## henpen 3 years ago F=ma. Therefore, is force a function of position or velocity?

1. ghazi

Force is a function of none, and this is what i have been thinking, and my question that i have posted is because of this confusion

2. henpen

http://www.youtube.com/watch?v=h96SW0PfQcg 9 minutes in is similar to this, but I can't see why you can' just know the position to work out acceleration

3. henpen

I also don't get how knowledge of instantaneous position is enough to work out velocity.

4. ghazi

well, if just define force in a general term then it is something that we push and pull, for example if we apply force on a wall, there is no displacement, no acceleration and no velocity which indicates force should be zero but there is force, newtons second law says rate of change of momentum is force but when we apply force on something that is stationary, there is force but net change in momentum is zero, therefore i am confused what exactly can we used to define force ?

5. henpen
6. henpen

Carl Pham's answer posted here: Force is something that causes an acceleration in a body that can move. It's directly experienced as a pressure or impulse. Why do we need a definition for a direct observation? That's like asking for a definition of length. Length is something we directly perceive, it needs no other definition than simply pointing to it. Where we need definitions is of things that we cannot perceive directly, like inertial mass, or energy. These thins must be defined in terms of things we can observe, like forces and accelerations. What you may be asking is what relationship force bears, mathematically, to the whole zoology of physics concepts. For example, force is a derivative of energy with respect to placement. But that's not a "definition" of force (if anything, it's a definition of energy), it's just the relationship between force and energy. That's because force comes first -- force is directly observable, energy is not. This is not to say that you can't build up a coherent theory of physics starting from abstract principles and *deriving* the nature of force. That's certainly possible (at least, we hope so). But that still isn't really a definition of force, so much as stating where force fits in your abstract construction. Because science is fundamentally empirical: the proof of an abstract construction is its consistency with what's observable. That is, you may "derive" force if you like from abstract ideas (like energy), but your ideas must end up proving that force has the properties we know it has from direct observation. So the "derivation" can't possible come up with any new properties -- it's more like a proof than a derivation, perhaps, speaking mathematically.

7. ghazi

most of the time i disagree and i condemn his line when he says " Why do we need a definition for a direct observation" i strictly disagree with this and i hope you are getting my logic that i just mentioned above

8. henpen

I think you're being too simplistic saying there is no displacement. There is a strain on the electromagnetic forces between the atoms in the wall, but the binding force increases its component horizontally as it is displaced very slightly horizontally in the other direction

9. henpen

To use a crude analogy:|dw:1352045776226:dw|

10. ghazi

when we talk about classical mechanics we don't go in to atoms if i am not mistaken

11. henpen

The definition of force is incorrect if you choose to ignore a large part of the world.

12. ghazi

exactly this my concern

13. AlexUL

The force itself is not a function of position or velocity, unless you're in a system that says so. Here's what I mean : A plane starts with a slow acceleration that grows until it reaches a critical point, where the resistance of the air and the limitation of the engine makes it accelerate less and less, to a point where it can no longer accelerate. What is the function that shows the NET force (air resistance is already substracted to the raw engine push) applied by the engines? acceleration is therefore a function of the speed of the plane : let's say a(v)=25-(v-5)^2 (i know... it's not a fast plane, only 10m/s) F(a)=ma F(v)=m(25-(v-5)^2) Force as a function of velocity Same can be done with position or time or whatever you want. The thing is, you have to include an element in your situation that will make either mass or acceleration a function of something else. You can also work backwards and make a force applied vary according to a position, a velocity, an electric charge, etc. Then, your mass will vary (decay, erosion, whatever) and/or your acceleration. That is the answer to your question, I believe.

14. AlexUL

force as a function of velocity doesn't mean a certain velocity will give you a certain force. It means that, according to everything you were told about a certain situation/system. If an object in this system has a certain speed, you can assume that a certain force (given by the functions) will be applied by something to something else, somewhere.

15. AlexUL

It's a reasoning mistake in philosophy and communication : thinking that because an object has a certain characteristic, something else will surely happen the same manner, every time. But because we're talking about physics, we are able to prove this statement empirically, and we work with this statement to achieve our goals.

16. henpen

Then why is it that physically (by Newton's laws), you can tell your acceleration by observing the physical laws, but not velocity or position (that is, you could do an experiment in a closed box to tell the acceleration).

17. henpen

*?

18. AlexUL

For the same reason that you can tell speed by knowing what distance you can cross in a certain amount of time ; force was defined this way. Let me get one of my books that explains the story behind the Newtons in SI system

19. AlexUL

Ok. Let's say we know nothing and we make an experiment, where we apply a certain force sideways on an object, and then we measure the acceleration. Then we apply another force on the same object, and measure the acceleration. We do that again and again: $\frac{ F _{1} }{ a _{1} }=\frac{ F _{2} }{ a _{2} }=\frac{ F _{3} }{ a _{3} }=C$ When we divide the force by the acceleration, we always get the same constant. We call it the inertia, and this is what restrains the change in movement the of an object. We then stopped measuring weight in sheeps, rocks or whatever. And started to use a value for C (mass for linear movement, inertia for rotational or circular) that would not matter whether we were in a rotating system or on the moon or had magnetic fields around, etc. Newtons are kg*m^2/s so they can be pressure*area, energy/distance, mass*acceleration, mass of fluid*area of observation/speed of fluid and many other things

20. henpen

Why would measuring in sheep make linear mechanics require a conversion factor when dealing with angular mechanics?

21. AlexUL

Linear and angular are totally different and the relation between the two of them is sorcery, until you see a full drawing of the force, velocity and acceleration vectors in a system that follows a curved path. Whether we use sheeps or newtons, we need to make a conversion when we go from linear to angular, unless we manage to separate angular motion into linear behaviors and go back to F=ma

22. AlexUL

what course is this btw?