Hooke's Law (Cambridge (CIE) A Level Physics)

Hooke's law

• A material demonstrating elastic behaviour obeys Hooke’s Law if its extension is directly proportional to the applied force (load)

• The Force-extension graph of an object obeying Hooke's law is a straight line through the origin 

• This linear relationship is represented by the Hooke’s law equation

• Where:

  • F is force applied in N

  • k is the spring constant in N m⁻¹

  • x is the extension of the spring

The spring constant

• k is the spring constant of the spring and is a measure of the stiffness of a spring

  • A stiffer spring will have a larger value of k

• k is defined as the force per unit extension up to the limit of proportionality

• The SI unit for the spring constant is N m^-1

• Rearranging the Hooke’s law equation shows the equation for the spring constant is

• Therefore, the spring constant k is the gradient of the linear part of a force-extension graph

Gradient of force-extension graph

Spring constant is the gradient of a force vs extension graph