Force-extension behaviour of rubber

Practical method

Aim

Investigate the loading and unloading behaviour of a rubber band and the energy dissipated (hysteresis).

Variables

Independent variable: load (adding then removing masses)
Dependent variable: extension
Control variables: the same rubber band; loading steps; temperature.

Apparatus

• Rubber band
• Clamp stand
• Slotted masses on a hanger
• Metre rule and pointer
• Safety goggles

Method

1. Hang the rubber band from the clamp and record the pointer position with a light hanger.
2. Add masses in equal steps, recording the extension after each.
3. Remove the masses in the same steps, recording the extension each time.
4. Plot force against extension for loading and unloading on the same axes.
5. Estimate the area between the curves, which is the energy dissipated per cycle.

Sample results

Loading and unloading in 1.0 N steps.

Analysis

The unloading curve lies below the loading curve: the band is longer for the same force when unloading. The area between the curves (about 0.04 J) is the energy dissipated as heat in the rubber per cycle — hysteresis. The band does not quite return to its original length at first.

Uncertainty

Rubber continues to stretch slowly (creep), so readings depend on the time waited. Take each reading after the same fixed time, for example 30 s.

Errors and improvements

Risk assessment

Common mistakes

• Joining points with straight lines rather than smooth curves.
• Calculating energy stored using ½Fx (rubber is non-linear).
• Ignoring the unloading curve.

Worked analysis

Counting squares, the area under the loading curve is about 0.36 J and under the unloading curve about 0.32 J. Energy dissipated ≈ 0.36 − 0.32 = 0.04 J per cycle (about 11%).

Common misconception

Rubber does not obey Hooke's law and does not return all the work done on it: some energy becomes thermal energy (hysteresis).