Investigating Force and Extension

This experiment explores how a spring stretches when a force pulls it. The extra length the spring gains is called its extension. For small forces, many springs follow Hooke’s law: the force is proportional to the extension.

Key ideas

• Extension (x): new length − original length.
• Force (F): the weight of the hanging masses, measured in newtons (N). Use weight, not mass.
• Spring constant (k): stiffness of the spring. Larger k means stiffer spring.

Hooke’s law: $F = kx$ (valid only up to the limit of proportionality).

Apparatus and setup

• Clamp stand secured with a G-clamp
• Steel spring with a pointer
• Ruler placed close to the spring (zero aligned)
• Mass hanger and slotted masses
• Optional: force meter (to read F directly)

Method (how to collect data)

1. Measure the spring’s original length at eye level.
2. Add a known mass gently. Record the new length. Calculate extension = new length − original length.
3. Increase the load in equal steps. Record force and extension each time.
4. Remove the loads and check if the spring returns to its original length.

Plotting and interpreting the graph

• Plot a load–extension graph with force (N) on the vertical axis and extension (m or cm) on the horizontal axis.
• A straight line through the origin shows proportionality (Hooke’s law region).
• The gradient (slope) equals the spring constant $k$: $$k = \frac{F}{x}$$
• Limit of proportionality: the point where the graph stops being a straight line. Beyond this, $F$ is no longer proportional to $x$, so $F = kx$ no longer applies.

Common mistakes

• Using mass (g) instead of weight (N). Always convert mass to force.
• Measuring total length instead of extension. Subtract the original length.
• Reading the ruler at an angle (parallax error). Keep your eye level with the pointer.
• Assuming rubber bands obey Hooke’s law. Many materials do not show a straight-line region.

Real-world link: Pens, trampolines, and weighing scales use springs. Their safe working range stays within the proportional region.