# The meaning/use of $F=m*a$, $F*t=J$

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This question was asked at SE and  was eluded with arrogance. I joined this site of TP to see if it can be adequately discussed, even if it may appear 'weird' to a superficial reading.

$F=m*a$ is Euler's first law of motion. It is wrongly identified with Newton's second law, since we know for sure he had seen the original proposal by Hermann in *Phoronomia* and refused to accept it because it was not his idea of  *vis motrix*. In particular, if the concept of force is tied to $a$, it cannot be geometrically represented.

The formula is indifferently used as an

-  *a priori* definition, as in the case of gravity, where $g$ is not a force but a rate of  uniform, constant and unlimited acceleration  $a=10m/s^2$: any mass, no matter how large, will get same a and the force can follow the mass any length: therefore the effect (RHS) is equal to the cause (LHS) : $F_g = m*g => m*10m/s^2$ and when we  know time: (s = 5) we can determine the increase of velocity (50) and the impulse the body acquires: $J=m*50m/s$ and if we know the value of mass and of $v_0$ we can determine the increase in Ke.

- *a posteriori* definition, in 99% of instances in real life, when not a force *at distance*, but a concrete push/pull is involved, when not a rate but an ordinary force expressed in newtons is involved. Consider a steel spring (k=200, d =.5) which when fully compressed can exert a force of 100 N and  body B (m ) , and B' (2m). The question is:

- " ..given the force, the time it is exerted $J=F*t=100*0.25$  (and , in this case, the distance d, to boot) can you determine the effective velocity acquired by B/B' if you do not know their mass, and consequently the change of momentum J"? If you can't, can you at least affirm that, according to the formula : $a=F/m$, $v_B = 2 v_{B'}$

-  "...even if you know the value of mass, can you determine the increase of v,p or Ke?

Before you downvote or post a negative comment, ask yourself if you understand how complex the question is, and if you can answer such an apparently simple or weird question.

If you cannot answer it, do not sweep it aside.

Closed as per community consensus as the post is not graduate-level. Might be more appropriate on PhysicsForums.com.
closed Jun 30, 2015

Physics Overflow is a graduate level site. Voting to close as high school level.

Physics forums might be a better home for this question.

@dimension10,  you can state it's a high-school level and close it if before that you can say that the answers are 'yes', 'yes, I can'. But if you can't answer it means you have not understood the question.

Being graduate level is a different matter, But i don't see the point of this question or why it is "complex". the question asked is the velocity in ratio 1:2 simply follows from definitions. If you know the impulse is the same, if you know the objects are in mass ratio 2:1 then it follows. And not to mention a pointlessly long introduction to the question.

I understand why your question got closed at Pse

"And if the applied impulse is 25 and m = 0.1 v will not be 250 m/s,  and if m = 0.2 it will not be 125.  That is an irrefutable truth."

This is completely incorrect.

$J = \int F dt = \int (m a)dt = m \delta v$

If you disagree with this first learn the subject better.

Ofcourse when you release mass m1 and m2 from a spring, energy is the same for the 2 situations not impulse

If you don't know the mass of course there is no way to tell what v is.

if m =.1 kg and J = 25Ns v =250m/s That is all there is to this situation.

AND YES IF A SPRING REALLY DOES give an impulse of 25Ns then it will speed up to 250meters/sec assuming all experimental conditions are IDEAL.

I don't want to continue this discussion any further.

you have not tried to understand the subject.

Calling me superficial shows how incomplete and fragmented your understanding is.