You are working with a company that has the contract to design a new, 700-foot h

Question

You are working with a company that has the contract to design a new, 700-foot high, 50-story office building in Minneapolis. Your boss suddenly bursts into your office. She has been talking with an engineer who told her that when the elevator is operating at maximum speed, it would take the 6500-lb loaded elevator one minute to rise 20 stories. She thinks this is too long a time for these busy executives to spend in an elevator after returning from lunch at the Minneapolis Athletic Club. She wants you to buy a bigger power supply for the elevator. You look up the specifications for the new supply and find that it is the same as the old one except that it operates at twice the voltage. Your boss's assistant argues that the operating expenses of the new power supply will be much more than the old one. Your boss wants you to determine if this is correct. You estimate that while the elevator runs at maximum speed, the whole system, including the power supply, is 60% efficient. The cost of electricity is $0.06 per kilowatt-hour (commercial rate).

Explanation / Answer

initially elevator took 2.5 minutes to climb 50 stroies (20 stories/minute)

let us denote the power required as k*V^2=P where k is constant. k depends on electrical elements present in lift and the power supply. (note for a simple resistor power is v^2/R)

energy consumed = 2.5/60*P

system is 60% efficient so actual energy consumed = (2.5/60*P)*100/60

cost =0.06*2.5/60*P*100/60= $ 0.0025P =0.004167P

now in case of new power supply let it run at twice the speed (40 stories/minute) there fore 1.25 minutes

power required =k*(2V)^2= 4k*V^2 =4P

energy consumed =1.25/60*4P

system is 60% efficient so actual energy consumed = (1.25/60*4P)*100/60

cost=0.06*1.25/60*4P*100/60= $0.005P =.008333P

operating cost of the new power supply elevator is twice the operating cost of the older power supply . if the new system operates at twice speed. however we also see that new system saves a lot of time of the executives . we can do a cost benefit analysis if we know how many employees work in the company. and give a dollar value to time wasted in lift/ waiting for lift.

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