A cart for hauling ore out of a gold mine has a mass of 405 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 405 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.65° from the horizontal. A 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 151 m by means of a rope that is parallel to the ground and makes an angle of 13.7° with the track. The coefficient of friction for the cart's wheels on the track is 0.0177. Use g = 9.81 m/s2. Find the work that the donkey performs on the cart during this process. _____J Find the work that the force of gravity performs on the cart during the process. ______J Calculate the work done on the cart during the process by friction. _____J

Explanation / Answer

The work done by gravity is equal to the change in potential energy:

W done by gravity = -m*g*h

It's negative because gravity pulls in the opposite direction to the cart's displacement.

h = (151 m) * sin(4.65°)  

W done by gravity = -(405 kg)*(9.81 m/s^2)*(151 m) *sin(4.65°)
W done by gravity = -4.86 * 10^4 J

W done by donkey = (151 m) * (404 N) *cos(13.7°)
W done by donkey = 5.927 * 10^4 J


Work done by friction:

F = -0.0177 * mg*cos(4.65°)

The negative sign is because force is in the opposite direction of displacement.

W done by friction = F * (151 m)
W done by friction = -0.0177 * mg*cos(4.65°) * (151 m)
W done by friction = -0.0177 * (405 kg) * (9.81 m/s^2) *cos(4.65°) * (151 m)
W done by friction = -1.058 * 10^4 J

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