Hooke's Law (Edexcel GCSE Physics: Combined Science)

• 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

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 is defined by the equation:

F = k × x

• Where:
  • F = force in newtons (N)
  • k = spring constant in newtons per metres (N/m)
  • x = extension in metres (m)

• The symbol x can represent either the extension or compression of an elastic object
• The Hooke's law equation can be rearranged using the following formula triangle:

• The spring constant represents how stiff a spring is
  • The higher the spring constant, the higher the stiffness

• The extension of an object can be calculated by:

Final length – Original length

• The extension of the spring can be measured by marking the position of bottom of the unstretched spring
• When the spring is stretched the final length must be measured from the bottom of the spring

The extension measured from its final and original length

Step 1: List the known quantities

• • Spring constant, k = 4900 N/m
  • Original length = 40 cm
  • Final length = 33 cm

Step 2: Write the relevant equation

F = kx

Step 3: Calculate the extension, x

x = final length – original length = 40 – 33 = 7 cm

Step 4: Convert any units

• • Since the spring constant is given in N/m, x must be in metres (m)

7 cm = 0.07 m

Step 5: Substitute the values into the Hooke's Law equation

F = 4900 × 0.07 = 343 N

• 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