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F=ma again

  1. Aug 7, 2007 #1
    We have F=ma (Newton 2nd law), and my questions are:

    1 Between F and a, which is the cause of the other? or is it a circular argument?

    2 If it is accepted as a kind of circular argument, then a=F/m, then under suitable unit transformation and for a given m, then F is a kind of acceleration, or vice versa.Please point out whether this argument is wrong.

    3 If possible, please point out whether the above two arguments work for f=ks (Hooker's spring elasticity,a special 1D stress-strain) as well as stress-strain (so called constitutive material relation).

  2. jcsd
  3. Aug 7, 2007 #2
    Accelerations don't happen without forces, but forces can happen without an acceleration. Forces cause accelerations, not the other way around. They're both completely different things, so under no transformation would either be equal to the other.

    F=ma is expressing a relationship, not actually saying that a force is the same thing as a mass times an acceleration. The same holds for your third question.
  4. Aug 7, 2007 #3

    "Forces cause accelerations, not the other way around"

    From my point of view in understanding the above comment, I would say the following

    No F then No a;
    No a then No F (the other way around).

    You mean acceleration does not cause Force (why do you take force as a more fundemental thing here). Does the resultal force has a "direct" reaction force?

    "F=ma is expressing a relationship, not actually saying that a force is the same thing as a mass times an acceleration."

    If you mean F=ma is not a complete definition of force (in this sense F and a is not the same thing), then I agree.

    The argument between F=ma and f=ks (or stress-strain) belongs to the same story?

    Last edited: Aug 7, 2007
  5. Aug 7, 2007 #4


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    You can have forces acting on an object, but with the net force = 0. Then the object won't accelerate. But the forces acting on the object can cause the object to be stretched or deformed. For example suppose an object is hanging from a spring vertically. The top of the spring is attached to the ceiling. The spring is stretched, not moving... so it has 0 net force acting on it... however it is stretched... and this is the effect of external forces acting on the spring (the weight of the hanging object downwards, and the ceiling holding the spring up)... If there were no external forces then it wouldn't be stretched.

    So this shows that force is a concept separate from acceleration... forces have an effect even when there is no acceleration.
  6. Aug 7, 2007 #5
    learning physics,

    Your external forces, to my understanding, is not net forces (your case is in quasi-equalibrium?). You seem to want to show: F=0 shows there is still force action (an apple on a table has 0 acceralation but..).But this is not the point I questioned about.

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