Hysteresis

Aim: To investigate the pattern in the amount by which a hanging piece of elastic stretches when a load force is applied and the amount by which the stretch is reduced when the load is removed.

Aim (in simpler terms): To determine the relationship between the force on a rubber band and its stretch, both during extension and retraction.

Hypothesis: Not required.

Method

1) Hang a piece of elastic on a clamp stand. Ensure the elastic is new.

2) Clamp a ruler using the clamp stand. Ensuring the markings on the ruler is as close to the elastic as possible.

- Draw a diagram

3) Measure the length of the elastic and record the data.

4) Hang masses on the elastic until it reaches it point of irreversible distortion. Take note of this weight; do not hang more than this weight in the experiment.

5) Add a weight of 100N (change appropriately). Wait for a few seconds for the system to "stabilise". Measure the length of the elastic and record the data. Special care must be taken to ensure that when the mass is added the elastic should not retract.

6) Add more weights, till the total weight is close to its point of irreversible distortion or till there are no more weights.

7) Remove the weights one by one. Wait a couple of seconds for the system to "stabilise". Measure the length of the elastic and record the data. Ensure that when the mass is removed the elastic should not be allowed to stretch further.

8) Repeat, till there is no more mass on the elastic. Measure the length of the elastic.

Equipment

Elastic Clamp stand

Ruler Different weights or a weight hanger

Variables

Independent: Mass hung on elastic

Dependant: Length that the elastic extends or retracts.

Controlled: Same conditions - thus the behaviour of the elastic is constant

Same equipment

Results

Force (N) Length of elastic (m)

Length that elastic was stretched

During extension During retraction For extension For retraction

0 1 1.2 0 0.2

100 1.5 1.4 0.5 0.4

..

..

..

..

..

..

.. ..

..

..

..

..

..

.. ..

..

..

..

..

..

..

900 .. ..

1000 .. ..

Note: To find the length that the elastic was stretched. Simple subtract the value "During extension" by the original length of elastic. Then write the result in the column "For extension" for the appropriate weight. Repeat for retraction.

Construct a graph of this data. For ease of data interpretation, graph force on y axis and length that elastic was stretched (that is the column "For extension" and "For retraction) on x axis. Also possible to have intervals of 0.98 N on y axis so that value of mass in grams can be plotted accurately (assuming g=9.8 m/s^2)

Plot the points and draw a smooth curve. Draw a smooth curve through the points "For extension" and another smooth curve through the points "For Retraction". Indicate which curve is which. (colour code and/or label)

A possible idea for further processing of results is to calculate the amount of work done. That is the area under the graph.

An example of what your graph should look like:

The graph may be shaded to help further understanding of the meaning of the graph. As shown in graph below:

The total shaded area (green + blue) shows the total work done on the rubber band.

W= F.d

The green area represents the work done by the rubber band. That is the energy that is restored. The green area is clearly less than the total area (green + blue). This shows that there is a loss in energy.

The blue area represents the energy lost.

Conclusion (well, what you should have concluded): The graph shows a hysteresis loop, the relationship between the two variables depends not only on the independent variable but also on whether the independent variable is increasing or decreasing. The area in between the extension and retraction line shows the energy lost. Thus, we may infer that the elastic is a non conservative force because the energy put into the system is not equal to the energy that is given out by the system. The force applied on the elastic is not recoverable.

Discussion

Scientific idea

An ideal spring that obeys Hooke's Law will extend and retract by the same amount. This implies that the work done to the spring is equal to the work done by the spring.

Consider