Investigating Springs and Hooke's Law

This experiment investigates how the extension of a spring depends on the applied force.

Method

1. Clamp the spring vertically. Record the original (natural) length $L_0$ using a ruler and set square.
2. Add a known mass (e.g. 100 g = 0.98 N) and measure the new length $L$.
3. Calculate the extension: $x = L - L_0$.
4. Repeat, adding masses one at a time up to the elastic limit.
5. Remove masses and check the spring returns to its original length.

Results and graph

Plot force ($F$, y-axis) against extension ($x$, x-axis).

The straight section through the origin confirms Hooke’s law: $F = kx$.

The gradient of this section equals the spring constant $k$ (in N/m).

Beyond the limit of proportionality, the line curves. The spring no longer obeys Hooke’s law and may be permanently deformed.

Improving accuracy

• Use a set square to avoid parallax when reading the ruler.
• Wait for the spring to stop oscillating before reading.
• Take readings while loading AND unloading to check for permanent deformation.

Common errors and how to correct them

• Measuring total length instead of extension.
• Exceeding the elastic limit so the spring does not return to its natural length.
• Not using a fiducial marker to reduce parallax.

How to apply this in an exam

Describe the key measurements (natural length, loaded length, extension), how to plot the graph, what the straight section shows, and where Hooke’s law breaks down.