A loaded ore cart has a mass of 950 kg and rolls on rails with negligible fricti

Question

A loaded ore cart has a mass of 950 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0 degree above the horizontal. The car accelerates uniformly to a speed of 2.20 m/s in 12.0 s and then continues at constant speed. What power must the winch motor provide when the car is moving at constant speed? What maximum power must the winch motor provide? What total energy has transferred out of the motor by work by the time the car moves off the end of the track, which is 1250 m long?

Explanation / Answer

a) When car is moving with constant moving ,a = 0

using F = ma

T - mgsin30 = 0

T = 4659.75 N

Power = T v ( in case of constant speed)

= 4659.75 x 2.20 = 10251.45 Watt

b) when cart is accelerated,

a = 2.20 / 12 = 0.183 m/s^2

T - mgsin30 = ma

T = 950(9.81sin30 + 0.183 ) = 4833.92 N

at last when v is just 2.20 m /s

P = Tv = 10634.62 W ................Max. POwer

distance traveled = 0.183 x 12^2 /2 = 13.176 m

work done = ( 4833.92 x 13.176 ) =63691.73 J

after that power is 10251.45W for 1250 - 13.176 = 1236.82 m

time = 1236.82 / 2.20 =562.19 sec

Energy = 562.19 x 10251.45 = 5763290.63 J

total energy = 5826982.36 W

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