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.

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

Explanation / Answer

The work done by gravity is equal to the change in potential energy:
Work done by gravity = - mgh
It's negative because gravity is in the opposite direction to the cart's displacement.
h = (109 m) * sin(4.11o) = 7.812 m

Work done by gravity = - 421 * 9.81 * 7.812 = - 32264.45 J

Work done by the donkey equals the distance moved multiplied by the component of the force applied in the direction of movement:
Work done by donkey = 109 * 372*cos(13.9o) = 39360.69 J

Work done by friction equals the distance moved multiplied by the frictional force which is opposite to the direction of movement. Frictional force = coefficient of friction * normal force on cart = 0.0157 * mgcos(4.11) = 64.67 N

Work done by friction = - 64.67 * 109 = - 7049.51 N

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