PE question

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Oct 5, 2011
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How much work is done by gravity on a 50-kg box that is pushed up a 5 m ramp to a new elevation 2 m higher than its initial height?

A. 2500 J
B. 1000 J
C. -1000 J
D. -2500 J


C) -1000 J

The work done by gravity is independent of the force provided by the people or the pathway. The work done by gravity is positive when an object moves downhill and is negative when an object moves uphill. In this problem, the box is moved uphill, so the work turns out to be negative. Because the term "against" is used, the value should be positive. The magnitude of the work done can be determined from the change in potential energy, because the box starts and finishes at rest, so KE did not change.

Wg = = ΔPE = - mgh = - (50 kg)(10 m/s2)(2.0 m) = - 1000 J

Changing the sign to positive, to correspond with "against gravity," makes C the best choice.



1. The problem never used the term "against" so I'm not sure if this free standing question originally came from another passage or something, so that confused me.

2. I'm confused what they mean by: "Changing the sign to positive, to correspond with "against gravity," makes C the best choice."

I thought they are saying the answer is negative?

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Not sure about their explanation. But, a force acting in the direction of motion does positive work; a force acting in the opposite direction of motion does negative work. So instantly, you would look at this problem and realize the direction of motion (up the ramp) is opposite gravity, so any work done by gravity will be negative. Multiplying out the terms (50*10*2) lets you easily decide between C and D.

Don't get hung up on their explanation if you understand the basic ideas involved in the problem.
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As @rabbott1971 stated, the force of gravity acts in the opposite direction of motion, so it does negative work.

You can think of it as W(gravity) = Fg*d*cos(theta), where theta is the angle between the force of gravity and "d". Since the displacement is "upward" (2 m) and the force of gravity is "downward", you can draw the free-body diagram and notice that these two vectors have an angle of 180° between them, and cos(180°) = -1. So you know the answer has to be negative as well (-1000J).

Another way to look at it is, what is happening to the potential energy when you lift or push an object upward? To increase the potential energy, you need to do work (+) on the object in order to counter gravity. That means gravity does negative work.
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