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Solved: In a charming 19th-century hotel, an old-style
Chapter 9, Problem 18E(choose chapter or problem)
In a charming 19th century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 2.50 m in diameter (Fig. E9.18). 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 at 25.0 cm/s?
(b) To start the elevator moving, it must be accelerated at \(\frac{1}{8} g\). What must be the angular acceleration of the disk, in \(\mathrm{rad} / \mathrm{s}^{2}\)?
(c) Through what angle (in radians and degrees) has the disk turned when it has raised the elevator 3.25 m between floors?
Questions & Answers
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 2.50 m in diameter (Fig. E9.18). 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 at 25.0 cm/s?
(b) To start the elevator moving, it must be accelerated at \(\frac{1}{8} g\). What must be the angular acceleration of the disk, in \(\mathrm{rad} / \mathrm{s}^{2}\)?
(c) Through what angle (in radians and degrees) has the disk turned when it has raised the elevator 3.25 m between floors?
ANSWER:
Solution 18E
Step 1:
Free body diagram is shown below.
One revolution of the disk will lift the elevator by the distance of one circumference of the disk.