An escalator is used to move 20 passengers every minute from the first floor of a department store to the second.The second floor is located 5.20 meters above the first floor. The average passenger's mass is 54.9 kg. Determine the power requirement of the escalator in order to move this number of passengers in this amount of time.
3 Answers
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Time = 1 minute = 60 s
Energy required = mgh = 20*54.9*9.8*5.2
Power = Energy /Time = 20*54.9*9.8*5.2/60 = 932.6 W
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A good strategy would involve determining the work required to elevate one average passenger. Then multiply this value by 20 to determine the total work for elevating 20 passengers. Finally, the power can be determined by dividing this total work value by the time required to do the work. The solution goes as follows:
W''1 passenger'' = F • d • cos(0 deg)
W''1 passenger'' = (54.9 kg • 9.8 m/s2) • 5.20 m = 2798 J (rounded)
W''20 passengers'' = 55954 J (rounded)
P ='W''20 passengers'' / time = (55954 J) / (60 s)
P = 933 W
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P=w/t,w=mgh
w=54.9*20*9.81*5.2=50011.18N
t=((2*9.81)/5.2)^1/2=1.942sec
p=50011.18/1.942=_____kw
