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 28.5° above the horizontal. The car accelerates uniformly to a speed of 2.05 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?

kW

(b) What maximum power must the motor provide?

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? J

Answer 1

given m = 950kg, angle = 28.5 deg,

a) F = m*g*sin28.5 = 950*9.81* sin28.5 = 4446.8 Newtons
once it reaches constant speed,
in one second, it moves 2.05 meters, so work = 4446.8*2.05 = 9115.9 Joules
since this is one second, that is a rate of 9115.9 watts

b) While accelerating, it must provide additional work.
average acceleration is 2.05/12.5 = 0.164 m/s²
distance = (1/2) *0.164*10.5*10.5 = 12.8 m
F = ma = 950*0.164 = 155.8 N
155.8 N over a distance of 12.8m is 1994.2 J. The power to do this is 1994.2/12.5 = 159.54 W
total power = 9115.9 +159.54 = 9275.4 W
c) for a distance of 1250m, = 1250*4446.8 = 5.558MJ