Hooke's Law (CIE IGCSE Physics)

Extended tier only

• 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

The extension of a spring due to an applied load

Hooke's Law states that a force applied to a spring will cause it to extend by an amount proportional to the force

• Hooke's law can be described by the following equation:

• Where:
  • = force applied, measured in newtons (N)
  • = the spring constant, measured in newtons per metre (N/m)
  • = extension of spring, measured in metres (m)
• The force applied to the spring is sometimes referred to as the load

 

Spring constant

• The spring constant is defined as:

The force per unit extension

• Therefore, the units are newtons per metre (N/m)
• The spring constant is a measure of how stiff the spring is
  • Stiff springs have a high spring constant
  • Stretchy springs have a low spring constant
• The spring constant can be applied to objects other than springs
• The Hooke's law equation can be used to calculate the spring constant of a material

The force-extension graph

• Hooke’s law is a linear relationship 
  • This is represented by a straight line on a force-extension, or load-extension graph

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

Force-extension graph for a spring

Hooke's Law is associated with the linear region of a force-extension graph. Beyond the limit of proportionality, Hooke's law no longer applies

Important features of the force-extension graph 

• The linear portion of the graph
  • This represents the load or force under which the spring obeys Hooke's law
  • Force and extension are directly proportional
  • The gradient of the linear portion is equal to the spring constant for a force-extension graph
  • The gradient of the linear portion is equal to for an extension-force graph
• The limit of proportionality
  • This is the point at which the graph begins to curve
  • Beyond this point, force and extension are no longer proportional
• The curved portion of the graph
  • This is where the material does not obey Hooke's law
  • Force and extension are not proportional