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Homework Help: 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


    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
  2. jcsd
  3. Apr 17, 2012 #2
    come on someone surely must know, it's just a matter of signs
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