Multiple choiceQuestion 1 · Recall
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By the end you can state Hooke's law, recognise the part of a load–extension graph where it applies, and use to predict an extension or a load.
Hang weights on a spring and measure the extension each time. A typical set of results:
| Load / N | Extension / cm | / (N cm⁻¹) |
|---|---|---|
| 1.0 | 2.0 | 0.50 |
| 2.0 | 4.0 | 0.50 |
| 3.0 | 6.0 | 0.50 |
| 4.0 | 8.0 | 0.50 |
Every row gives the same ratio. That is what directly proportional means: doubling the load doubles the extension, and the ratio is constant.
This behaviour has a name, after Robert Hooke.
Hooke's law
The extension of an object is directly proportional to the load applied, provided the limit of proportionality is not exceeded.
As an equation:
where is the load in newtons, the extension in metres, and a constant for that object called the spring constant (next lesson).
Hooke's law is not a law about all materials at all loads. It is a statement about the straight part of the graph.
Think of a rubber band. A gentle pull and it behaves itself: twice the force, twice the stretch. Pull harder and it suddenly gives a lot more for the same extra force — the graph curves, and gives nonsense.
So the recipe is always the same: check the graph (or the question) says you are within the limit of proportionality before you use the equation.
Worked example: Worked example: using the pattern without the equation
A spring extends 12 mm when a 3.0 N load hangs on it, and the spring is within its limit of proportionality.
What load would make it extend 20 mm?
Worked example: Worked example: is the spring still obeying Hooke's law?
A student's results for a spring are: 2.0 N gives 5.0 cm, 4.0 N gives 10.0 cm, 6.0 N gives 17.0 cm.
Is the spring obeying Hooke's law throughout? Explain.