A cart for hauling ore out of a gold mine has a mass of 403 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 403 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.71% from the horizontalA donkey, trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 404-N force for a distance of 177 m by means of a rope that is parallel to the ground and makes an angle of 12.7° with the track. The coefficient of friction for the cart's wheels on the track is 0.0177. Use g= 9.81 mls. Find the work that the donkey performs on the cart during this process. Number 12.70 track Find the work that the force of gravity performs on the cart during the process. -- rope Number Calculate the work done on the cart during the process by friction. .71 -- track incline horizontal ground Number

Explanation / Answer

"Trudging along" implies constant velocity, which in turn implies equilibrium.

Parallel to the track, we have
net force = applied force - downslope weight - friction force
0 N = T*cos4.71º - 403kg*9.8m/s²*sin12.7º - 0.0177*403kg*9.8m/s²*cos12.7º
0 N = 0.9966*T - 936.45N
T = 939.64 N

a) The donkey does
work = 936.45N * 177m = 165750 J

b) gravity does
work = mgh = -403kg * 9.8m/s² * 177m * sin12.7º = -153682 J

c) friction does
work = µmgd = 0.0177 * 403kg * 9.8m/s² * 177m = 12373 J

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