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ame of Thron Google G G G2G-Movies S YouTube subscene-passionate S IMDb Movies, TV an G D aukali IEgo ame te Print Calculator Periodic Table Question 4 of 6 A Sapling Learning A cart for hauling ore out of a gold mine has a mass of 405 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.47 from the horizontal. A donke trudging along and to the of the track, has the unenviable job of pulling the cart up the slope with a 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. Useg 981 m/s Find the work that the donkey performs on the cart during this process. Number 12.3 track Find the work that the force of gravity performs on the cart during the process. Number 47 o Calculate the work done on the track incline cart during the process by friction. horizontal ground Number likin check Answer Next d Exit Previous Give up View HintExplanation / Answer
As we know that
work done by gravity = change in potential energy:
W done by gravity = -m*g*h
negative because gravity pulls in the opposite direction to the cart's displacement.
where h = (173 m) * sin(4.47°)
so:
W done by gravity = -(405 kg)*(9.81 m/s^2)*(173 m) *sin(4.47°)
W done by gravity = 6.67244 * 10^5 J
Work done by they donkey equals the distance moved * the component of the force applied in the direction of movement:
W done by donkey = (173 m) * (385 N) *cos(12.3°)
W done by donkey = 6.4256 * 10^4 J
Work done by friction:
As we also know that Energy is conserved,
so we know that
the work done by the donkey + the work done by gravity + work done by friction = 0
Work done by friction = -Work done by gravity - Work done by donkey
Work done by friction = - 6.67244 * 10^5 - 6.4256 * 10^4 J
Work done by friction = -7.315 * 10^5 J
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