Imagine pulling on a spring. When you apply a force, it will stretch and **extend. **In fact, the amount of force will affect the extension of the spring.

If you double the force on the spring, the extension will double. Why? Because springs are an example of a material that follows **Hooke's Law. **Let's learn about Hooke's Law, and practise using it in calculations.

Hooke's Law states that, for certain materials, the extension of the material is **directly proportional **to the force acting on the material. So, if we double the force, we double the extension. If we triple the force, we triple the extension.

**Example**

Someone applies 3 Newtons of force when they stretch a spring. The spring extends by 4 cm. What would the extension of the spring be if a force of 6 Newtons was applied instead?

**Answer **

In this situation, the spring is experiencing double the force, so it must extend by double the amount.

4 cm × 2 = 8 cm

We can express Hooke's Law, just like many other proportional relationships, with an equation.

**Force = Spring Constant × Extension**

Or, simplified,

**F = k × e**

F stands for force and is measured in Newtons (N)

k stands for spring constant and is measured in Newtons per metre (N/m)

e stands for extension and is measured in metres.

What does 'spring constant' mean?

The spring constant is a measure of how stretchy a material is. The spring constant is a number that is different for each material.

The greater the spring constant, the harder it is to stretch a material. The smaller the spring constant, the easier it is to stretch.

**Example**

** **A material has a spring constant of 0.6 N/m. It has an extension of 0.2 m. What is the force on the material?

**Answer**

First, we write down the equation. Then, we substitute in the values that we know.

F = k × e

F = 0.6 N/m × 0.2 m = 0.12 N

We can also **rearrange **the equation for Hooke's law, for situations when we want to calculate the spring constant, or the extension, instead.

**Example**

** **What is the spring constant for a stretchy material, if it experiences a force of 2.5 Newtons, and extends by 8 cm?

**Answer**

We actually have to convert the extension from cm to m before we do anything else!

8 cm ÷ 100 = 0.08 m

Now we can use the rearranged equation.

k = 2.5 N ÷ 0.08 m = 31.25 N/m

Now that we have seen Hooke's Law in action, let's try some practice questions!