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When a force acts on an object but there is no displacement in the direction of force whatsoever, when will we call it No Work Done and when will we say Zero Work Done? Do both terms refer to the same thing or there is some subtle difference?

My friend was telling me there's a difference but he couldn't explain it properly. I even searched online but did not get anything fruitful.

Golden_Hawk
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2 Answers2

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I think both are inherently the same , No work done and zero work done both refer to there being no work being done as zero means nothing!

Naveen V
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  • Or maybe it could have been the force acting perpendicular for displacement to be zero work done but it is the same overall – Naveen V Feb 23 '23 at 17:50
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It may only be a matter of semantics, but it appears, based on the following link, that zero and no (none, or nothing) are, at least mathematically, different. See : http://www.differencebetween.net/language/words-language/difference-between-zero-and-nothing/

So since mathematically,

$$W=\int \vec F \cdot d \vec x$$

If the force results in no displacement, zero physics work is done.

To be clear, I do not mean that saying "no work done" is necessarily wrong, just that it is not a mathematical response to what is the value of $W$ in the equation for work if $dx$ is zero.

Hope this helps.

Bob D
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  • I would also add that in the case of conservative forces you can get zero work by moving in a closed loop. See this answer: https://physics.stackexchange.com/a/92768/219488 – VinalV Feb 23 '23 at 18:26
  • @VinalV Good point, but if you move in a closed loop, isn't the displacement zero (since displacement is a vector pointing from the original location to the final location)? – Bob D Feb 23 '23 at 18:35
  • @VinalV Also, it’s net work that is zero for a conservative force in a closed loop – Bob D Feb 23 '23 at 18:56
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    Because you've unilaterally equated "No work" to "nothing," a questionable premise, this answer will give the OP and unaware readers the impression that "no work" is incorrect or imprecise wording. This is not useful. "No work" is used everywhere in the physics literature, and nobody gets the wording confused with the concept of an empty set. – Chemomechanics Feb 23 '23 at 19:25
  • @BobD those are fair points – VinalV Feb 23 '23 at 19:31
  • @Chemomechanics I said it may only be a matter of semantics, not that the use of the term "no work" is necessarily incorrect. But if one asks what is the value of $W$ in the equation for work if $dx$ is zero, one would generally not respond "no work done" or "nothing" or "none". In any case, I will update to say it is not wrong to say "no work". – Bob D Feb 23 '23 at 19:41
  • Then maybe they are fundamentally the same thing, after all – Golden_Hawk Feb 24 '23 at 03:01