A cart for hauling ore out of a gold mine has a mass of 423 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 423 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.87° 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 436-N force for a distance of 179 m by means of a rope that is parallel to the ground and makes an angle of 13.5 with the track. The coefficient of friction for the cart's wheels on the track is 0.0173. Use g = 9.81 m/s2. Find the work that the donkey performs on the cart during this process. Number 13.5° track rope d the work that the force of gravity erforms on the cart during the process. Number 87° Calculate the work done on the cart during the process by friction. track incline horizontal ground Number

Explanation / Answer

Work done by donkey = 179 * 436*cos(13.5) J
Work done by donkey = 7.58 * 10^4 J


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

Work done by gravity = -m*g*h
Work done by gravity = - 423 * 9.8 * 179 * sin(4.87) J
Work done by gravity = - 6.3 * 10^4 J

Using Energy Conservation,
Work done by friction = Work done by gravity + Work done by donkey
Work done by friction = -6.3 * 10^4 + 7.58 * 10^4
Work done by friction = 12800 J
Work done by friction = 1.28 * 10^4 J

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