So far we've dealt only with constant forces. Springs are more complicated - not only does the magnitude of the spring force vary, the direction of the force depends on whether the spring is being stretched or compressed.

Measuring all distances from the equilibrium length of the spring, the force from an ideal spring is given by Hooke's Law:

F = -kx

k is the spring constant, a measure of the stiffness of the spring in units of N/m.

The minus sign means that the spring force is opposite in direction to the displacement.

The spring for our demonstration stretches about 10 cm for every 100 g (about 1 N).

The spring constant is

k

=

1 N 0.1 m

=

10 N/m

The spring in the simulation above has a different spring constant, which you should be able to determine by dragging the mass.

The potential energy of a spring is given by:

U = ½ kx²