You operate a small grain elevator near Champaign, Illinois. One of your silos u

Question

You operate a small grain elevator near Champaign, Illinois. One of your silos uses a bucket elevator that carries a full load of 700 kg through a vertical distance of 45 m. (A bucket elevator works with a continuous belt, like a conveyor belt.)

(a) What is the power provided by the electric motor powering the bucket elevator when the bucket elevator ascends with a full load at a speed of 2.4 m/s?
kW

(b) Assuming the motor is 90 percent efficient, how much does it cost you to run this elevator, per day, assuming it runs 60 percent of the time between 7:00 a.m. and 7:00 p.m. with an average load of 85 percent of a full load? Assume the cost of electric energy in your location is 18 cents per kilowatt hour.
$

Explanation / Answer

(A) speed is constant so a = 0

Fnet = F - m g = 0

F = (700 x 9.8) = 6860 N

P = F.v = 6860 x 2.4

P = 16464 Watt or 16.5 kW ....Ans

(B) Peffective = (16.5)(0.85)(0.60)/0.90

= 9.33 kW

time for which it operate per day = 12 hrs

Energy requierd = P t = 112 kWh

cost = 18 x112 = 2015 cents or 20.15 dollars

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