Question

Why is there a negative sign in F =- ks?

Answer 1

Hooke's Law

1. Hooke's Law states that the stress developed inside an elastic body is directly proportional to the strain responsible for it.
2. The force needed to extend or compress a spring by distance $s$ is directly proportional to the amount of expansion or compression.

Hooke's law for a spring:

This force $F_s$ can be written as:

$F_s=-ks$

Where, $F_s$ = force applied on the spring

$k$ = spring constant

$s$ = spring stretch or compression

The negative sign shows that the force applied by the spring will always be opposite to the direction of stretch or compression of the spring.

Thus, there is a negative sign in $F=-ks$.