The Taipei 101 in Taipei, Taiwan is presently the fifth tallest building in the

Question

The Taipei 101 in Taipei, Taiwan is presently the fifth tallest building in the world, standing stories above the ground. However, it's now best known for having some of the fastest elevators in the world. These elevators carry passengers to the observation deck on the 89^th floor, and can reach a constant maximum speed of 1,010. m/min on ascent, and 600 m/min on descent, for many floors in a row. An elevator basically consists of a cab which holds the passengers, tied to a cable which is tied to a counterweight at its other end, as shown in the figure. The cable is draped over a pulley, and a winch which is rotated by a motor. The cable cannot slip on the winch. Take the pulley to be massless and frictionless. The maw of the empty cab is 2,400 kg. It can hold a maximum payload of 1,600 kg. The counterweight has a mass of 3.040 kg. a) If each floor is 4.34 m high, how powerful a motor is required for the elevator to reach maximum speed on ascent? (On ascent, it readies its maximum speed in 13.0seconds after ascending 26 floors) Give your answer in horsepower. b) How powerful a motor is needed for the elevator to reach the maximum speed on descent? (On descent, it reaches its maximum speed in 7.00seconds after descending 9floors.) Give your answer in horsepower. c) The 2017 Chevrolet Corvette Grand Sport has a curb weight of 3.452 lb. It has a naturally aspirated, 16 valve push rod V-8 engine which develops a peak of 450hp @ 6000 rpm and 465 lb-ft @ 4600 rpm. It's top speed is 170. mph. If it can do 0-60mph in 3.7seoonds, what's the average horsepower it uses in accelerating from 0-60 mph? d) If the Corvette can do 0-1/4 mile in 12.1 seconds @ 117.0 mph, what's the average horsepower it uses in doing the 1/4 mile? e) Compare your answers in Parts a and b to your answers in Parts c and d. Explain the fact that the loaded cab with a weight of 8,8181b accelerates to 37.7 mph. while the Corvette with a weight of 3.452 lb accelerates to 117 mph, in view of the horsepowers you found for each.

Explanation / Answer

total height=26*4.34=112.84 m

initial velocity=0 m/s

final velocity=1010 m/min=16.83 m/s

we get acclerarion=v/t=1.29 m/s^2

force motor need to provide=toal mass*(g+a)=78073.6 N

power=force*velocity=1761.36 HP

while coming down

a=10/7=1.43 m/s(downwards)

force motor need to apply upwards is F

(2400+1600+3040)*9.8-F=(2400+1600+3040)a

F=7031.62 N

power=94.26 HP

(c) let average power be P

v=60 mph=26.82 m/s

energy=P*t=0.5*mv^2=0.5*(3452/2.2)*(26.82)^2

P=204 HP

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