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Hooke's Law Direction of Force

  1. Apr 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi I know for Hooke's Law F=-kx where -ve sign implies a restoring force back to equilibrium in the opposite direction of x.

    My question is:
    I have a mass being displaced attached to a spring - consider M2 and z2(t) and K2 in the link below


    http://gyazo.com/dfba23fbc16916940c25a02b1d96566e

    So as z2 move downwards (in the image) the spring stretches and a the restoring force acts upwards. The total force is going to be the force from the spring plus the force from the displaced mass, which is

    [tex]M_{2}\ddot{z_{2}} - K_{2}(\ddot{z_{2}} - \ddot{z_{1}}) = 0[/tex]
    note the -ve sign infront of the k2.

    but why do we write a PLUS instead?

    [tex]M_{2}\ddot{z_{2}} + K_{2}(\ddot{z_{2}} - \ddot{z_{1}})) = 0[/tex]
    (see answers below)

    So, basically why do we not write

    [tex]M_{2}\ddot{z_{2}} - K_{2}(\ddot{z_{2}} - \ddot{z_{1}})) = 0[/tex]

    as doesn't that make more sense. Because then the force of the spring restoration force equals the mass force, which is when the mass is at rest.


    The answers
    http://gyazo.com/80ef4fc8e73dd510bd8c6489758471e7
     
  2. jcsd
  3. Apr 17, 2012 #2
    come on someone surely must know, it's just a matter of signs
     
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