Hooke's Law (DP IB Physics: HL): Revision Note

Hooke's Law

• When a force is applied to each end of a spring, it stretches

  • This phenomenon occurs for any material with elasticity, such as a wire or a bungee rope 

• A material obeys Hooke’s law if:

The extension of the material is directly proportional to the applied force (load) up to the limit of proportionality

• Hooke’s law can also be expressed as an equation:

• Where:

  • F_H = elastic restoring force (N)

  • k = spring constant (N m^–1)

  • x = extension (m)

• The spring constant k is a property of the material being stretched and measures the stiffness of a material

  • The larger the spring constant, the stiffer the material

• Hooke's law applies when a material is extended or compressed:

  • The extension of an object is determined by how much it has increased in length

  • The compression of an object is determined by how much it has decreased in length

• The extension x is the difference between the unstretched and stretched length 

extension = stretched length − unstretched length

Stretching a spring with a load produces a force that leads to an extension

Force–Extension Graphs

• The way a material responds to a given force can be shown on a force-extension graph

• Every material will have a unique force-extension graph depending on how brittle or ductile it is

• A material may obey Hooke's law up to a point

  • This is shown on its force-extension graph by a straight line through the origin

• As more force is added, the graph starts to curve slightly, as Hooke's law no longer applies

The Hooke's law region of a force-extension graph is a straight line. The spring constant is the gradient of that region

• The gradient of the linear portion of this graph is equal to the spring constant k