In a charming 19th-century hotel, an old-style elevator is connected to a counte
ID: 1471878 • Letter: I
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 (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. At how many rpm must the disk turn to raise the elevator at 35.0 cm/s? To start the elevator moving, it must be accelerated at 1/8 g. What must be the angular acceleration of the disk, in rad/s^2? Through what angle (in radians) has the disk turned when it has raised the elevator 2.60 m between floors?Explanation / Answer
Part-A
we have the relation =r*omega
Omega = v/r =35/125 = 0.28/sec =2.675 rpm
PART-B
Angular Acceleration = a/r = g/8/125 = 0.0098 rad/s2
PART-C
Through what angle (in radians ) has the disk turned when it has raised the elevator 3.10m between floors?
angle = h/(2PI*r)*2PI = h/r = 2.6/1.25 = 2.08 rad
PART-D
Through what angle (in degrees ) has the disk turned when it has raised the elevator 3.10m between floors?
angle = 2.08 rad*360/(2PI) °/rad = 119.23 °