# Hooke's Law Direction of Force

1. Apr 17, 2012

### thomas49th

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

$$M_{2}\ddot{z_{2}} - K_{2}(\ddot{z_{2}} - \ddot{z_{1}}) = 0$$

but why do we write a PLUS instead?

$$M_{2}\ddot{z_{2}} + K_{2}(\ddot{z_{2}} - \ddot{z_{1}})) = 0$$

So, basically why do we not write

$$M_{2}\ddot{z_{2}} - K_{2}(\ddot{z_{2}} - \ddot{z_{1}})) = 0$$

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.