# Hookes Law Formula

Hooke’s law states that the force required to extend or compress a spring by some distance is directly proportional to that distance. The stiffness of the spring is a constant factor characteristic. The property of elasticity states that it takes twice the much force to stretch a spring twice as long. This linear dependence of displacement on stretching is known as Hooke’s law. This law is named after 17^{th} century British physicist Robert Hooke.

It says that the amount of stress we apply on any object, that amount of stress is observed on it, which means **Stress **∝ **Strain.**

**Hooke’s Law Formula** is given as

**F = -K x**

Where,

F = amount of force applied in N,

x = displacement in the spring in m,

k = spring constant or force constant.

Hooke’s law formula can be applied to determine the force constant, displacement and force in a stretched spring.

**Example 1**

A spring is stretched by 10 cm and has a force constant of 2 cm /dyne. Determine the Force applied.

**Solution:**

Given parameters are

Force constant k is 2 cm/dyne,

Extension x = 10 cm.

The force applied formula is given by

F = – k x

= – 2 × 10 cm

= – 20 cm/dyne

**Example 2**

Determine the force constant if a force of 100 N is stretching a spring by 0.8 m.

**Solution:**

Given parameters are

Force F = 100 N,

Extension, x = 0.2 m.

the force constant formula is given by

k = – F / x

= – 100 / 0.8

= – 125 N/m.