A cart for hauling ore out of a gold mine has a mass of 445 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 445 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.39 degree 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 416-N force for a distance of 147 m by means of a rope that is parallel to the ground and makes an angle of 14.3 degree with the track. The coefficient of friction for the cart's wheels on the track is 0.0159. Use g = 9.81 m/s2. Find the work that the donkey performs on the cart during this process. Find the work that the force of gravity performs on the cart during the process. Calculate the work done on the cart during the process by friction.

Explanation / Answer

force along track = 416cos14.3 = 403.11 N

force perpendicular to track = 416sin14.3 = 102.75

net normal reaction = 102.75 + 445*9.8*cos4.39 = 4358.95 N

friction force = 0.0159*4358.95 = 69.30 N

gravity force = 445*9.8*sin4.39 = 333.81

work done by donkey = 403.11*147 = 59257.17 J

work done by gravity = 333.81*147 = 49070.07 J

work done by friction = 69.30*147 = 10187.1 J

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