# Hooke's Law

## Hooke’s Law

The extension of an object, whilst **elastically deforming**, is **directly proportional __to the force applied - provided that the __limit of proportionality** is not exceeded.

The limit of proportionality is the point where the object no longer deforms elastically, and starts to deform **inelastically**.

This law is also known as **Hooke’s Law**.

It comes with an equation which you need to be able to recall and apply:

The extension can still show if an object is **compressed** by having a minus sign. This means that the extension is going in the opposite direction, therefore a compression.

Let’s do an example together: calculate the force required to stretch a spring 5cm. The spring constant of the spring is 120N/m.

The first step is to convert the 5cm into **metres**. 5cm = 0.05m.

Now we can substitute and calculate: **F = k x e**

F = 120 x 0.05 = 6N

Don’t forget units.

## Energy

Who remembers this from the Energy topic?

Yeah!! Me too!!! Anyway, it is good time to use this again (since it comes up again).

A spring has a **spring constant of 25N/m** and it has an **original length of 2.5cm**. If is it extended to __18cm __how much elastic potential energy will be stored in the spring? (4 marks)

The first step is to work out the extension in metres.

0.18 - 0.025 = 0.155m

Then we can calculate this in our equation:

Ee = 0.5 x 25 x x0.1552 = 0.30 J

This second line of calculation contains three marks! One for working, one for the answer and one for units.

A spring has an **original length of 2.5cm** which extends to **8cm __when a force of __3N** has been added to it. Calculate the elastic potential energy which will be stored in this spring once it has been extended.

Step 1: Find the extension

e = 0.08 - 0.02 = 0.055m

Step 2: Calculate the spring constant

**F = ke**

k = F/e

k = 3 / 0.055 = 54.5N/m

Step 3: Plug this into the elastic energy formula.

Ee = 0.5 x 54.5 x 0.0552 = 0.0824J

## Force and Extension

Wherever a material obeys Hooke’s Law, the relationship between force and extension are directly proportional. However if the material distorts **inelastically**, force and extension are **not proportional**.

A more detailed graph is shown below, but the above graph is one required for examinations.

- A spring has been extended by 10cm from its original length. Calculate the spring constant given the spring currently stores 0.3J of elastic potential energy?
- 60N/m
- A spring has an original length of 3cm which extends to 9cm when a force of 4.5N has been added to it. Calculate the elastic potential energy which will be stored in this spring once it has been extended.
- 0.135J