Hooke's Law

Understanding Hooke’s Law

  • Hooke’s Law states that the extension of a spring is directly proportional to the force applied, provided the elastic limit is not exceeded.
  • The law can be represented by the equation F = kx, where F is the force, k is the spring constant, and x is the extension.
  • Force (F) is measured in newtons (N).
  • The spring constant (k) is a measure of the stiffness of the spring, measured in newtons per metre (N/m).
  • The extension (x) is the amount the spring has stretched or compressed from its original length, measured in metres (m).

Applying Hooke’s Law

  • To calculate the force, multiply the spring constant by the extension (F = kx).
  • To calculate the extension, divide the force by the spring constant (x = F/k).
  • To calculate the spring constant, divide the force by the extension (k = F/x).

Limitations of Hooke’s Law

  • Hooke’s Law only applies up to the point known as the elastic limit.
  • Beyond the elastic limit, a material or spring will not return to its original shape after the force is removed. It has been permanently deformed. This is called plastic deformation.
  • The point beyond which a material becomes plastic and no longer obeys Hooke’s Law is called the yield point.
  • The exact yield point and elastic limit vary depending on the material.

Energy Stored in a Spring

  • When a spring is stretched or compressed, it stores energy. This is known as elastic potential energy.
  • The amount of elastic potential energy stored in a spring can be calculated using the equation E = ½kx², where E is the energy in joules (J), k is the spring constant, and x is the extension.
  • Elastic potential energy is a form of potential energy and can be converted into other forms of energy such as kinetic energy.

Practical Applications of Hooke’s Law

  • Hooke’s Law is crucial in many scientific and engineering applications including springs, rubber bands, vehicle suspensions, and construction materials.

Exam Tip

  • Make sure to always pay close attention to unit conversions when dealing with Hooke’s Law equations. For example, when working with the spring constant, confirm whether it is given in N/m or other units. Likewise, check if the extension is given in metres or possibly centimetres. Clear and careful management of units can prevent errors in your calculations.