# Difference between F=ma and F=m1*m2/d^2

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### Luigi Fortunati

Apr 10, 2021, 5:40:14 AMApr 10
to
In the formula F=ma force is related to acceleration.

If acceleration exists in all references, the force is real, otherwise,
if it exists in one reference and "disappears" in the other, then the
force is "apparent".

On the other hand, in the formula F=m1*m2/d^2 there is NO acceleration
and this is the difference between the second formula and the previous
one.

In F=m1*m2/d^2 the force depends exclusively on the presence of the two
masses m1 and m2 (which always exist) and on the square of their
distance (which always exists).

Therefore, if the masses m1 and m2 and the distance d^2 never disappear
(in any reference) the force F=m1*m2/d^2 is always real.

And what is the force F=m1*m2/d^2? It's gravity.

So gravity is not "apparent" because (the formula says so and not me)
its force does not disappear by changing the SDR.

### Phillip Helbig (undress to reply)

Apr 10, 2021, 2:45:53 PMApr 10
to
In article <s4qdb4\$1tfg\$1...@gioia.aioe.org>, Luigi Fortunati
<fortuna...@gmail.com> writes:

> In the formula F=ma force is related to acceleration.
>
> If acceleration exists in all references, the force is real, otherwise,
> if it exists in one reference and "disappears" in the other, then the
> force is "apparent".

You can always transform an acceleration away by using an accelerating
reference frame

> On the other hand, in the formula F=m1*m2/d^2 there is NO acceleration
> and this is the difference between the second formula and the previous
> one.

It looks like you forgot the gravitational constant; that gives the
right-hand side the dimensions of ma.

> In F=m1*m2/d^2 the force depends exclusively on the presence of the two
> masses m1 and m2 (which always exist) and on the square of their
> distance (which always exists).

And on the gravitational constant.

> Therefore, if the masses m1 and m2 and the distance d^2 never disappear
> (in any reference) the force F=m1*m2/d^2 is always real.

Acceleration is always "real". (That is actually still a puzzle:
acceleration relative to what? As far as I know, no-one has ever shown
quantitatively that Mach's principle can explain that.)

> And what is the force F=m1*m2/d^2? It's gravity.

Right, which is why the expression usually includes the gravitational
constant.

> So gravity is not "apparent" because (the formula says so and not me)
> its force does not disappear by changing the SDR.

An acceleration is real; you can feel it. You can find an accelerating
reference frame and transform it away (at least locally).

The essence of general relativity is that gravitation, in some sense, IS
acceleration, but as far as I know no-one knows why the gravitational
constant has a non-zero value or has the value it has (apart from
weak-anthropic explanations).

### Alex

Apr 19, 2021, 2:35:24 PMApr 19
to
On 10 Apr 2021 09:40:11 GMT, Luigi Fortunati wrote:

Let me try a simpler, and clearer, answer.

> In the formula F=ma force is related to acceleration.

I always write this formula as a=F/m in order to stress the fact that if a
force F acts on a body/particle of mass m, then the particle will get an
acceleration a given by a=F/m. This is the Newton's second law.

F is the CAUSE (of the acceleration) and a is the EFFECT. I put the effect
on the left hand side, and the cause on the right hand side,

I DO NOT take the formula F=ma to be DEFINITIONS for F !!!

In a=F/M, F is ANY force, of any nature, coming from various sources, for
example:

- a spring acting on the body or particle: k*x (x is the displacement from
the equilibrium position
- a rope - F = tension in the rope
- a surface with which the body is in contact
- an static electric force (Coulomb) Q1*Q2/d^2
- or gravitational force: m1*m2/d^2
- or friction, etc.

Correspondingly, if on the body/particle acts, for example, only a spring,
then the Newton's second law gives that the acceleration will be
a=F/m=k*x/m

Please note that the Newton's second law is only valid with respect to

IF you believe this was useful for you, please let me know and I will

### p.ki...@ic.ac.uk

Apr 29, 2021, 3:54:37 AMApr 29
to
Alex <alexl...@removesolnet.ch> wrote:
> > In the formula F=ma force is related to acceleration.

> I always write this formula as a=F/m in order to stress the fact that if a
> force F acts on a body/particle of mass m, then the particle will get an
> acceleration a given by a=F/m. This is the Newton's second law.

I prefer to write: dv/dt = F/m

> F is the CAUSE (of the acceleration) and a is the EFFECT. I put the effect
> on the left hand side, and the cause on the right hand side,

You might therefore like this paper:

"How to be causal: time, spacetime, and spectra",
Eur. J. Phys. 32, 1687?1700 (2011)
doi:10.1088/0143-0807/32/6/022

with a longer version at arxiv:1106.1792

Mind you, some physicsts find the proposal intensely annoying,
and they disagree with it quite strongly - despite its deliberately
limited scope (i.e. on the interpretation of temporal differential
equations). There are thus several extra appendices in the arxiv