Understanding Force: Defining F=ma and Other Equations

[ucanihl]

What is the exact definition of force leading to F=ma? Couldn't we define another equation for force, say F=mj or maybe F=2ma? I think it is because of our senses and the force is defined by the Hooke's Law F=kx, but I am not sure..

 

[ShayanJ]

Actually F=ma is the definition of force. But it should also be noted that Newton's theory requires the natural amount of intuition and the three laws+natural intuitions build up Newton's theory.

 

[Drakkith]

Actually F=ma is the definition of force.

Can an equation be called a definition?

 

[ShayanJ]

Can an equation be called a definition?

Let me state it more clearly! We can define force as something that gives massive objects an acceleration according to F=ma.

 

[Drakkith]

Let me state it more clearly!

No need. It was an honest question that I don't know the answer to.

 

[ShayanJ]

No need. It was an honest question that I don't know the answer to.

In that case, I should give you a clarifying example. The concept of power is the rate of change/transfer of energy. If you think about it, this definition has nothing in excess of ## P\equiv \frac{dE}{dt} ##.

 

[sophiecentaur]

Because Physics is not an Axiomatic study, I don't think you can tunnel down within it to find any true 'definitions'. You can never do better than link the definitions of quantities to personal experience and observation.
Maths, otoh, starts from definitions and builds a coherent structure on them.
Of course, we quote Physics 'definitions' every day but, apart from definitions in the form of a relationship of other quantities, I think the process ends up as a matter of faith..

 

[rumborak]

My 2 cents is, labeling m*a as an entity that you can treat as a "currency" in your physical system analysis, makes for a definition.

 

[Dale]

Can an equation be called a definition?

I would say, yes.

In physics I tend to think of two kinds of definitions: experimental and theoretical. The theoretical ones are usually equations, and the experimental ones are basically instructions for measuring a quantity. At least, that is how I think of definitions in physics.

 

[A.T.]

We can define force as something that gives massive objects an acceleration according to F=ma.

That would define net force, not force in general. It doesn't account for static forces.

 

[sophiecentaur]

That would define net force, not force in general. It doesn't account for static forces.

I don't think that's a serious problem. You can always consider the initial acceleration whilst the velocity is still zero.

 

[A.T.]

You can always consider the initial acceleration whilst the velocity is still zero.

You can have forces acting with zero acceleration.

 

[sophiecentaur]

You can have forces acting with zero acceleration.

Of course but you only have to consider removing the opposing force and allow the force to produce some virtual acceleration. That force is conceptually no different with or without acceleration occurring.

 

[A.T.]

That force is conceptually no different with or without acceleration occurring.

Then acceleration shouldn't be used to define force in general.

 

[Drakkith]

You can have forces acting with zero acceleration.

This is one reason why I don't think equations are definitions.

What is the exact definition of force leading to F=ma?

The simple definition is that force is any interaction that results in the acceleration of a mass. But, as shown above, this simple definition may not hold up to scrutiny. Of course, a definition is not the same thing as a full description of something, so it may not matter too much.

 

[ShayanJ]

That would define net force, not force in general. It doesn't account for static forces.

As I stated in my post #2, Newton's laws+some natural intuitions builds up Newton's theory. If you exclude the intuitions, you'll have problem with Newton's laws and which came from where and what are the definitions. So here I think we should do some work to reach a full theory. At first this definition says that, unlike Aristotle's thoughts, force doesn't maintain velocity, but acceleration. Next we should do some experiment with objects that are in accelerated motion and find out more about forces. Then after gathering that information about different kinds of forces, we'll understand that such forces can cancel each other. Then we change the definition to "force is something that gives massive objects an acceleration according to F=ma, if acted alone on the object."

 

[Dale]

This is one reason why I don't think equations are definitions.

You just have to use the right equations. E.g. ##\Sigma f=ma## instead of ##f=ma##.

 

[sophiecentaur]

This is one reason why I don't think equations are definitions.

Whether you use an equation or an arm waving description, the quantities in Physics are all referenced to each other. There ain't no pure definition of anything. Our personal experience may make us lean towards particular quantities as more fundamental than others. Resistance is a good example of this; it's really only, by 'definition' a ratio of two other quantities (an equation is its basis) yet people keep posting questions on PF about "What Is Resistance?".

 

[ucanihl]

Shyan you said "force is something that gives massive objects an accelaration to F=ma..". However isn't this an assumption? Ok we can define "a" directly from distance and time sense. Mass is as well from accelaration and weight senses. I mean, you see objects falls with different accelarations and after some examination you just find out that the weight sense is directly proportional with accelaration and the ratio is something constant named as mass so it is sensely meaningful. How about the force? Can we define it with using the sense of press, the sense of weight?

 

[sophiecentaur]

Can we define it with using the sense of press, the sense of weight?

That's ok in principle (and it's the way we mostly measure forces in everyday life) but you have to ask yourself how you would 'calibrate' this force using this definition. If it to be a useful quantity then you would have to be able to tell other people (other laboratories) the conditions in which they could reproduce your standard unit force. Springs etc. are difficult to specify accurately and you would need to specify a certain deformation of a certain shape, made of a particular substance (metal?). Accuracy would be very dodgy. too, we can measure mass to a high degree of accuracy (using standard kg as a starter) and also, distance and time can be measured reliably to fantastic degrees of accuracy. So defining Force in terms of mass length and time is really a no brainer.

 

[Unified28]

A definition does not describe the "real" objective reality since according to philosophy nothing can be proven, right? A definition describes a model of reality. Equations function as such a model, as long as you understand the variables and what they describe and when they apply. Any model can be further refined, such as how Shyan explained about how forces can neutralize each other and in which case they cause acceleration.