CalculateQuestion 1 · Recall
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By the end you can define the spring constant, calculate it from a load and an extension, and read it as the gradient of a load–extension graph.
The main symbols used in this lesson:
| Symbol | Meaning |
|---|---|
| a change in, so means "the change in " |
Hooke's law says . The constant collects everything about the object that makes it hard or easy to stretch: its material, its thickness and its length.
Rearrange it and you get the definition:
So is the load needed to produce unit extension — how many newtons per metre.
A big means a stiff object: it takes a large force to stretch it. A small means a soft one.
Spring constant
The force per unit extension of an object, , measured in newtons per metre ().
It is the reciprocal of the gradient of an extension–load graph, and equal to the gradient of a load–extension graph.
Put load on the vertical axis and extension on the horizontal axis, as in the diagram. Then
A steep line means a large for a small — lots of newtons for little stretch — so a large : stiff.
A shallow line means a small load already stretches it a lot, so a small : soft.
Trap: if a graph is plotted with extension on the vertical axis, the gradient is , not . Always check which quantity is on which axis before quoting a gradient.
Worked example: Worked example: finding k, then using it
A spring extends 4.0 cm when a 6.0 N load hangs on it.
(a) Find the spring constant. (b) Find the extension with an 11 N load, assuming Hooke's law still applies.
Worked example: Worked example: k from a graph
A load–extension graph for a rubber cord is a straight line through the origin. It passes through the point (extension 0.050 m, load 7.5 N).
Find the spring constant of the cord.