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F= ma

  1. Dec 4, 2004 #1
    Please could someone explain to me why doubling the mass ( therefore doubling number of atoms) means that twice as much force is needed to accelerate object 1m/s2?
  2. jcsd
  3. Dec 4, 2004 #2
    f=ma so the force required is f.

    If f=ma,then
    substituting this into F=(2m)a=2(ma)=2(f),
    so the new force required, F, for double the mass, is twice the amount.
  4. Dec 4, 2004 #3
    No sorry, i didnt quite explain - I meant without the use of the equation. :-) HOw do we explain in terms of physics why twice as much mass needs twice as much force and why twice as much force means twice as much acceleration.

  5. Dec 4, 2004 #4


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    The equation IS the physics involved.
  6. Dec 4, 2004 #5
    No, i mean WHY when we double mass.... etc. It isnt just because an equation says so. Let me give you an example - we know V=IR, but the reason when we double the resistance we half the current is not just because the equation says so! It is because the increased resistances impeeds the electrons forming the current from getting through. Get me? :-)

  7. Dec 4, 2004 #6
    If you need to accelerate an object, you need to overcome its inertia thus exert some force on it. If you have a single atom, lets say you exert f magnitude of force and have it accelerate at A rate.. Now you have 2 atoms. If you use the same force, it will be divided among the atoms so lets say each of them gets f/2 force on them so accelerate at A/2. Therefore u need to use 2f to have both of the atoms accelerate at the same rate as before. I hope this helps.

    Think of it like this. Force is the input and acceleration is output. You get as much as you give. :biggrin:
  8. Dec 4, 2004 #7


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    There is only one possible answer to a question about physical science: that is the result of experiment.

    your example with resistance doesn't really make a lot of sense. How do you KNOW that "the increased resistance impedes the electrons"? All you are really saying there is, roughly, that current is inversely proportional to resistance- and the formula says that more accurately and more concisely.
  9. Dec 4, 2004 #8
    Because its a law of nature that forces add vectorial. To see how this answers your problem consider this simple example: Take one object and place it in your hand and accelerate it at a fixed rate a. Call the force you need to exert on it F_1, Take object 2, which is identical to object one in respects, and place it in your right hand and accelerate it at the same fixed rate that you did object 1. Call the force required to do it F_2. Since the situations are identical then it follows that the total force is F_total = F_1 + F_2 = F + F = 2F. Therefore if you double the mass you must double the force.

  10. Dec 4, 2004 #9
    It's the simple things that are hard to explain. Twice the mass means the object is twice as heavy and have more atoms that have to be moved in order for the whole object to be moved. One needs to exert a force proportional to the number of atoms that is strong enough to move all the atoms of the object.
  11. Dec 4, 2004 #10
    I think it should be fairly intuitive that if something is twice as heavy, you have to push it two times as hard in order to move it.
  12. Dec 4, 2004 #11
    Twice as much mass means twice as much force because you need 2 people to throw 2 baseballs.

    Unless you're being philosophical, I think you're into this equation too deeply, chill.:cool:
  13. Dec 4, 2004 #12
    That does not make any sense, Baseballs? Two people to throw them? Your analogy has no meaning. Please revise or remove it. (I can throw two baseballs at once, I just use both hands :rofl: , so techincally, one person could do what you claim.)
    Last edited: Dec 4, 2004
  14. Dec 4, 2004 #13


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    I could be totally off the mark here, but I think the thread author is asking a more fundamental question than classical mechanics claims to answer. All we can glean from Newton's laws is that there is a quantity known as inertial mass, to which the acceleration of an object being acted on by a force is inversely proportional. In this sense, mass is "inertia quantified", in that it is a physical quantity that directly indicates an object's resistance to a change of state in its motion. But if mass is a physical quantity...surely that means we can, and have measured it? Well, from what I understand, just as with other quantities like electric charge, we don't know much about what it actually is, except that it is associated with matter and has "such and such" properties. So as far as the SI system goes, a unit of mass was simply defined by an arbitrary platinum cylinder in France or something, establishing a scale with which we could measure the effects of greater/lesser mass on the acceleration of an object acting under a force.

    In general we observed (over the ages of course, not only since the French revolution and the metric system with it's platinum can, :biggrin: ) that the mass of an object seemed to be related closely to the amount of matter or "stuff" it contained. However, this was merely an experimental observation. To ask, based on that observation, what is it about more matter (and therefore mass) vs. less matter that makes it have more inertia? To me this question is like asking, why is inertia, as it has been defined, a property of all matter in the universe, and what is it about the fundamental structure of matter involved that more of it resists a change of state in its motion more (i.e has more inertia)? (Well, note we didn't even define force! For that matter, what is motion anyway?) I don't know about you guys, but I think we're getting into things about the nature of the Universe and (WHY it is so) that I am certainly not prepared to answer, and I wonder whether physics is. On the other hand, I don't yet have a good background in either relativity or quantum mechanics, but from vague things I've heard here and there, the term "mass" and the question of what it is has only become more complicated in relativity.

    I'm just voicing some thoughts about this that have been going around in my head, any corrections or clarifications are welcomed. What do you think of my assessment?
  15. Dec 4, 2004 #14


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    It isnt just because an equation says so. Let me give you an example - we know F=ma, but the reason when we double the mass we double the force for the same acceleration is not just because the equation says so! It is because the increased mass impeeds the object from moving.

    This is a little bit tongue-in-cheek, but my intention is to demonstrate that you have little reason to think you have a deeper insight into V=IR than you have in F=ma.
  16. Dec 4, 2004 #15
    Cheman, heres another way to look at it. Maybe this will help. It is because we DEFINE F=ma that doubling the mass doubles the acceleration. What if we did not define F=ma, but said it was F= m^4a. If that were the case, then changing the mass would not be a linear function. The reason it is linear is because we OBSERVE it to be linear. We could have said F=m^4a, and that would be fine, but experiments would show our equation to be wrong. What if the experient did confirm that f=m^4a? Well then the nature of the universe would be different. Its simply a matter of how nature works. It amounts to asking why does an object fall with F=ma and not F=m^4a, no one can tell you exactly why, we just know that to be truth because we have never seen otherwise.

    You actully did this yourself in your own statement.


    Why is it you double the resistance it is HALF the current? Who says it has to be half, just like who says it has to be double the force? It is what it is becuase we observe it to be that way. We obesrve something, and we try to model an equation that fits with our observations.
    Last edited: Dec 4, 2004
  17. Dec 5, 2004 #16
    Thankyou cepheid - thats exactly what I meant! :-) Why when we double the amount of stuff in an object does it double its resistance to acceleration, etc?
  18. Dec 6, 2004 #17
    In fact, what is this strange property of matter, "mass", that resists acceleration? Why will it take x force to push 1 atom but 2x to push 2 bonded together?

    Can anyone offer some further insight? :smile:

    Thanks. :wink:
  19. Dec 6, 2004 #18
    I dont know if your question has an anwser. That is just how mass reacts in the universe. That is a fundamental question, like asking why blue is blue and not green. There is wavelengths and what not, but its blue because it just is. I would mention inertia, but then you would ask why inertia. Thats just the way it works.
  20. Dec 6, 2004 #19


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    Be careful with the notions used and with their range of applicability.U cannot "push" atoms,they push themselves via mutual interractions,usually specified in the potential of interraction (in usual/standard/Copenhagen/textbook QM,interactions are asumed conservative (deriving from conservative forces,though the concept of "force" is strange to QM,and that basically due to Sir William Rowan Hamilton).Judging relativistically (assuming the identity mass=energy),two atoms together will act very differently than just one of them with the mass equal to the sum of the masses for each atom.This thing is classically possible as long as you neglect interactions between bodies.I'm saying that quantum phenomenology cannot explain classical concepts like "inertia",which is the one commonly used to define (inertial(=gravitational)) mass.
    I'm saying again,and i'm willing to say it whenever necessary:each theory has its own domain of aplicability and mixing theories to get a horrible tasting soup is a dumb idea.
    My guess.

  21. Dec 6, 2004 #20


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    From an abstract point of view, cyrusabdollahi is completely correct: we DEFINE force as "rate of change of momentum"= d(mv)/dt. If m is doubled, then the force is doubled.

    But I will still stand by my first response: we DEFINE force that way because the experimental evidence.
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