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Consider the following question:

In which of the following situations would a force be exerted on an object and no work be done on the object?

I. a centripetal force is exerted on a moving object

II. a force in the opposite direction as the object is moving

III. a force is exerted on an object that remains at rest

A.) I only

B.) I and II

C.) I and III

D.) II and III

E.) I, II, and III

My response to this question is only II, but this is not a choice. I do not understand how I or III could have work. My logic is that in I, the force is centripetal and therefore is not parallel to the object's path, in any case it would be perpendicular because centripetal is towards the center. Work must be parallel. In III, if an object remains at rest, $d = 0$. And $W = fd$, so $W = 0$.

I can't find the flaw in my logic. Any help is appreciated!


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Doesn't the question ask you to give the situations where no work is being done? – Alfred Centauri Feb 20 '14 at 1:49
W is also $\int \vec F \cdot d\vec r$ – Shubham Apr 18 '14 at 17:50
up vote 2 down vote accepted

You have the right idea, but the question asks for situations where there is a force and no work. Centripetal force does do no work but there is a force, so I is true. In III you are exactly right, but it says there is a force and no work, which falls under the question. I think you have misunderstood the question. II is false because a force in the opposite direction does negative work on the object. Negative is not 0. The answer is C.

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You have the ideas down, I think, but for some reason, you seem to have not yet noticed the disagreement between your thoughts. For instance, if you've already stated that $W = fd$, and that you're looking for examples of measurable force with no work, what would that tell you about $f*d$?

So if work is $f*d$, then in order to have work, you must have some force and some movement.

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