Required Practical: Investigating Force & Extension

Purpose of the Practical

This practical investigates how the extension of a spring changes as different forces are applied. It helps you understand the elastic behaviour of materials 6how they stretch and return to their original shape when forces are removed. The experiment allows you to apply Hooke's Law practically by measuring how force relates to extension.

Equipment and Setup

• Spring attached to a clamp stand
• Ruler fixed vertically next to the spring to measure extension accurately
• Set of known weights or a force meter to apply force
• Pointer or marker attached to the spring to measure extension from the original length

Ensure the ruler is aligned so you can read the extension without parallax error. The spring should hang freely without touching anything else.

Method Procedure

1. Measure the original length of the spring with no load applied.
2. Add a known weight (or apply a known force using the force meter) to the spring.
3. Measure the new length of the spring and calculate the extension by subtracting the original length.
4. Record the force applied and the corresponding extension in a table.
5. Repeat steps 2 64 for increasing forces, adding weights incrementally.
6. For accuracy, repeat each measurement and calculate an average extension for each force.
7. Stop adding weights before the spring is permanently stretched (beyond its elastic limit).
8. Ensure the spring is unstressed and the force meter reads zero before starting measurements.

For example, if the spring 27s original length is 10.0 cm and after adding a 2 N force it stretches to 12.5 cm, the extension is $12.5 - 10.0 = 2.5 \text{ cm}$.

Data Analysis

Plot a graph of force (y-axis, in newtons, N) against extension (x-axis, in metres, m). The graph should show a straight line through the origin in the elastic region, indicating a proportional relationship.

The gradient of the linear region gives the spring constant $k$, calculated by:

$$k = \frac{\text{Force}}{\text{Extension}}$$

The spring constant $k$ is a measure of the stiffness of the spring. A larger $k$ means a stiffer spring.

If the graph curves or does not pass through the origin, the spring may have been stretched beyond its elastic limit and is no longer obeying Hooke 27s Law. This deviation indicates the elastic limit has been exceeded.

For instance, if a force of 5 N causes an extension of 0.02 m, the spring constant is:

$$k = \frac{5}{0.02} = 250 \text{ N/m}$$

Safety and Accuracy

• Handle weights carefully to avoid dropping them on feet or damaging equipment.
• Do not overstretch the spring beyond its elastic limit to prevent permanent deformation or snapping.
• Take multiple readings at each force to improve reliability and identify anomalies.
• Ensure the ruler and spring are vertical to avoid errors in measuring extension.
• Avoid parallax error by reading the ruler at eye level.
• Check the spring for any damage or wear before starting the experiment.