Fall : Analytical PhysicsI PHY-133 Section 60 The Taipei 101 in Taipei, Taiwan s
ID: 1770799 • Letter: F
Question
Fall : Analytical PhysicsI PHY-133 Section 60 The Taipei 101 in Taipei, Taiwan stories above the ground. However, it's now best in the world. These elevators for having some of the fastest elevators carry passengers to the observation deck on the 89th floor, and can reach a constant maximum speed of 1,010. m/min on ascent, and 600 m/min on descent, for 4) is presently the fifth tallest building in the world, standing 101 4) a. e many floors in a row An elevator basically consists of a to a counterweight at its other end, as shown in the figure. The cable is draped over a pulley, a winch which is rotated by a motor. The cable cannot slip on the winch. Take the pulley e. to be massless and frictionless. e mass of the empty cab is 2,400kg. It can hold a maximum payload of 1,600kg. 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 reaches its maximum speed in 13.0 seconds after ascending 26 floors.) Give your answer in horsepower b) How powerfial a motor is needed for the elevator to reach the maximum speed on descent? (On descent, it reaches its maximum speed in 7.00 seconds after descending 9 floors.) Give your ariswer in horsepower. c) The 2017 Chevrolet Corvette Grand Sport has a curb weight of 3,4521b. It has a naturally aspirated, 16 valve pushrod V-8 engine which develops a peak of 450 hp6000 rpm and 465 lb-ft a 4600 rpm. It's top speed is 170. mph. If it can do 0-60 mph in 3.7 seconds, 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 117.0mph, what's the average horsepower it uses in doing the 1/4 mile? Compare your answers in Parts a and b to your answers in Parts e and d. Explain the fact e) that the londed cab with a weight of 8,818 lb accelerates to 37.7 mph, while the Corvette with a weight of 3,452lb accelerates to 117 mph, in view of the horsepowers you found for each. Motor Winch Pulley Cab Counterweight Figure 4 - A simplified diagram of an elevator.Explanation / Answer
total weight of the elevator = 2400 +1600 = 4000 kg
counter weight = 3040 kg
both move with the same speed max.speed = 1010 m/min on ascent
=16.83 m/s
c) weight = 3452 lb
speed = 60mph = 88 ft/s
Total energy supplied =0.5*3452*882 /32 = 417693 foot-pound
time = 3.7 s
Power =417693/3.7*550 = 205 HP
d) speed =117 mph = 171.6 ft/s
time t=12.1s
power = (0.5*3452*171.62 /32)/(12.1*550) = 238.66 HP
Total KE = 0.5*7040*16.832 =997036 J
When the elevator moves up the counter weigth moves down
change is PE = mgh
net mass moved up = 4000-3040 = 960 kg
h = 4.34*26 = 112.84m
PE = 960112.84*9.8 = 1061599J
Total energy supplied = 2058635 J
time t = 13 s
Power = 2058635/13 =158357 W
= 211 HP
While descending
max.speed = 600 m/min = 10 m/s
KE =0.5*7040*102 = 352000 J
net mass descent = 960 kg
height h = 4.34 *9 = 39.06 m
PE change = 960*9.8*39.06 = 367475 J
while descending change in PEis -ve , hence net enrgy supplied
=352000 - 367475 = -15475 J
while descending the motor power is used to retard the elevator from free falling
time t = 7 s
power = 15477/7*750 = 2.95 HP
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