In a charming 19th century hotel, an old-style elevator is connected to a counte
ID: 1697141 • Letter: I
Question
In a charming 19th century hotel, an old-style elevator is connected to a counter-weight by a cable that passes over a rotating disk 2.50m in diameter. The elevator is raised and lowered by turning the disk, and the cable does not slip on the rim of the disk but turns with it.
a) At how many rpm must the disk turn to raise the elevator 25.0cm/s?
b) To start the elevator moving it must be accelerated at 1/8g. What must be the angular acceleration of the disk in rad/s^2
c) Through what angle (in radians and degrees) has the disk turned when it has raised the elevator 3.25m between floors?
Explanation / Answer
One revolution of the disk will lift the the elevator by the distance of one circumference of the disk. (1 rev = pi* D meters) w (rpm) = 15 cm/s * (60 sec/1 min) * (1 m/100 cm) * (1 rev/pi* 2.50 m meters) w(rpm) = 1.15 rev/min Angular acceleration (A) = acceleration/radius (I think?) A = (1/8)(9.81 m/s^2)/(1.25 m) A = 0.981 rad/sec^2