A loaded ore car has a mass of 950 kg and rolls on rails with negligible frictio

Question

A loaded ore car 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 30.5 degree above the horizontal. The car accelerates uniformly to a speed of 2.25 m/s in 12.5 s and then continues at constant speed. (a)What power must the winch motor provide when the car is moving at constant speed? find the force that must be exerted by the cable in order to keep the cart moving at constant velocity and use that force to find the power required. kW (b)What maximum power must the motor provide? Use the given information to find the acceleration of the cart and the total force that the cable must exert. Then use that information to find the maximum power expended. kW (c)What total energy transfers out of the motor by work by the time the car moves off the end of the track, which is of length 1, 250 m?

Explanation / Answer

The motor overcomes the component of weight directed along the track during the period of constant speed.

F = W*sin(30.5) = m*g*sin(30.5) = 4725.18 N

(a) P = F*v = 4725.18*2.25 = 10.63e3 W

During the initial part, the acceleration is

a = v/t = 2.25/12.5 = 0.18 m/s**2

and the force applied (F0) by the winch to get this acceleration is

F0 - W*sin(30.5) = m*a
F0 = 4725.18 + 950*.18 = 4896.18 N

The winch applies this force right up to the end of the initial phase when the speed has just reached 2.25 m/s

(b) P_peak = F0*vmax = 4896.18*2.25 = 11.01e3 W

(c) U_total = m*g*d*sin(30.5) = 950*9.8*1250*sin(30.5) = 5.91e6 J

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