The philosophy of squaring > Why no f=ma^2

1. Jul 31, 2013

MinnesotaState

Force = Mass x Acceleration

So for example,

F=10 grams x 3 acceleration

What that really means is,

F=10 grams x 1 acceleration

F=10 grams x 1 acceleration

F=10 grams x 1 acceleration

So for every X amount of mass, you get X amount of acceleration. There's a relation here. The amount of mass you get for every acceleration is constant. It has to be. That's the logic behind multiplication. If you have 3 balloons, & multiply them by 3, you get 9. Because 3 x 1 + 3 x 1 + 3 x 1 = 9. If 3 x 1 didn't always equal 3, then the equation would collapse.

Let's go back to the example,

F= 10 grams x 3 acceleration = 30

If I double the mass, I get 20 grams. So, 60.

If I double the acceleration, I get 6. So, 60.

I'm not seeing this "building up of squares."

Leibniz was convinced that the energy of an object was made up of it's mass x it's velocity, squared

So why no f=ma^2

I guess I don't understand the difference between energy & force.

Last edited by a moderator: Sep 25, 2014
2. Jul 31, 2013

voko

F = ma because this is how the nature works. We can measure this. We can also derive this from some other principles, which may be regarded as more general, and we can again establish experimentally that those principles hold independently. So F = ma is a physically true statement any way you look at it. The question such as "why no f = ma^2" then has a simple answer: because that is not true.

3. Jul 31, 2013

WannabeNewton

You're basically asking: why is a definition defined to be what is given in the definition? This is of course a pointless question.

4. Jul 31, 2013

MinnesotaState

Where am I going wrong with energy & force?

They are different,

e=mc^2
f=ma

I do not understand the philosophy of squaring either.

5. Jul 31, 2013

johnqwertyful

First off, e=mc^2 is not true (at least not complete). The real equation is

E$^{2}$=m$^{2}$c$^{4}$+p$^{2}$c$^{2}$
which when p=0, is equal to the Hollywood equation.
I also don't see how the equations are related it anyway, other than both being equations in physics.

6. Jul 31, 2013

MinnesotaState

If I drop a ball from the empire state building, what will be the force 5 ft from the tip assuming mass of 10 grams.

If I drop a ball from the empire state building, what will be the energy 5 ft from the tip assuming mass of 10 grams.

Now,

If I drop a ball from the empire state building, what will be the force 5 ft from the ground assuming mass of 10 grams.

If I drop a ball from the empire state building, what will be the energy 5 ft from the ground assuming mass of 10 grams.

I still don't see any building up of squares with force as leibniz proposed.

& energy, well acceleration is irrelevant because e=mc^2 is assuming at rest?

7. Jul 31, 2013

Staff: Mentor

Yes. They are nowhere close to the same thing.
Huh? An object in free fall isn't exerting any force on anything other than on the earth due to its weight. This line of discussion is a bit odd because while it is common for people to not understand what energy is, it is not common for people to not understand what force it. Force is just what you feel on your hand when you push something or what a table "feels" when a book is sitting on it. A book sitting on a table is not expending energy because it isn't moving.

8. Jul 31, 2013

MinnesotaState

I'm picturing people standing at 10 ft intervals from the bottom of the empire state to the tip. This free falling object is slamming into each one of these individuals. Well theoretically.

9. Jul 31, 2013

Staff: Mentor

What happens when it hits the first one? Does it stop?

Again, since energy is not directly related to force alone, trying to relate energy to force in this way is mostly an exercise in futility. The question is not unlike asking how "car" and "white" are related. My car is going 60 mph. What color is it?

10. Jul 31, 2013

Staff: Mentor

When the object slams into them, does it slow down? By how much? That change of speed is acceleration, caused by an individual person applying a force on the object and the object applying an equal and opposite force on the person.

11. Jul 31, 2013

Staff: Mentor

Worse, mechanical energy is not conserved in such a situation, so analysis using energy isn't optimal.

 It is really best at first attempt to look at energy and momentum as just bookkeeping concepts. Just relationships between "more real" quantities that some scientist once upon a time discovered was useful to use in calculations.

Last edited: Jul 31, 2013
12. Jul 31, 2013

MinnesotaState

Thank you for your responses. I found what I was looking for here,

"If you hold a ball from the top of the empire state building, that ball has something called gravitational potential energy. This means that the ball, because of its position in earth's gravitational field, has the capability to release a certain amount of energy that is proportional to it's height."

13. Jul 31, 2013

Jorriss

How is it a pointless question? Are you saying it's pointless to ask why definitions are as they are?

14. Aug 1, 2013

SteamKing

Staff Emeritus
Never get into an argument with a philosopher. Neither of you will get satisfaction, and the argument never ends.

15. Aug 1, 2013

technician

Wrong forum but.....
the joy of philosophy is the argument.
seeking satisfaction is very satisfying.
When the argument ends it could be called Physics.........

As I say.....wrong forum

16. Aug 1, 2013

MinnesotaState

Can we go over the philosophy of squaring?

:)

17. Aug 1, 2013

voko

The philosophical debate between Leibniz and the Cartesians was not about the absurd idea of "building up of squares", but about the conserved quantities of motion and the meaning of the concept "force", which, back in the day, had no common understanding, as it does today.

Here is an article that highlights the issues: http://nature.berkeley.edu/departments/espm/env-hist/articles/2.pdf

18. Aug 1, 2013

technician

If you don't mind me saying so, this is a somewhat arrogant response to a question.
'Definitions' have changed over time (second, metre etc, etc) and the reasons for these changes are part of the history of physics (not philosophy).
In a physics forum worth it's salt we should welcome such questions and think carefully about what lies behind them and where they fit in the story of physics.
Clearly the discussion here shows that he question was not 'pointless'

19. Aug 1, 2013

MinnesotaState

WOOT WOOT!

Thanks!

20. Aug 1, 2013

WannabeNewton

We take a physically meaningful quantity that arises naturally out of experiment and decide to label/define it as 'net force'. Asking why this label doesn't stand for something else is pointless, it's just a label. The important part is that the quantity represented by it is tied to something physically meaningful. There's a difference between asking "why should we care about this quantity at all?" and "why not arbitrarily redefine this quantity to something else and call that net force?".

21. Aug 1, 2013

voko

It took a few centuries for that physically meaningful quantity to arise naturally out of experiment.

That much is true, but it takes some culturing to be able to see that difference and not be carried away by pop sci movies featuring extravagantly dressed actors and actresses.

22. Aug 1, 2013

WannabeNewton

Certainly, there's no denying that.

:rofl: Morgan Freeman is the man indeed.

23. Aug 1, 2013

technician

Here is an interesting electrical example for you:
2 circuits, they look identical. Each circuit has a box labelled 'power supply' and 2 other boxes connected in series to their respective power supply. In circuit 1 the boxes are labelled A and B, in circuit 2 they are C and D.
You measure the voltages Va and Vb in circuit 1 and find that they are 2V and 3V. You guess that the supply voltage Vs is 5V.... and you are correct!
You now measure Vc and Vd and find that they are 3V and 4V.
You guess that the supply voltage is 7V and you are wrong!! it is 5V.
In the first circuit 2 and 3 add to give 5, in the second circuit 3 and 4 add to give 5.
If you are familiar with AC circuits you know the explanation.
however you look at it, in the second circuit the voltages need to be squared to give an answer.
As soon as you see 3+4 = 5 I hope you want to draw a right angle triangle.
With this insight you can formulate (practically) all of the relations in AC theory without meeting sine waves or complex numbers.
This is all based on squaring quantities to deal with them

24. Aug 1, 2013

Staff: Mentor

Because the answer to a definition is always the same and there is nothing philosophical about it: someone noticed that the thing was useful and gave it a name. That's it. That's all the "why" of energy is.

25. Aug 1, 2013

Staff: Mentor

Definitions of values are different from definitions of concepts.