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

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Discussion Overview

The discussion revolves around the relationship between force and energy, specifically questioning why the equation for force is expressed as F=ma rather than F=ma². Participants explore the philosophical implications of squaring in physics, the definitions of force and energy, and the historical context of these concepts.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Historical

Main Points Raised

  • One participant suggests that the relationship in F=ma implies a constant relation between mass and acceleration, questioning the absence of a squared term.
  • Another participant asserts that F=ma is a physically true statement and that F=ma² is not true, indicating a clear distinction between force and energy.
  • Some participants express confusion over the differences between energy and force, with references to e=mc² and its completeness.
  • A participant challenges the relevance of energy in the context of free fall, suggesting that energy and force are not directly related.
  • There is a discussion about the philosophical implications of definitions in physics, with some arguing that questioning definitions is valid and important for understanding the evolution of concepts.
  • One participant notes that mechanical energy is not conserved in certain situations, suggesting that energy analysis may not be optimal in those cases.
  • Another participant highlights the historical debate between Leibniz and the Cartesians regarding the concept of force and conserved quantities of motion.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between force and energy, with some asserting clear distinctions while others seek to understand their connections. There is no consensus on the philosophical implications of squaring or the definitions involved.

Contextual Notes

Some participants reference historical definitions and their evolution, indicating that the discussion may be influenced by varying interpretations of foundational concepts in physics.

MinnesotaState
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Please watch 05:00 to 08:00



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.
 
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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.
 
You're basically asking: why is a definition defined to be what is given in the definition? This is of course a pointless question.
 
Where am I going wrong with energy & force?

They are different,

e=mc^2
f=maI do not understand the philosophy of squaring either.
 
MinnesotaState said:
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.

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

E[itex]^{2}[/itex]=m[itex]^{2}[/itex]c[itex]^{4}[/itex]+p[itex]^{2}[/itex]c[itex]^{2}[/itex]
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.
 
johnqwertyful said:
I also don't see how the equations are related it anyway, other than both being equations in physics.

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?
 
MinnesotaState said:
I guess I don't understand the difference between energy & force.
Yes. They are nowhere close to the same thing.
Where am I going wrong with energy & force?

They are different...
[separate post]
...
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.
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.
 
russ_watters said:
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.

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.
 
MinnesotaState said:
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.
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
MinnesotaState said:
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.

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

[edit] 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.
 
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  • #12
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
WannabeNewton said:
You're basically asking: why is a definition defined to be what is given in the definition? This is of course a pointless question.
How is it a pointless question? Are you saying it's pointless to ask why definitions are as they are?
 
  • #14
Never get into an argument with a philosopher. Neither of you will get satisfaction, and the argument never ends.
 
  • #15
SteamKing said:
Never get into an argument with a philosopher. Neither of you will get satisfaction, and the argument never ends.

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
Can we go over the philosophy of squaring?

:)
 
  • #17
MinnesotaState said:
Can we go over the philosophy of squaring?

:)

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

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
voko said:
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

WOOT WOOT!

Thanks!
 
  • #20
Jorriss said:
How is it a pointless question? Are you saying it's pointless to ask why definitions are as they are?
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
WannabeNewton said:
We take a physically meaningful quantity that arises naturally out of experiment and decide to label/define it as 'net force'.

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

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?".

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
voko said:
It took a few centuries for that physically meaningful quantity to arise naturally out of experiment.
Certainly, there's no denying that.

voko said:
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.
:smile: Morgan Freeman is the man indeed.
 
  • #23
MinnesotaState said:
Can we go over the philosophy of squaring?

:)

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
Jorriss said:
How is it a pointless question? Are you saying it's pointless to ask why definitions are as they are?
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
technician said:
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'
Definitions of values are different from definitions of concepts.
 
  • #26
russ_watters said:
Definitions of values are different from definitions of concepts.

I know.
My issue was with rating someone's question as 'pointless'
There has been some interesting discussion around an apparently 'pointless' question.

The 'silly' question is the first intimation of some totally new development
 
  • #27
technician said:
I know.
My issue was with rating someone's question as 'pointless'
There has been some interesting discussion around an apparently 'pointless' question.
Frankly, this thread has baffled me from the beginning and I've seen very little value in spending so much time trying to explain something so basic as what force is.
 
  • #28
SteamKing said:
Never get into an argument with a philosopher. Neither of you will get satisfaction, and the argument never ends.

I rest my case.
 
  • #29
russ_watters said:
Frankly, this thread has baffled me from the beginning and I've seen very little value in spending so much time trying to explain something so basic as what force is.

I only come here when I know I have spare time.
If you want a textbook lesson in how not to do it check this thread...now closed

https://www.physicsforums.com/showthread.php?t=703041
 
  • #30
SteamKing said:
I rest my case.

And I mine.
 

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