1
$\begingroup$

If I am pushing a block with variable force, we come up with an equation where force is a function of position. But in reality, that makes no sense because it is my force that is causing a change in position and not a distance that is causing my change in force. The mathematics fail to account for the physical cause and effect.

If we look at a typical $F*d$ diagram, the independent variable is position and the dependent variable is force. I am arguing that the math should stay consistent with the reality and they should be switched.

I believe it also makes sense conceptually. As the change in force becomes infinitesimal, we will approach a fixed change in distance. The equation would look like: $$w=\int D(F)*dF$$ where D(F) is the distance at force F.

P.S. A point was made that many forces in nature are indeed a function of distance. I'd like to counter by discussing PV work. We know that for an ideal gas in a piston: $$w=\int P*dV$$ There is no question here that the only way work can be achieved here is that the pressure must change. This change in pressure will then cause a change in volume. Therefore, I propose that the independent variable should be changed to pressure: $$w=\int V(P)*dP$$

Perhaps the answer to my question has to do with the fact that pressure and volume are state functions while work is a path function?

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ While the definition of work seems very arbitrary when you first encounter it, there are both shallow and deep reason for using the standard definition. The shallow reason is that you can built a useful set of ideas off of it (the whole conceptual structure of energy in its many types and the conservation thereof); this is something that you will be equipped to appreciate shortly after learning it. The deep reason turns on Noether's theorem and you'll have to study for some time to appreciate it. But short message: you can't just change the definition of work because you like it better. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Mar 18, 2017 at 17:42
  • 1
    $\begingroup$ Actually, in nature, most of the time the force does depend strictly on your location, look at gravity or coulomb's law for example. $\endgroup$
    – Ofek Gillon
    Commented Mar 18, 2017 at 17:52
  • 1
    $\begingroup$ In your formulation constant forces do no work. $\endgroup$
    – garyp
    Commented Mar 18, 2017 at 18:53
  • $\begingroup$ @dmckee That looks like an answer rather than a comment. $\endgroup$
    – sammy gerbil
    Commented Mar 18, 2017 at 19:24

1 Answer 1

Reset to default
1
$\begingroup$

If I am pushing a block with variable force, we come up with an equation where force is a function of distance. But in reality, that makes no sense because it is my force that is causing a change in distance and not a distance that is causing my change in force.

(Although this my be irrelevant, but I suppose that you mean position instead of distance)

When one says a force is a function of position, it does not mean that a change in position is the reason of change in the force or vise versa. It is just a mathematical concept that defines a relation between force and position. In other words, the force does not obey the position; it just might vary with position.

Improve this answer
$\endgroup$
1
  • $\begingroup$ I do. I'll correct it. $\endgroup$
    – Nova
    Commented Mar 18, 2017 at 19:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.