Hooke's Law (AQA GCSE Physics: Combined Science)

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Hooke's Law

What is Hookes' 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 the force is increased, the extension increases 
    • If the force is doubled, then the extension will double
    • If the force is halved, then the extension will also halve
  • The limit of proportionality is the point beyond which the relationship between force and extension is no longer directly proportional 
    • This limit varies according to the material

Load extension and force, downloadable AS & A Level Physics revision notes

Hooke's Law states that a force applied to a spring will cause it to extend by an amount proportional to the force, this can be tested by this Hooke's Law experiment

Using Hooke's Law

Hooke's Law Equation

  • 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

Hookes Law Diagram, downloadable IGCSE & GCSE Physics revision notes

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:

Hookes Law Formula Triangle, downloadable IGCSE & GCSE Physics revision notes

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.Hookes Law Worked Example, downloadable IGCSE & GCSE Physics revision notesThe 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

Examiner 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

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Ashika

Author: Ashika

Expertise: Physics Project Lead

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.