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Why F = m * a ?

  1. Jun 16, 2012 #1
    Good morning everyone,

    Can someone please tell me the full answer and reason why should the F = m * a?

    Why not F = m + v ?

    For me, it does make sense.

    If I throw a ball, it results a moving mass.

    Thus F = m + v.

    Thank you

  2. jcsd
  3. Jun 16, 2012 #2
    It's basically the definition of force. Newton defined a force as something which changes the momentum of an object. Since momentum is m*v and m is a constant (unless you're talking about rocket ships burning fuel or something) then this change in momentum is due to a change in velocity...which is how we define acceleration. So F=m*a. So basically it follows from our definitions of acceleration, momentum, and force. Newton's first two laws are basically all about defining force.
  4. Jun 16, 2012 #3

    Vanadium 50

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    You cannot add two quantities with different units. What is one foot plus six watts?
  5. Jun 16, 2012 #4
    Thank you very much for the information.

    Now I do understand about it more better than before.
  6. Jun 16, 2012 #5
    Yes, I know pretty good about the mathematical properties such as the summation, subtraction, division, and the multiplication.

    Please correct me if I am wrong.
  7. Jun 16, 2012 #6

    D H

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    You can't add dislike units. F=m+v doesn't make a bit of sense.
  8. Jun 17, 2012 #7
    Even if you add dislike units and write F=m+a it would be wrong because a force can then cause acceleration in the opposite direction, and there's also a case wherein the body will accelerate without any force. We know this doesn't happen.
    If you wrote F=m+v it would mean that a force changes the velocity of a body to v at the instant it is applied(infinite acceleration) and then the velocity doesn't change(zero acceleration). All this is weird, can't be true.
    Last edited: Jun 17, 2012
  9. Jun 17, 2012 #8


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    it's seven foot-watts.

    that's easy.
  10. Jun 17, 2012 #9
    Now thats a question even I asked many.
    What I know is that practically, the equation F = MA stands very convincing as it governs REALLIFE aspects. Take acceleration A simply as change in velocity, and you'll see that F=m+v is incorrect.
    Reallife incidents will turn out to be very much convincing with Newton's.
    Good that you asked 'why'.
  11. Jun 17, 2012 #10

    Vanadium 50

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    I know you're trying to be funny, but let's not confuse the OP.
  12. Jun 17, 2012 #11
    Nowadays we know that that equation is not exact, but it works fine for usual problems.

    Newton and others discovered that without an extenal force (F=0), the product m*v is constant.
    That is even so when objects collide, as illustrated with "Newton's cradle" ( http://en.wikipedia.org/wiki/Newton's_cradle ).

    Further, it was discovered that when you apply a force, the change of speed is proportional to the force.
    Thus it was figured out that F ~ m * Δv/Δt or F ~ m * a.

    This means that F =k * m *a , with k=proportionality constant. A long time ago the units such as kg and Newton were chosen to make calculations easy, from which we got k=1 and thus F= m *a
    Last edited: Jun 17, 2012
  13. Jun 17, 2012 #12
    acceleration is change

    net Force is the agent of change

    mass is the resistance to change

    change is directly proportional to the agent of change and inversely proportional to the resistance to change ...

    [tex]a = k \cdot \frac{F}{m}[/tex]

    since [tex]k = 1[/tex] , [tex]a = \frac{F}{m} \implies F = ma[/tex]
  14. Jun 17, 2012 #13
    What is the mathematical basis for this? Both mass and speed are modeled by field of real numbers, how come we can multiply freely anything with anything, but add only members of the same field?
  15. Jun 17, 2012 #14


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    Because in physics, those numbers have units. And they're different units.

    You can multiply apples-per-crate times the # of crates to get a # of apples. But you can't add crates to apples and get anything meaningful. The point of adding is that you are adding like things.

    apples/crate * crates = apples

    apples+crates = ?

    What does 10 grams plus 60 miles per hour get you? 70 something-or-others.
    Last edited: Jun 17, 2012
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