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For a physics project I'm changing the temperature of a rubber band and measuring elasticity. The rubber band will be tied to a mass and will be heated in a water bath.

Some sources show data of the rubber band becoming softer and stretchier (there is data of this), whereas others list that the entropic force results in the rubber band contracting. There are demonstrations of this on Youtube, but no data.

Here are a few examples of the sources that say the band will become stretchier when heated:

http://tuhsphysics.ttsd.k12.or.us/Research/IB08/FrazPoinFurm/index.htm#Graph https://www.1000sciencefairprojects.com/Physics/elasticity-vs-temperature.php http://tuhsphysics.ttsd.k12.or.us/Research/IB10/RajeJaneHerm/index.htm#Background:

Graph from source 1 Table from source 2 Table from source 3

Why is there a contradiction? If I were to try this myself with a heat bath, which would be the most likely outcome? I am going to use the same type of rubber band as used in the sources above.

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The apparently contradictory results can be explained as follow.

There are two ways that temperature affects the length of a stretched rubber band. The first is thermal expansion - an unstretched rubber band will, like most materials, tend to expand when heated. The second is a change to the Young's modulus - the proportion by which the rubber band will stretch when subject to a given stress or load. The Young's modulus of rubber increases when it is heated (see this Wikipedia article. As the Young's modulus increases, the proportion by which the band is stretched by a given load decreases.

Notice that these two effects act in opposite directions. Which one is greater depends on the load placed on the rubber band.

For example, supposed a rubber band at room temperature has an unstretched length of $10$ cm and a load of $100$ grams stretches it by $25\%$ to $12.5$ cm. A load of $200$ grams will then stretch it by $50\%$ to $15$ cm.

Now suppose the rubber band is heated and its unstretched length increases to $10.5$ cm. But its Young's modulus increases so that a load of $100$ grams now only stretches it by $20\%$. Its stretched length with a load of $100$g is therefore $10.5 \times 1.2 = 12.6$ cm, so the stretched length with the smaller load has increased by $0.1$ cm.

However, a load of $ 200$ grams will now stretch the band by $40\%$ so its stretched length with a load of $200$ grams is $10.5 \times 1.4 = 14.7$ cm. So the stretched length with the higher load has decreased by $0.3$ cm.

So at a higher temperature the stretched length of a rubber band may increase with small loads, and at the same time decrease with larger loads.

I suggest you try the experiment for yourself, collecting data over a range of light, medium and heavy loads.

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  • $\begingroup$ Thank you for your explanation! If the mass is kept constant (at 100g lets say) but the temperature is increased, would it be accurate to assume that the stretched length will be consistently greater? (for selected temperature values before plastic deformation occurs). I'm asking this as in my experiment, the Independent variable is the temperature. I will personally try this out for myself too, as I believe that this would help greatly. $\endgroup$ Oct 4 '20 at 11:58
  • $\begingroup$ @elasticityvsheat That depends on the characteristics of your rubber band. I made up numbers in order to give an illustration. In general, light loads should show an increase in stretched length, heavy loads should show a decrease. $\endgroup$
    – gandalf61
    Oct 4 '20 at 12:04
  • $\begingroup$ Thank you for the clarification, I will perform a test experiment this week and will mark this as the accepted answer if it works. Thanks once again for your help, @gandalf61 :) $\endgroup$ Oct 4 '20 at 12:07
  • $\begingroup$ So I asked my Physics teacher about this and she verified what you said. She also recommended that I try it out as it is extremely variable depending on the rubber band and the mass attached to it. She also recommended that if the mass causes it to contract, that I should reduce the mass so I can measure the thermal expansion without the entropic force induced by a larger mass creating the opposite result. An immense thank you for answering my question, have a good day! $\endgroup$ Oct 5 '20 at 16:18

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