A cart for hauling ore out of a gold mine has a mass of 425 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 425 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.31° 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 3.90 x102-N force for a distance of 185 m by means of a rope that is parallel to the ground and makes an angle of 12.1 with the track. The coefficient of friction for the cart's wheels on the track is 0.0163. Use g = 9.81 m/s Find the work that the donkey performs on the cart during this process. Number 12.10 .track Find the work that the force of gravity performs on the cart during the process. Number 31 Calculate the work done on the cart during the process by friction. track incline Number horizontal ground

Explanation / Answer

wg = -mgh

wg = -425*9.81*185sin(4.31)

wg = -5.79*10^4 J

work done by gravity

wd = 185*390cos(12.1) = 7.05*10^4 J

friction f = -0.0163*425*9.81cos(4.31) =- 67.8 N

wf = -67.8*185 = -1.25*10^4 J

or

Work done by friction = -Work done by gravity - Work done by donkey = -1.26*1064 J

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