Hooke's Law (Edexcel GCSE Physics)

• 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 more force is applied, the greater the extension (and vice versa)
• The limit of proportionality is where if more force is added, the object may extend but will not return to its original shape when the force is removed (it will be inelastically distorted)
  • This 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