# Force as mass*acceleration

1. Apr 22, 2005

### chandran

i understand force as mass*acceleration. In statics(beam bending)
there is no acceleration involved in the internal to beam and we call that
a force exist how is this true?

2. Apr 22, 2005

### arildno

A beam at rest can be in a state of STRESS, not being subject to a NET force.
To take an example:
Suppose you're pulling with a force F on a beam of cross section A jutting out from the wall.
The beam itself might well be at rest, because the wall will pull at the wall with a force -F
(in sum, no EXTERNAL force on the beam)

But, now, focus on the beam HALF you're actually pulling on.
That part of the beam is clearly at rest; evidently, the other part of the beam pulls at it with a force -F, since you're pulling with F.
"Your" half pulls back on the other half with force -(-F)=F, in virtue of Newton's 3.law.

Thus, an internal STRESS of magnitude F/A exist within in the beam, even though the beam is at rest.

3. Apr 22, 2005

### rayjohn01

interesting

Forces are not due to some 'quite' effect -- they are due to the internal motions of molecules atoms and the like . When these are in balance then the result is no net motion even tho' the whole thing is in dynamic motion at the atomic scale .
Take a Human exerting a force on a mass --- I exert a force -- what does that mean ?? it means I am burning body mass to produce atomic or molecular motion ( above my surroundings ) I then apply this to the mass --it feels the extra motion and begins to both heat and move .
All motion is due to original motion in the birth of the Universe and the implied energy . The net motion in any direction is about zero ( due to random directions ) but the temperature (local speeds ) varies from place to place and is determined by your surroundings ( in our case the SUN ) .

It is the Sun which determines at earth surface what Motion takes place
(i.e your average temperature ) If I use a lens to heat some local spot it's temperature rises ( it has more energy or motion ) but it will communicate this to it's surroundings (by contact radiation etc)
Gradually it will come into balance -- that is when it's local surroundings are moving as fast as it .

All is motion Ray.

4. Apr 22, 2005

### arildno

And why do you have this need for obfuscation?

5. Apr 22, 2005

### rayjohn01

You keep on using the term 'at rest ' but a beam in tension is NOT at rest it is very much not at rest , but it's agragate motion is zero .
The motion of all atoms or molecules has been enhanced due to other motions the forces at work .
Btw obscufation is a local term ( I am not such ) All motion is due to an inherent motion of elementary particles -- but some are far more energetic than others --- I will leave you to figure it out .
Ray .

6. Apr 22, 2005

### arildno

Why are you always so damn anal, rayjohn!

What you should start learning, is about proper levels of explanation, instead of posting your worthless quibbles.

Last edited: Apr 22, 2005
7. Apr 22, 2005

### Staff: Mentor

Give us a break, Ray! You know perfectly well what "at rest" meant in this context.

8. Apr 22, 2005

### FredGarvin

You know, I try telling my boss this...even though I may be sitting idly at my computer, on the cellular level, I am really quite busy. He never buys into that though. Rayjohn just helped me to prove this. Thanks.

9. Apr 23, 2005

### chandran

fred,
you are yet to reply my 3d mohr circle question.

10. Apr 23, 2005

### rayjohn01

Anal ?? Did you miss a B ?

The original question asked how force but (no accelleration ) could exist in a beam under stress.
The answer is in the motion of atoms /molecules in the beam, are they both being compressed and stretched .
It is very clear that this effects internal motion as they are gaining or loosing applied energy without change in mass.
That is why I said it is not at simple rest -- it's pretty obvious that I am not refering to simple translation.
It is clearly not in equilibrium AND will accellerate if released The beam (or parts ) was also accellerated in the action of bending .
So F = m.a also applies here , both in the sense of bending and the internal actions.
I do not think that is a quibble , I believe it answers the question.
Ray.

11. Apr 23, 2005

### arildno

You're wrong; there has been a gain in the potential energy of the system (like in a spring), not necessarily an increase of the random kinetic energy of the constituent molecules.
That would have meant a large-scale temperature increase in the beam.
It does not seem you understand the difference, your "microscopic approach"
is therefore not only pointless, it is also misleading.

And, by the way, why did you stop your previous "explanation" with input of energy from the Sun?
It's not as if the Sun is the ultimate source, you know; what you really should explain, is the beam's history from the Big Bang and onwards to present time.

You are absolutely right in that matter has a microscopic structure consisting of vibrating molecules, though.
But it is neither necessary nor relevant to bring this to the forefront every single time you choose to post something at PF.

Last edited: Apr 23, 2005
12. Apr 23, 2005

### rayjohn01

And where does potential energy come from may I ask ??
Whilst it's true that the random motion has probably increased -- for an elastic material this will be small and will equalize after a short time .
So called potential energy is due to any energy exchange between two objects be they massive gravitational objects or atoms or molecules -- there are always mediating particles photons gravitons gluons and so on .
Any change of motion includes accelleration
If I compress a gas the temperature will rise -- after a time it's temperature will re equalize but pressure remains . This means the average wall collision has increased
an increase in direction change is accelleration.
What are you arguing about ??? All I am saying is that F=ma has not been violated in a bending beam . As per the original question .
I have to admit I was trying to avoid the 'big bang ' But to say it is irrelevant
is like an Ostrich '-- it is THE way of explaining forces -- but I will leave that alone here .
Ray.

Last edited: Apr 23, 2005
13. Apr 23, 2005

### FredGarvin

My apologies. I will go and dig up that thread. It hasn't been coming up as containing new posts on my screen.

14. Apr 23, 2005

### Tom Mattson

Staff Emeritus
LOL, there's a much simpler answer to this question. If there is a force acting on an object (such as a beam) and that object is not accelerating, it means that there is another force acting along the same line of action, in the opposite direction, with the same magnitude. Remember that Newton's 2nd law does not say that $\mathbf{F}=m\mathbf{a}$, it says that $\Sigma \mathbf{F}=m\mathbf{a}$. That is, the sum of the forces is equal to the mass times acceleration. The indivdual forces may not be zero, but if they add up to zero then you are in either static or dynamic equilibrium.

15. Apr 23, 2005

### arildno

Well, that's what I started out with, and said that we usually say the beam is in a state of stress, rather than that there is a force inside it.

Last edited: Apr 23, 2005
16. Apr 23, 2005

### Gokul43201

Staff Emeritus
When what are in balance ? And what does "in balance" mean ? This is not any terminology that is in accepted usage within the physics community.
What if you free-fall onto an object. Are you burning body mass ?

there already exists atomic and molecular motion. You are not producing it. And in any cse, you can increase the means square rate of atomic and molecular motions by simply heating an object. This involves no net accelecration of the object.

What ???

"Motion" is not a physical quantity. What extra motion are you talking about. You have not previously mentioned any "extra motion" that is being applied to the mass.

No, the universe in not deterministic. You are proposing a theory that is counter to our current understanding of the way things work.

I repeat : motion is not a physical quantity. What on earth do you mean by "the net motion is zero" ? Temperature is not a measure of local speeds, but really a measure of a statistical mean of the squares of the atomic speeds in the center of mass frame of the body.

This has nothing to do with the OPs question. So, it is irrelevant, besides being grossly imprecise and unacceptably cavalier with respect to the choice of terminology.

Last edited: Apr 23, 2005
17. Apr 23, 2005

### Gokul43201

Staff Emeritus
On any element of the beam that you consider (or the whole beam itself) the net force is zero in equilibrium (ie: after the beam has completed bending).

This is just the same as stretching a spring or rubber band. Initially, there is an unbalanced force which causes stretching (or bending, in the case of the beam). A consequence of the stretching (bending) is that the elastic reaction force within the material increases with the extent of stretching (bending).

This is because the interatomic electrostatic interaction is approximated very well by a harmonic oscillator potential (0.5kx^2) within the elastic regime, giving rise to the kind of reaction force predicted by Hooke's Law. As the stretching (bending) increases, the elastic reaction force increases roughly proportionately, till at some value of the stretch (bend), the reaction force is exactly equal (in magnitude) and opposite (in direction) to the applied force on the element.

At this point, there is no net force on the element, and the stretching (bending) stops. We say that the spring (beam) is in equilibrium, and there is no net force (or torque/moment) on it.