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 4.17° 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 374-N force for a distance of 123 m by means of a rope that is parallel to the ground and makes an angle of 12.3° with the track. The coefficient of friction for the cart's wheels on the track is 0.0167. Use g = 9.81 m/s2.

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

___________J

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

___________J

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

___________J

Explanation / Answer

given,

mass = 417 kg

force = 354 N

distance = 123

angle = 12.3 degree

coefficient of friction = 0.0167

work done = F.d

work done by donkey = 374 * 123 * cos(12.3)

work done by donkey = 44946.05 J

gravitational force = mg * sin(4.17)

gravitational force = 417 * 9.81 * sin(4.17)

work done by gravity = 417 * 9.81 * sin(4.17) * 123

work done by gravity = 36588.122 J

frictional force = 0.0167 * 417 * 9.81 * cos(4.17)

work done by friction force = 0.0167 * 417 * 9.81 * cos(4.17) * 123

work done by friction = 8380.605 J

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