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 4.59 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 525-N force for a distance of 111 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 function for the cart's wheels on the track is 0.0101. Take 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

Knowns: m = 421-kg ; g = 9.8 m/s^2 ; h=d=111m ; Force of Donkey = Fd = 525-N ;
Force of friction = Ff = 0.0101 ; angle of track = 4.59 degrees ; angle of rope 14.3


Work done by the donkey equals the distanced he moved it * the component of the force applied in the direction of the movement:
W = (Fd)d = (525-N) * cos(14.3) *(111m) = 5.65 * 10^4 J

Work done by gravity:
W = -mgh = -(421-kg)(9.81 m/s^2)((111m * (sin 4.59)) = -3.67 * 10^4 J

Work done by friction:
W = -( Ff)d = -(0.0101)(mg cos 4.59)(111m)
= -(0.0101)(421-kg)(9.81 m/s^2)(cos 4.59)(111m) = - 4.62 * 10^3

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