pling A cart for hauling ore out of a gold mine has a mass of 449 kg, including

Question

pling A cart for hauling ore out of a gold mine has a mass of 449 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.83 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 4. force for a distance of 155 m by means of a rope that is parallel to the ground and makes an angle of 14.5 with the track. The coefficient of friction for the cart's wheels on the track is 0.0161. Useg 9.81 m/s2 Find the work that the donk click to edit h the cart during this process. Number 68428.67 14.5 o track Find the work that the force of gravity rope performs on the cart during the process. Number 43290 ,83 o Calculate the work done on the track incline cart during the process by friction. horizontal ground Number 43392.15

Explanation / Answer

Force due to mass along the track = 449*9.81 sin4.83 = 370.873 N

Force due to mass perpendicular to the track = 449*9.81* cos4.83 = 4389.05 N

Force due to 456 N perpendicular to track = 456 sin 4.83 = 38.4 N

So normal force = 4389.05 + 38.4 = 4427.45 N

Frictional force = 4427.45 * 0.0161 = 71.2818 N

Force due to 456 N parallel to track plan = 456 cos 4.83 = 454.38 N

Force due to 456 cos 4.83 N along the track line, parallel to track = 456 cos 4.83 cos 14.5 = 439.9076 N

Distance moved along the track = 155 m

Work done by donkey on cart = force of donkey along motion * distance = 439.9 * 155 = 68185.68 J

Work done by gravity = force of gravity along motion * distance = -370.873 * 155 = - 57485.33 J

Work done by friction = frictional force along motion * distance = -71.2818 * 155 = - 11048.69 J

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