Dean Summers
2022-07-17
Answered

In the equation $\overrightarrow{F}=m\overrightarrow{a}$ is the acceleration vector always in the direction of the force vector, I mean why can’t they be in the opposite direction? Will this relationship break down in some scenario?

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tiltat9h

Answered 2022-07-18
Author has **14** answers

That equation is how force is defined, so it is correct by definition. You could certainly define a new quantity ecrof (force backwards) and define it as $\overrightarrow{E}=-m\overrightarrow{a}$. You could write all of physics in terms of ecrof $\overrightarrow{E}$ instead of force $\overrightarrow{F}$, but it would be a rather pointless exercise. You wouldn't learn or predict anything new about the universe using that concept.

Without redefining force the only way to have force in the opposite direction of acceleration would be for mass to be negative, $m<0$. We have never found any material with a negative mass, and there are some good theoretical reasons (e.g. negative energy density) to expect that we never will.

Without redefining force the only way to have force in the opposite direction of acceleration would be for mass to be negative, $m<0$. We have never found any material with a negative mass, and there are some good theoretical reasons (e.g. negative energy density) to expect that we never will.

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In my lecture today my professor briefly mentioned that force is the derivative of energy but I did not really get what he meant by that. I tried to express it mathematically:

$\frac{d}{dt}{K}_{E}=\frac{d}{dt}\left(\frac{1}{2}m{v}^{2}\right)=mv\frac{dv}{dt}$

This looks really close to Newton's second law $F=ma$ but there is an extra "v" in there. Am I missing something here?

$\frac{d}{dt}{K}_{E}=\frac{d}{dt}\left(\frac{1}{2}m{v}^{2}\right)=mv\frac{dv}{dt}$

This looks really close to Newton's second law $F=ma$ but there is an extra "v" in there. Am I missing something here?

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