# Force and Mass

1. Dec 21, 2008

### sganesh88

Which is "more" fundamental? force or mass? A few books i read specifies mass to be fundamental but i have difficulty in accepting it.
A line of thought that satisfies me is this:
A spring stretched to a given length is assumed to exert a particular force- x meter --> y units of force) correspondingly the force varies linearly with the stretching. (k*x meter --> k*y units of force (hooke's law))
Only now does Newton's 2nd law enter the picture. He says that for a particular body, a particular number can be given which equals the ratio of the net force acting on it(that can be independently found out by measuring the stretching of a band or spring) to it's acceleration (by pre-existing conventions on length and time) and that this number (F/a) is unique to that body and doesn't vary with the force exerted or any other parameter. This we call it as mass.
Have i gone wrong somewhere.?
If i haven't, it means force is more fundamental than mass right?

2. Dec 21, 2008

### swraman

A mass is more fundamental. Why? Because the definition of a force uses Mass in it.

Force = mass * distance * time^-2

It doesnt matter whether the force is a weight, a spring's force, a gravitational force, or whatever but the the way which physics is taught is that a force's definition is based on mass.

3. Dec 21, 2008

### sganesh88

can you tell what "a mass of 1 kg" means without ever using the word "force"?

4. Dec 21, 2008

### Hootenanny

Staff Emeritus
Yup: The kilogram is defined as being equal to the mass of the International Prototype Kilogram.

5. Dec 21, 2008

Staff Emeritus
I suspect this conversation will go around in circles until someone finds a way to quantify "fundamentalness" (fundamentality? fundament?)

6. Dec 21, 2008

### schroder

I tend to think that “fundamental” means to exist independently of something else. In the SI system we have length, time and mass as the fundamental units of measurement. Force, on the other hand, is a derived unit. Mass can exist independently of force, although we may use force to measure it. Force cannot exist independently of some mass which creates it or allows for it to act, as far as I know. Even light cannot exert a force unless there is some mass for it to act on. Maybe this is not the most rigorously convincing argument that can be made, but I cannot imagine a stronger argument in favor of force.

7. Dec 21, 2008

### HallsofIvy

Staff Emeritus
Yes, but that "fundamentalism", as Vanadium50 put it, is entirely an artifact. It would be more "natural" to use speed as a "fundamental" unit because there is a "natural" fixed speed- the speed of light. Similarly since Plank's constant, a natural constant, is in units of "action", that would be a fundamental unit. G, the gravitational constant (NOT "g"), which has units of "force times distance squared over mass squared" would also be "fundamental".

I have seen that done in some texts but it is not "convenient". The unit of distance, for example, turns out to be the diameter of an electron and the unit of time the time required for light to cross that unit distance!

8. Dec 21, 2008

### Gnosis

Yes. The following defines mass:

mass = volume x density

9. Dec 21, 2008

### sganesh88

And how will you decide whether the given mass is "equal" to the international prototype? without applying a force? You cannot. Whereas force can exist independently as you could say you're exerting y units of force, when the band or spring stretches to x meters. It depends only on the measurement of distance.

10. Dec 21, 2008

### sganesh88

Where's Mac?
Infront of Ron.
Oh. good. And where's this Ron?
Well.. Behind Mac.

11. Dec 22, 2008

### schroder

When the spring stretches x meters, and you measure that, all you are measuring is distance! There is no force unless a mass is acted on by the spring. However, a mass can exist quite independently of force. Maybe we need to exert a force to measure it, but it's existance does not depend on our ability to measure it. A force requires a mass in order to exist. It is very logical to say the mass is more fundamental than the force.

12. Dec 22, 2008

### Hootenanny

Staff Emeritus
You didn't ask me to measure it without using the notion of a force, you merely ask me to define it.

Your claim that force is somehow 'independent' is a fallacy. Can you define for me what a force of one Newton is without referencing any other quantities?

13. Dec 22, 2008

### sganesh88

Mass is a quantity. It is an attribute of a 'thing', not the 'thing' itself. So it doesn't make any sense to say that mass can exist independently. Unless you try to whack that thing with a known force, it is impossible to measure it's 'attribute' namely mass. Using the term 'mass' for 'thing' has just become a general practice.

14. Dec 22, 2008

### Hootenanny

Staff Emeritus
I know that we're in the classical physics forum here, but one can determine the mass of an electron by measuring the energy/momentum of photons emitted from electron-positron annihilation. No application of a 'known' force required.

15. Dec 22, 2008

### sganesh88

First of all, i'm not claiming anything. I'm just asking whether force or mass is "more" fundamental. And i've given the way i thought about this problem, concluding that force is more fundamental. If there's a fault in that line of thinking, i'd like to know about it. If force and mass are dependent on each other for their definitions, then it's downright circular.

And as to the definition of 1N, i would rather define "1 unit of force"(could be named 1 Gan :) ) as that produced when a spring of a particular material stretches through a distance of x meters under the action of that force. And it is impossible to define force without referencing "any" quantity. Note that i have not included mass in the definition. Can you define mass in such a way? This definition of force could be used to measure and compare forces with the standard 1 unit without considering the quantity of mass. Whereas to compare a given mass with the international prototype, you got to apply a force.

16. Dec 22, 2008

### sganesh88

oh.. thats an interesting info.

17. Dec 22, 2008

### Hootenanny

Staff Emeritus
Okay, fair enough, but you need to be willing to listen to other people's opinions.
Indeed, I agree that it is impossible to define force without referencing any other quantities. However, it is possible to define mass (or rather the kilogram) independently of other quantities as it currently is in the SI system.
As I said before, YES!
As you say, measuring mass is a different matter all together, but that is not the discussion here.

18. Dec 22, 2008

### schroder

Several people have pointed out the fault in your line of reasoning. It is quite obvious that you do not want to know about it. Have a nice day!

19. Dec 22, 2008

### baywax

Can you have mass without distance?

20. Dec 22, 2008

### Math Is Hard

Staff Emeritus
What do we actually gain in understanding of anything in nature or our natural laws if we determine that mass is more "fundamental" than force or vice versa?