A 127.6 N carton is pulled up a frictionless baggage ramp inclined at 27.0 above

Question

A 127.6 N carton is pulled up a frictionless baggage ramp inclined at 27.0 above the horizontal by a rope exerting a 76.6 N pull parallel to the ramp's surface. The carton travels 5.60 malong the surface of the ramp.

Calculate the work done on the carton by the rope.

Calculate the work done on the carton by the gravity.

Calculate the work done on the carton by the normal force of the ramp.

What is the net work done on the carton?

Suppose that the rope is angled at 47.6 above the horizontal, instead of being parallel to the ramp's surface. How much work does the rope do on the carton in this case?

Explanation / Answer

Weight W = mg

mass = W/g = 127.6/9.81 = 13 kgs

1. work done By Rope W = Fd = 76.6* 5.6 = 428.9 J
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2. Work Done By Gravity W = mgh cos theta
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W = 127.6 * 5.6 * sin 27 = 324.4 Joules
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3. Work DOne By Normal Force W = Nd

W = Nd cos 90 = 0

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4. Net Work done W = 428.9 - 324.4 = 104.5 J

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5. Work Done By force W = F d

W = mg d cos (47.6 - 27)

W = 76.6 * 9.81 * cos 20.6

W = 703.39 N

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