Hysteresis and Rubber Bands

Introduction

When one performs a Hooke’s Law type experiment with a rubber band, it can be noticed that the band does not behave exactly like a spring. A rubber band, made of latex and rubber, does not return to its exact original shape after being stretched. This is an example of a phenomenon called hysteresis. By studying the relationship between the rubber band during stretching and unstretching, one can determine the amount of work done on the rubber band, and the amount of energy (in joules) lost by the band.

Design

A retort stand with clamp should be used to hold a ruler and rubber band. The ruler should be accurate to ± 0.5mm. Masses should be added to the band in increments of 100g. The device holding the masses in this experiment had a mass of 50g; therefore, the progression of masses went: 0g, 50g, 150g, 250g, 350g, etc. up to 1.05kg.

One should use a ruler (or some sort of straight edge) to find the position of the rubber band on the held ruler—this should be done to avoid parallax.

The image (on the left) is a representation of the set up.

To measure data in this experiment, masses should be added slowly and gently. The stretch should be recorded in meters. Once 1.05kg have been added, masses should be removed in the same increments as they were added and the new stretch should be recorded. This data will therefore be split into two sections: stretching and unstretching.

Results

Masses were added from 0-1.05kg and then removed in the same way they were added. Stretch was noted in meters, and mass was noted in kilograms. The following tables represent the raw data with unites and uncertainties:

For the data to be processed mass was converted into force. In doing this conversion, it was assumed that acceleration due to gravity was 10ms-2 and thus 0.25 kg exerted a force of 2.5N on the rubber band.

Analysis

Then, force (N) was plotted against stretch (m) on a xy scatter graph. These variables are important for finding work because work is expressed in Nm (Newton Meters). Thus, if we plot our points and find lines of best fit, we will be able to integrate the function to find the amount of work needed for stretching and unstretching, and the difference in values will indicate the amount of energy lost by the band in joules.

The measurements taken in this lab were taken with degrees of uncertainty (as cited by the collected data). The overall uncertainties were calculated as such:

Force: 10*[0.005/( ∑mass/n )]=10%
Stretch: 0.0005/( ∑stretch/n )=0.2%

Graph 3: On the next page is a graph representing the recorded data. The graph contains points (taken off of the raw data), and then a line of best fit. One line represents the stretching process, the other, unstretching. Both lines of best fit are third order polynomial functions, which will be used to find work.

The lines of best fit are as follows:

Stretching: y = 1071x3 - 619.62x2 + 148.97x - 8.0586
Unstretching: 1629.1x3 - 885.28x2 + 180.18x - 9.5871

Both fits are >99% accurate in regards to the raw data. This means that the average variance between data points and the line of best is less that a 1% offset. Therefore, the line of best fit can be considered to be a direct representation of the data collected.

These functions will later be integrated (which is better than finding the area under the raw graph which is not smooth).

Integration—finding work done:

The graph above represents the polynomial lines of best fit found for the data. Just as before, the x-axis represents stretch in meters while the y-axis represents force in Newtons. Both functions were integrated to find the area under the curve.

Thus, roughly 1.25J were put into the band to stretch it, and only ~.99J were released to unstretch it, which means that the band lost roughly .26J with a 2% uncertainty.

Conclusion

It is clear from the force curve that the rubber band does not obey Hooke's Law. The force curve for a rubber band is said to be a hysteresis loop, and the area between the two curves represents lost energy.

Some of the work done on the rubber band is against internal friction, which increases the temperature of the rubber band and its surroundings. There is thus less energy available to raise the weights back up.

The rubber band lost ~0.26J ± 2% based on the 10% uncertainty in Force measurements and 0.2% error in stretch.

Cite Our Experiments & Research

If you have used any of this information or any of these images please go ahead and cite them in your bibliography. For your convenience, this is what the citation would look like in MLA format:

Family, Afrooz. “Hysteresis and Rubber Bands.” April 13, 2006 Mad Physics. dd mmm. yyyy