A cart for hauling ore out of a gold mine has a mass of 417 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 417 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.79° 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 429-N force for a distance of 101 m by means of a rope that is parallel to the ground and makes an angle of 14.7° with the track. The coefficient of friction for the cart's wheels on the track is 0.0179. Use g = 9.81 m/s2.

Find the work that the donkey performs on the cart during this process in Joules.

Find the work that the force of gravity performs on the cart during the process in Joules.

Calculate the work done on the cart during the process by friction in Joules.

Please show work.

Explanation / Answer

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

W done by gravity = -m*g*h

                              = -417*(101 m) * sin(4.79)=-3.52*10^3 J

Work done by the donkey:

W done by donkey = (101 m) * (429 N) *cos(14.7) = 4.2 * 10^4 J

Work done by friction:

The magnitude of the force of friction is:

F = -0.0179* 417*9.8*cos(4.79)=-73 N

W done by friction = F * (101 m)=-73*101

W done by friction = -7.30 * 10^3 J

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