Force–Extension Graphs (OCR Gateway GCSE Physics: Combined Science)

• Hooke’s law is the linear relationship between force and extension
  • This is represented by a straight line on a force-extension graph

• Materials that do not obey Hooke's law, i.e they do not return to their original shape once the force has been removed, have a non-linear relationship between force and extension
  • This is represented by a curve on a force-extension graph

• Any material beyond its limit of proportionality will have a non-linear relationship between force and extension

Linear and non-linear regions of a force-extension graph

• 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