# Second Law

1. Feb 14, 2008

### Chombo

This may be a weird question, but oh well. Way back during the Scientific Revolution it would have been possible to define mass as acceleration divided by force right? Then you'd have F = a/m, and the units for force would be different than they are now.

2. Feb 14, 2008

### Danger

Welcome to PF, Chombo.
You can define things any way that you want to, and use any units that you want to. Reality will remain real. The trick is to make sure that everyone is speaking the same language.
And incidentally, the 'Scientific Revolution' never officially began or ended. It goes on constantly. Perhaps you mean the Industrial Revolution'?

Last edited: Feb 14, 2008
3. Feb 14, 2008

### Chombo

Thanks for the reply Danger, that cleared things up a bit. By 'Scientific Revolution' I meant the period of time when Galileo and others began to reject Aristotle's medieval view of the universe (i.e. the sixteenth and seventeenth centuries).

4. Feb 14, 2008

It's actually a good idea. Does it mean, mass is generated after a force gives you an acceleration? It will also mean, massless particles can accelerate whenever they 'wish' without force -- this is violation to 1st law... so it's a nice question to probe.

Explanation:

m = F/a. (definition)

So when there's no force, mass = 0/a = 0, provided a != 0 .. Particles, if they have acceleration without force, they are massless, so if we find a massless particle, it can actually violate first law.

If F = 0, a = 0, m=0/0 , means undefined. therefore, for mass to appear as something real, there must be first force, and resultant (?) acceleration.

Yet another point. Mass've been the key between force and acceleration. Since mass is now an 'aftereffect' of F and a, what's the key between them?

Your question is very interesting to think.
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5. Feb 14, 2008

### Danger

Ahhh... that would be part of what we generally refer to in the western world as the 'Renaissance'. It spanned roughly the 14th - 17th centuries. While predominantly associated with art, it also saw large upsets in the field of science.

6. Feb 15, 2008

### TVP45

But, that's not really a definition; it's a statement of what can be experimentally observed. F = a/m leads to the extreme conclusion that one could move very large masses with a gnat's sneeze and that's not what was observed.

7. Feb 15, 2008

### Lojzek

Define your mass m' like this:

m'=1/m

And your Newton's law will be: m'=a/F

8. Feb 15, 2008

### Micha

Chombo, I think your problem is, you didn't reflect what F = m * a actually means. Mass is define as the resistance of a body to change his velocity as a responce to force
With your definition, the bigger the mass of a body, the easier it would change its velocity.
Maybe this would be something just to get used to.
But furthermore you would lose the very nice property, that the mass of a composed body is the sum of the masses of its components.

9. Feb 17, 2008

### Claude Bile

The "standard" way of formulating known theory, including the definitions and unit systems are by no means unique. In most instances the "standard" way has come about because it is the easiest and most intuitive way of doing things.

The "standard" for unit systems we have adopted is the SI system, but people still frequently work in other unit systems. The imperial system for example is wholly consistent with known science, however the SI system is more widespread because unit conversions are so much easier (i.e. convenience). The SI system is not the most convenient in every case, CGS units are frequently used in electromagnetism because they streamline formulas by removing most of the recurring constants that pop up using SI units.

Claude.

10. Feb 18, 2008

### Micha

Claude, what you write is true. But I think it is not quite hitting the point.

Chombo's proposal means a different definition of the physical quantity mass. This is a deeper change to physics than just the change from kilogramms to pounds.
Different units usually mean just a constant linear conversion factor.
The only exception I can think of is temperature where you have an additive constant involved when going from degrees Celsius to absolute temparature.
And even here you use different symbols for the temparature in degrees Celsius versus degrees Kelvin and probably talk about different physical quantities.
Chombo's definition clearly leads to a different physical quantity (maybe best called lightness) and not just to different units.