An elevator hangs from a cable that goes through a pulley of diameter 6.4 feet. If the elevator climbs 215 feet in 13.8 seconds, determine the angular velocity of the pulley in revolutions per minute.
2007-10-21 10:28:58 · 3 answers · asked by aha51806 2 in Science & Mathematics ➔ Mathematics
This comes down to calculating the circumference of the pulley and converting 215ft/13.8 sec into revolutions/sec.
D = 6.4ft Circumference = Pi * D = 6.4 * 3.28 = 20.992 ft
Thus for every 20.992 ft the elevator climbs, the pulley does 1 revolution.
Ang Vel = 215 ft/13.8 sec/20.992 ft/rev = 0.74 revolutions/sec
2007-10-21 10:35:56 · answer #1 · answered by Scott W 3 · 0⤊ 1⤋
First, know that 215 feet of cable will pass around the circumference of the pulley. So, what's circumference? It's diameter*pi.
C = 6.4pi
And what's angular velocity? Well, it gives you units - revolutions per minute. One revolution will occur with 6.4*pi feet of cable.
So divide 215/6.4pi to find out how many revolutions will occur.
That's 105.5379 revolutions, over
13.8 seconds / 60 (seconds/minute) = .23 minutes
105.5379 revolutions / .23 minutes = 458.860 revolutions per minute
2007-10-21 17:38:05 · answer #2 · answered by cathaychris 3 · 0⤊ 0⤋
Circumference = pi*d = 6.4pi
215/(6.4pi) = 10.69 revolutions
10.69 revolutions per 13.8 seconds = 10.69*60/13.8
= 46.06 rpm
2007-10-21 17:38:35 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋