Talk:Work (physics)/Archives/2020/December

How to phrase that work can be positive or negative, though it doesn't have direction?

The introduction says,

"Work is a scalar quantity, so it has only magnitude and no direction."

I thought about adding, "but it can be either positive or negative". What is the best way to phrase the idea that being a scalar, work doesn't really have direction but people do talk about it being positive or negative? editeur24 (talk) 04:28, 7 December 2020 (UTC)

Rewrite of the Work Done by a Spring subsection

I rewrote the Work Done by a Spring subsection, since it was written for the case of a spring with positive velocity, which is irrelevant to the work the spring does. I took out the velocity parts, and added more explanation. In particular, I talked about positive versus negative work in the context of a spring. I hope I got it right--please edit if I did not or my phrasing is clumsy. I did not draw from a published source---mea culpa!--- but I think it's an improvement over the old version. — Preceding unsigned comment added by Editeur24 (talk • contribs) 18:11, 7 December 2020 (UTC)

I think I was confused in my edit, so I undid it. The current subsection is unsatisfactory. If someone better at physics than me can look over the following and use it to replace the currect subsection if it is correct, I'd be grateful. What I'm confused about is positive versus negative work.

Suppose we have a spring stretched by amount ${\overline {x}}$ with a block attached to the right end. Hooke's Law says it will exert a force $k\Delta x$ on the block in the direction back to its unstretched state ($x=0$), where $k$ is a constant that depends on the spring's material and shape. If we let the spring go back to its unstretched state, the block has been moved distance $\Delta x=-{\overline {x}}$ by a force $-kx$ that varies over the course of its movement. We can compute the work done by the spring on the block by integrating the force over the distance travelled from the starting point to the ending point:

$W=-\int _{\overline {x}}^{0}kxdx=\left[-{\frac {1}{2}}kx^{2}\right]_{\overline {x}}^{0}={\frac {1}{2}}k{\overline {x}}^{2}$

This work is positive. If we then exerted a force on the block to compress the spring and move it to $x=-{\overline {x}},$ the spring would do negative work on the block, resisting the compression, so the work done by the spring would be $-(1/2)k{\overline {x}}^{2}.$

editeur24 (talk) 21:05, 7 December 2020 (UTC)

Path dependence

Gravity F = mg does work W = mgh along any descending path

It isn't clear what's going on in this diagram. I know it's meant to illustrate how the work done by gravity doesn't depend on the path from initial down to final location, but a new diagram might be able to do this better. --editeur24 (talk) 05:08, 9 December 2020 (UTC)