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B Definition of Force

  1. Sep 16, 2017 #1
    Can we say that the First law of Newton defines the force whereas the Second law gives the magnitude of force?
  2. jcsd
  3. Sep 16, 2017 #2
    No, Newton's I law only states that In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
    If you accept mass and acceleration as primitive notion, then Newton's second law (In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma.) defines force.
  4. Sep 16, 2017 #3


    Staff: Mentor

    I'd say the first law defines the absence of force and the second has not only magnitude but also direction in it. Turned into the positive direction, the first law says that the change in motion requires a force. It doesn't say what force is.
  5. Sep 16, 2017 #4
    All three laws together define force.
  6. Sep 16, 2017 #5
    Are you sure? First Newton's law concludes from the second Newton's law (you also have to assume that if force is not acting then F=0). Therefor the first Newton's law is not needed to define force.

    \text{Newton's II law}
    \\\text{force does not act} \to F=0
    \ a=\frac{F}{m}
    \\\text{force does not act} \to F=0
    \end{cases}\Rightarrow \text{force does not act} \to a=0 \Rightarrow \text{force does not act} \to _\Delta v=0 \Rightarrow \text{Newtons I law}##
    Last edited: Sep 16, 2017
  7. Sep 16, 2017 #6
    According to the first law force is the reason for changes of motion. This causality doesn't follow from the second law. You can omit the first law if you have no problem with an identity of force and the change of motion. But that's not what Newton had in mind.
  8. Sep 16, 2017 #7
    Newton's laws involve the effect of an unbalanced (net) force on rest or motion. I don't think they define force. If I have a spring attached to a wall at one end and some kind of gauge at the other end and I pull on the spring, I can measure the force.
  9. Sep 16, 2017 #8
    ##a=\frac{F}{m} \to \frac{\partial v}{\partial t}=\frac{F}{m}##⇒change of velocity(motion) is proportional to force.
  10. Sep 17, 2017 #9
    That just means that force is a measure for the change of motion. It doesn't mean that force is the reason for the change of motion as the first law says.

    PS: Motion means momentum and not velocity. Newtons term for momentum is "motus" and his term for velocity is "velocitate". In the second law he used the term "motus". That means that force is proportional to the change of momentum but not necessarily to the change of velocity.
  11. Sep 17, 2017 #10


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    ∫ F dt = Δ mv.
    ∫ F dx = Δ K D' Alembert
  12. Sep 17, 2017 #11
    I agree. Newton's II law only defines netforce.
  13. Sep 17, 2017 #12
    Force is basically the change of momentum per second.
  14. Sep 17, 2017 #13
    Netforce is change of momentum per timeunit.
  15. Sep 17, 2017 #14
    Or to be more exact, that.
  16. Sep 17, 2017 #15
    Force is equal to the corresponding change of momentum and netforce is equal to the total change of momentum per time unit.
  17. Sep 18, 2017 #16


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    It seems that force is proportional to velocity with : ∫ F dx = ∫xxo mv dv/dx (dx) = ∫vv0 mvdv = 1/2mv2 - 1/2mv02 , Δ KE ≅ v - v0
    As opposed to ∫tt0 F dt = tt0 m dv/dt = ∫t0t d/dt mv = dp/dt
    F ≅ t - t0
    Last edited: Sep 19, 2017
  18. Sep 19, 2017 #17
    I don't know what you are talking about.
  19. Sep 19, 2017 #18
    Does this statement contain any information, that equation ##\frac{\partial^2 x}{\partial t^2}=\frac{F_x}{m}## doesn't?
  20. Sep 19, 2017 #19
    Law I establishes the equivalence of inertial reference frames. It is not, as many textbooks report in error, a special case of Law II. In modern physics it's the Principle of Relativity

    Law II defines force. For a particle acted upon by a single force, it equals by definition the rate of change of the particle's momentum. A definition that remains valid in modern physics.

    Law III, taken together with Law II implies conservation of momentum. In modern physics Law III is not valid, but that conservation law is.
  21. Sep 20, 2017 #20


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    And also with ∫ F dt
    Edit: ∫ F dt = ∫tt0 dp/dt dt = Δp = mv2 - mv1
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