A cart for hauling ore out of a gold mine has a mass of 435 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 435 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.01° 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 387-N force for a distance of 129 m by means of a rope that is parallel to the ground and makes an angle of 14.5° 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. Number 14.5 .track ...rope Find the work that the force of gravity performs on the cart during the process. Number 01o Calculate the work done on the cart during the process by friction. -track incline horizontal ground Number

Explanation / Answer

Work done = F.d = F d cos(theta)

Work done by donkey = (387) ( 129) (cos14.5 cos4.01)

= 48215 J ........Ans

Work done by gravity = (435 x 9.81) (129) (sin4.01)

= 38496 J .......Ans

friction force = f = uk N

N = (387 sin4.01) + (435 x 9.81 x cos4.01) = 4284 N

f = 76.7 N

Work done = - 76.7 x 129 = - 9892 J ........Ans

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