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 900 kg through a vertical distance of 41 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?

(b) Assuming the motor is 80 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

part A : power = mgh/t    = force * velcoity

m is mass = 900 kg

g is accclertion due to grvaity

h is hheight

t is time

Work done W = mgh

time = distance/speed

t = 41/2.4   = 17.08 secs

Power = (900* 9.8 * 41/17.08) = 21.17 kWatts
----

part B :

Cost = 0.15*(0.8)*(18*60*60*0.6)(0.8*21170)

Cost= 79016.6 cent

cost =   $ 790.16

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