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

  1. Jul 31, 2013 #1
    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.
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Jul 31, 2013 #2
    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.
  4. Jul 31, 2013 #3


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    You're basically asking: why is a definition defined to be what is given in the definition? This is of course a pointless question.
  5. Jul 31, 2013 #4
    Where am I going wrong with energy & force?

    They are different,


    I do not understand the philosophy of squaring either.
  6. Jul 31, 2013 #5
    First off, e=mc^2 is not true (at least not complete). The real equation is

    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.
  7. Jul 31, 2013 #6
    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.


    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?
  8. Jul 31, 2013 #7


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    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.
  9. Jul 31, 2013 #8
    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.
  10. Jul 31, 2013 #9


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    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?
  11. Jul 31, 2013 #10


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    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.
  12. Jul 31, 2013 #11


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    Staff: Mentor

    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.
    Last edited: Jul 31, 2013
  13. Jul 31, 2013 #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."
  14. Jul 31, 2013 #13
    How is it a pointless question? Are you saying it's pointless to ask why definitions are as they are?
  15. Aug 1, 2013 #14


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    Never get into an argument with a philosopher. Neither of you will get satisfaction, and the argument never ends.
  16. Aug 1, 2013 #15
    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
  17. Aug 1, 2013 #16
    Can we go over the philosophy of squaring?

  18. Aug 1, 2013 #17
    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
  19. Aug 1, 2013 #18
    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'
  20. Aug 1, 2013 #19

  21. Aug 1, 2013 #20


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    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?".
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