# 5.3.2 Hooke's Law

### Hooke's Law

• The relationship between the extension of an elastic object and the applied force is defined by Hooke’s Law
• Hooke’s Law states that:

The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality

• Directly proportional means that as more force is applied, the greater the extension (and vice versa)
• The limit of proportionality is where if more force is added, the object may extend but will not return to its original shape when the force is removed (it will be inelastically deformed)
• This varies according to the material Hooke’s Law states that a force applied to a spring will cause it to extend by an amount proportional to the force

### Using Hooke's Law

• Hooke’s Law is defined by the equation:

F = k × e

• Where:
• F = force in newtons (N)
• k = spring constant in newtons per metres (N/m)
• e = extension in metres (m)
• The symbol e can represent either the extension or compression of an elastic object
• The spring constant represents how stiff a spring is
• The higher the spring constant, the higher the stiffness
• The extension of an object can be calculated by:

final length – original length

• The extension of the spring can be measured by marking the position of bottom of the unstretched spring
• When the spring is stretched the final length must be measured from the bottom of the spring Force, extension and spring constant are used to define Hooke’s Law

• The Hooke’s Law equation can be rearranged with the help of the following equation triangle: #### Worked Example

The figure below shows the forces acting on a child who is balancing on a pogo stick.

The child and pogo stick are not moving. The spring constant of the spring on the pogo stick is 4900 N/m. The weight of the child causes the spring to compress elastically from a length of 40 cm to a new length of 33 cm.

Calculate the weight of the child.

Step 1: List the known quantities

• Spring constant, k = 4900 N/m
• Original length = 40 cm
• Final length = 33 cm

Step 2: Write the relevant equation

F = ke

Step 3: Calculate the extension, e

e = final length – original length = 40 – 33 = 7 cm

Step 4: Convert any units

• Since the spring constant is given in N/m, e must be in metres (m)

7 cm = 0.07 m

Step 5: Substitute the values into the Hooke’s Law equation

F = 4900 × 0.07 = 343 N

#### Exam Tip

Look out for unit conversions! Unless the spring constant is given in N/cm, make sure the extension is converted into metres (÷ 100) before substituting values into the Hooke’s Law equation ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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