The physics North elevator has a mass of 340 Kg and is rated to carry up to 10 p

Question

The physics North elevator has a mass of 340 Kg and is rated to carry up to 10 passengers. It is attached to a steel rope, (actually five ropes) which goes over a circular drum in the equipment room on the roof, and back down behind the elevator to a weight ( a counterweight) mounted on similar sliding poles as the elevator. Assuming the passengers on average have a mass of 75Kg, what is the maximum tension on the rope when the elevator is stationary and loaded to capacity?

The cicular drum is provided with a reversible electric motor and an electrically operated brake system to move the elevator between floors. What is the optimum mass of the counterweight to minimize the average work done in winding the elevator, sometimes empty, sometimes fully loaded, between floors?

What then would be the minimum horsepower of the motor needed to wind a fully loaded elevator from the subasement to the fourth floor Theory Institute in 25 seconds? (Assume that it is 6 floors of three meters height per floor). ( one horsepower is 746 watts )

Explanation / Answer

The mass of the elevator M = 340kg The mass of each passenger m = 75kg the no.of passengers carry n = 10 therefore the maximum tension T = (M + nm) g = ( 340 + (10)(75))(9.8) = 10682 N The optimum mass of the counterweight is M + m/2 = 340 + (75*10)/2 = 715kg Therefore the mass is 1090 - 715 = 375kg The wok needed W = mgh = (375kg)(9.8)(18m) =66150J This be done in time t = 25s therefore power P = W/t = 66150 / 25 = 2646 W and 1hp = 746w so the power p = 3.55hp

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