A cart for hauling ore out of a gold mine has a mass of 421 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 421 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.11° 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 372-N force for a distance of 109 m by means of a rope that is parallel to the ground and makes an angle of 13.9° with the track. The coefficient of friction for the cart's wheels on the track is 0.0157. 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.

Explanation / Answer

now we find the work done by the gravity

Wg=mghsin(theta)

=421*9.8*109*sin(4.11)

=-32231.6 J

now we find the work done by the donkey

Wdonkey =Fhcos(theta)

=372*109*cos(13.9)

=39360.6 J

now we find the work done by the friction

Wf=0.0157*421*9.8*cos(4.11)*109=7042.3 J

work done by force of gravity =-32231.6-39360.6=711592.2 J

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