## Hooke's Law

**Hooke's Law:** Stress and strain take different forms in different conditions. Usually, for small deformations, the stress and strain are proportional to each other. This is what we called as Hooke's Law. Hooke’s law is a factual law and is found to be valid for most of the materials. Historically, this law was named after British physicist Robert Hooke. He established a relationship between force and displacement in the year 1660 and published it in the year 1678.

**According to Hooke’s Law, “The force applied to compress or stretch the spring is directly proportional to the distance with which the spring is deformed”**

Therefore, stress ∝ strain

Stress = k × strain

Or, **F = -k x**

where,

F is the force applied

k is the distance with which the spring deformed

k is the constant of proportionality and is called the modulus of elasticity. The negative sign in Hooke’s law explains the restoring force which is trying to return the spring to its equilibrium position.

SI unit of Hooke’s law is **Newton or N (kg.m.s-²)**

## Hooke's Law for Spring

Hooke’s law for spring states that the force (F) that is required to extend or compress a spring by some distance varies proportionately with respect to that distance. This indicates that more force will be required to elongate a spring more and vice versa. When elastic materials like springs are stretched using a force (F), disfigurement of atoms and molecules occurs until stress is applied and they get back to their initial state when the stress is removed.

## Stress-Strain Curve

The stress-strain curve is a relationship graph that shows the change in stress as strain increases. It is a widely used reference graph for metals in science relating to materials and manufacturing. Even a small amount of change in length (the strain)to apply the force needed to cause the strain is recorded. The applied force is slowly and steadily increased in steps and the change in length is recorded.

## Hooke’s Law Applications

The application relating to Hooke's Law is -

- It explains the fundamental principle behind the manometer, spring scale, and the balance wheel of the clock.
- This law is even applicable to the foundation for seismology, acoustics and molecular mechanics.

## Real-Life Examples of Hooke's Law

Some of the real-life examples of Hooke's law are-

- Retractable Pens (Also called Click pens) has to spring attaches to them at the top and bottom which works on Hooke's Law.
- The recoil of a Toy Gun which has a spring at the end of the spring also works on Hooke's law principle.
- Inflating a Balloon
- Manometer
- Spring Scale
- The balance wheel of the Clock
- Bathroom scale

## Solved Exercises on Hooke's Law

**Exercise 1: How much force is needed to pull a spring scale with a spring constant of 20 N/m at a distance of 20 cm?**

**Solution:** According to the question, k = 20 N/m

x = 20 cm = 0.20 m

As we know, F = k x

**Therefore, F = 20 N/m x 0.20 m = 4N**

**Exercise 2: **A spring scale is pulled to 15 cm and held in place with a force of 500 N. What is the spring constant of the spring scale?

**Solution: **According to the question, F = 500 N

x = 15 cm = 0.15 m

As we know, Formula: F = k x

**Therefore, k = F/x or, k = 500 N/0.15 m = 3333.33 N/m**

**Exercise 3: **What is the force required to stretch a 30 cm-long retractable spring, with a spring constant of 160 N/m, to a length of 34 cm?

**Solution: **According to the question,

l1 = 30cm

l2 = 34cm

k = 160 N/m

Therefore, x = l2 – l1 = 34 cm – 30 cm = 4 cm = 0.04 m

As we know, F = k x

**F = 160 N/m x 0.04 m = 6.4N**