0
$\begingroup$

We know that kinetic energy is mathematically represented as $$E_k = \frac{1}{2} m v^2$$

Similarly, potential energy is defined as $$E_p = mg\Delta x$$

Considering these mechanical quantities in a system, is it possible to define them as multivariable functions such as

$$E(m, v)\ or \ E(m, \Delta x)$$

I know why this may be invalid, it is because they are simply equations defined physically. But, if we take either of the dependent variables as a non-constant, then I think that the multivariable definition is valid.

Improve this question
$\endgroup$
4
  • $\begingroup$ Do you have a way of varying mass at the same time that you vary velocity, for your object of interest? My first idea that would give a "yes" answer involves rockets in flight. $\endgroup$
    – David White
    Commented Aug 9, 2018 at 16:36
  • $\begingroup$ @DavidWhite yeah, that's sort of where I got the idea. Rockets expel mass and have changing velocities, so a function of mass and velocity sounds appropriate. $\endgroup$
    – PartialDifferentials
    Commented Aug 9, 2018 at 16:42
  • $\begingroup$ Yes, they are by definition multivariable functions. Why do you ask? $\endgroup$
    – Qmechanic ♦
    Commented Aug 9, 2018 at 17:24
  • $\begingroup$ Translational KE: $$K(\mathbf{p})=\frac{p^2}{2m}=\frac{p_x^2+p_y^2+p_z^2}{2m}$$ Hence, $$\mathbf{v}=\frac{\partial K}{\partial \mathbf{p}}$$ $\endgroup$
    – Ng Chung Tak
    Commented Aug 9, 2018 at 17:26

1 Answer 1

Reset to default
1
$\begingroup$

You are right and the approach is feasible. The kinetic energy concept, where mass varies with time, is used for example in jet propulsion theory.

Improve this answer
$\endgroup$

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.