6.1.2 Hooke's Law

• A material obeys Hooke’s Law if its extension is directly proportional to the applied force (load)
• The Force v Extension graph is a straight line through the origin (see “Extension and Compression”)
• This linear relationship is represented by the Hooke’s law equation

Hooke’s Law

• The constant of proportionality is known as the spring constant k

• 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

• It is defined as the force per unit extension up to the limit of proportionality (after which the material will not obey Hooke’s law)
• 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

Spring constant equation

• The spring constant is the force per unit extension up to the limit of proportionality (after which the material will not obey Hooke’s law)
• Therefore, the spring constant k is the gradient of the linear part of a Force v Extension graph

Spring constant is the gradient of a force v extension graph

Combination of springs

• Springs can be combined in different ways
  • In series (end-to-end)
  • In parallel (side-by-side)

Spring constants for springs combined in series and parallel

• This is assuming k₁ and k₂ are different spring constants
• The equivalent spring constant for combined springs are summed up in different ways depending on whether they’re connected in parallel or series