Hooke's Law
- A material obeys Hooke’s Law if its extension is directly proportional to the applied force (load)
- The Force v Extension graph is a straight line through the origin (see “Extension and Compression”)
- This linear relationship is represented by the Hooke’s law equation
where F is force applied, k is the spring constant in N m−1 and x is the extension of the spring
Worked example
A spring was stretched with increasing load.
The graph of the results is shown below.
What is the spring constant?
Answer:
Step 1: Rearrange Hooke's Law:
- Spring constant, k, is:
Step 2: Relate the gradient of this graph to k :
- The y axis of this graph is length L and the x axis is load F
- Gradient is change in y over change in x:
where change in length is just extension x
- Therefore
Step 3: Determine the gradient of the graph:
- Choose a large section of the graph line to determine the changes in the x and y axes
- Convert the extension from cm to m
Step 4: Calculate the spring constant:
- The spring constant is
Exam Tip
Double check the axes before finding the spring constant as the gradient of a force-extension graph. Exam questions often swap the load onto the x-axis and length on the y-axis. In this case, the gradient is not the spring constant but 1 ÷ gradient is.