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Question

a cart for hauling n × M A small boat is crossing a la lXTM formu ahoo Sea rch Result × the dot product of vectors- C Search s/mod/ibis/view.php?id-4167607 Jump to... 125- Fall17- BROOKS Activities and Due Dates Chapter 7: Work and Kinetic Energy 2017 11:00 PM 30/100 eh Print Calculator St. Periodic Table Ma Sapling Learning A cart for hauling ore out of a gold mine has a mass of 423 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.57 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 411-N force for a distance of 173 m by means of a rope that is parallel to the ground and makes an angle of 14.3 with the track. The coefficient of friction for the cart's wheels on the track is 0.0163. Use g 9.81 m/s? Find the work that the donkey performs on the cart during this process. Nurnber You may have forgotten to take into account the 71103 J angle between the track and the donkey's rope 14.3 . track Find the work that the force of gravity performs on the cart during the process. rope Number 4149.63 57° Calculate the work done on the cart during the process by friction .-track incine horizontal ground Number Previous Try Again O Next Ext

Explanation / Answer

The work done by gravity is equal to the change in potential energy:

W done by gravity = -m*g*h

It's negative because gravity pulls in the opposite direction to the cart's displacement.

where h = (173 m) * sin(4.57°)

so:

W done by gravity = -(423 kg)*(9.81 m/s^2)*(173 m) *sin(4.57°)
W done by gravity = -5.72 * 10^4 J

Work done by they donkey equals the distance moved multiplied by the component of the force applied in the direction of movement:

W done by donkey = (173 m) * (411 N) *cos(14.3°)
W done by donkey = 6.89 * 10^4 J

When the force is constant and the force is parallel to movement, work equals force times displacement.

W done by friction = F * (173 m)
W done by friction = -0.0163 * mg*cos(4.57°) * (173 m)
W done by friction = -0.0163 * (423 kg) * (9.81 m/s^2) *cos(4.57°) * (173 m)
W done by friction = -1.17 * 10^4 J

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