Hooke's Law
- When a force F is added to the bottom of a vertical metal wire of length L, the wire stretches
- A material obeys Hooke’s Law if:
The extension of the material is directly proportional to the applied force (load) up to the limit of proportionality
- This linear relationship is represented by the Hooke’s law equation:
- The spring constant, which is sometimes called the force constant k, is a property of the material being stretched and measures the stiffness of a material
- The larger the spring constant, the stiffer the material
- Hooke's Law applies to both extensions and compressions:
- The extension of an object is determined by how much it has increased in length
- The compression of an object is determined by how much it has decreased in length
Worked example
A spring was stretched with increasing load.
The graph of the results is shown below.
What is the spring constant?
Examiner Tip
Always double-check the axes before finding the force constant as the gradient of a force-extension graph.Exam questions often swap the force (or load) onto the x-axis and extension (or length) on the y-axis. In this case, the gradient is not the force constant, it is 1 ÷ gradient instead.
