Experiment: Find the spring constant

Hooke's law experiment

The spring constant of a spring can be found by carrying out an experiment.

The unloaded length of a spring is measured.

Slotted masses are added to the spring.

Record each stretching force in N and the corresponding length of the spring.

The extension is the new length minus the unloaded length.

Graph showing Hooke's Law.Graph showing Hooke's Law, force is plotted against extension

Provided that the limit of proportionality is not exceeded, a graph of stretching force against extension is a straight line through the origin, because Hooke’s Law is obeyed.

The gradient of the line \frac{\text{F}}{\text{e}} is the spring constant, k.

The gradient of the graph of force F, (y-axis), and extension e, (x-axis), is equal to the spring constant k.

Hooke’s Law is obeyed up to the limit of proportionality.

Beyond this point, stretching force and extension are no longer directly proportional and the graph begins to curve.

If a material is stretched further still, and beyond a point known as the elastic limit, it does not return to its original length when the force is removed.

A force extension graph. Linear section drawn from origin to occupy half of graph area. Non linear section has decreasing gradient. Change from linear to non-linear is marked and labelled.
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