• If you plot the extension of a spring vs. the attached mass,…

• …why doesn't the line go through the origin?

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Physics
age: 10 – 16

# Hooke's law

Most textbook authors see it as their calling to make things simple, and that's usually a good thing. When it comes to Hooke's law, they like to draw the expansion vs. the applied force as straight line going through the origin. Now, if you ask any engineer, she will tell you that she hardly ever gets to see such a spring. Most tension springs come with an initial tension, meaning that a minimum force has to be applied before they start to expand linearly.

Learning objective

For many springs, the extension is approximately proportional to the applied force.

This linearity is limited to a specific range of forces, which depends on the spring design.

Visualizing measurement results and critically interpreting plots.

Tension spring
Weights
Tape-measure or ruler
Preparation

Calibrated weights are costly, especially if you want a full set for each student group. Taking a jar and filling it with water gives you a flexible alternative at practically no cost.

1. Measure the length of a spring with different weights attached to it. Visualize your results in a plot.

2. In case your plot differs from that in the textbook – how do you explain this?

Guiding Questions (if needed)

How does the spring length change with increasing load?
› It increases linearly.

What is the slope of the straight line you can draw through your data points?
› That is the spring rate.

Does this linear behavior apply to any load?
› No. For very large forces, the spring will be damaged, and for very small forces, the spring shows no extension.

Findings

Hooke's law, stating that the extension or compression of a spring changes linearly with the applied force, is more of a design feature of the spring than a law of nature: Most, but not all springs are specifically manufactured to demonstrate such a linear behavior for a specific range of forces.

Notwithstanding these limitations, Hooke's law is often a useful approximation for solid materials under relative small deformations – not only in mechanics, but in many other fields of science too.