Hooke's Law (Cambridge (CIE) IGCSE Physics): Revision Note

Hooke's law

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 

• The force applied to the spring is sometimes referred to as the load

• 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

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:

$F=kx$

• Where:

  • $F$ = force applied, measured in newtons (N)

  • $k$ = the spring constant, measured in newtons per metre (N/m)

  • $x$ = extension of spring, measured in metres (m)

Spring constant

• The spring constant is defined as:

The force per unit extension

• Therefore, the units are newtons per metre (N/m), though newtons per centimetre (N/cm) is equally acceptable and is often more convenient when extensions are measured in centimetres.

• 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

• Any elastic object has a spring constant, not just springs

• The Hooke's law equation can be used to calculate the spring constant of a material

$k=\frac{F}{x}$

The load-extension graph

• Hooke's law is a linear relationship 

  • This is represented by a straight line on a load-extension, or force-extension graph

Load-extension graph for a spring

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

Important features of the load-extension graph 

• The linear portion of the graph

  • This represents the load or force under which the spring obeys Hooke's law

  • Load and extension are directly proportional

  • The gradient of the linear portion is equal to the spring constant for a load-extension graph

  • The gradient of the linear portion is equal to $\frac{1}{k}$ for an extension-load graph

• The limit of proportionality

  • This is the point at which the graph begins to curve

  • Beyond this point, load and extension are no longer proportional

• The curved portion of the graph

  • This is where the material does not obey Hooke's law

  • Load and extension are not proportional