In a charming 19th-century hotel, an old-style elevator is connected to a counte

Question

In a charming 19th-century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 3.00 m in diameter (the figure(Figure 1) ). 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.

Part A

At how many rpm must the disk turn to raise the elevator at 30.0 cm/s ?

Part B

To start the elevator moving, it must be accelerated at 18g. What must be the angular acceleration of the disk, in rad/s2?

Part C

Through what angle (in radians ) has the disk turned when it has raised the elevator 2.70 mbetween floors?

Part D

Through what angle (in degrees ) has the disk turned when it has raised the elevator 2.70 mbetween floors?

.

Explanation / Answer

Part A. In 1 minute, the elevator rises = 30 x 60 cm = 1800 cm = 18 m
Hence, rotational speed of disk
= 18/(pi.3.0) rpm = 1.9108 rpm...............Ans.

Part B.

Angular acceleration = (18g)/(3.0/2) rad/s^2 = 120 rad/s^2
where g is taken to be 10 m/s^2

Part C. Angle turned by the disk
= 2.70/(3.0/2) rad. = 1.8 radians

Part D. Angle turned in degrees
= 1.8 x (180/pi) degrees = 103.18 degrees

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