed of the drum? And at what Velocity is the elevator rising throughout? (Hint: Remember it lifted at a constant rate) Give your answers to the nearest rad/s and m/s

rad/s

m/s

Part 3. What amount of Torque must the winch produce in order to lift this elevator load? (Hint: Net torque is 0, so the torque the winch is producing is equal to the torque from the mass) Give your answer to the nearest whole number.

   N*m

Part 4. What amount of Work is done to move this elevator?  Give your answer to the nearest kilo-Joule ( 1 kJ = 1000 J).

kJ

Part 5. How much Power must the winch doing the lifting have? Give your answer to 3 significant digits in terms of kW.

kW

Part 6. What is the Moment of Inertia of the shaft? (Hint: I = 1/2 MR²for this shaft) Give your answer to 3 significant digits.

kg*m²

Part 7. What is the Kinetic Energy of the rotating drum? Kinetic Energy of the rising elevator? Give your answers to the nearest Joule.

Drum:  J

Elevator:  J

Part 8. What is the Potential Energy of the elevator setting at the top? Give your answer to the nearest kJ.

kJ

Part 9. If the gears in the winch snap and the elevator begins to freely fall and the drum spins to unwind as the elevator pulls the cable down, what is the maximum velocity the elevator achieved while falling? Give your answer to 3 significant digits.

Velocity:  m/s

Part 10. What is the Kinetic Energy of both the elevator and drum right before the elevator strikes the ground? Give your answer to the nearest kJ.

Elevator:  kJ

Drum:  kJ

Answer 1