"Hooke's Law" and Rubber Bands
Name: Lachlan McBride W.
Date: Tuesday, May 21, 2002
I am doing a school project on ELASTICITY and rubber
bands. I have seen the answers to past questions posed in this area which
have been helpful. I have conducted an experiment which involved
attaching a load(450 grams) to 1 band then 2 ,3,4 etc through to 20 bands
measuring the distance the bands stretched in the first 60 seconds
,measured that they returned to their original size when the load was
removed and recorded my results. I then did the same experiment again but
this time I wet the bands with water . The same load was attached but
this time the wet bands did not stretch nearly as far as they did when
they were dry. Why is this? I have read that when rubber is heated it
shrinks( but then return to original size when they return to room temp)
and suspect that if I attached the load to heated rubber bands they would
not stretch as far as the ones at room temperature -- is this the case
--- has the water increased the temperature of the rubber bands or there
I do not know whether temperature is the cause for what you see, but I do
know a way to find out. Do the same experiment again with ice water. Then
use hot water. See whether you see a similar effect in all three water
If all three water temperatures produce similar effects, temperature is
probably not the main cause. It may be a chemical reaction with the water,
changing the elasticity by slightly changing the chemical structure.
If hot water has greater effect(more like room temperature water) than cold,
then extra heat in the rubber band is a good conclusion. If the ice water
behaves more like the room temperature water while the hot water is more
like dry rubber bands, then the water is taking heat away from the rubber
bands to make them stretch less. You have the ability to find out.
Dr. Ken Mellendorf
Illinois Central College
More likely, the wet rubber bands are cooled somewhat as the water
evaporates. It is true that STRETCHED rubber contracts when heated:
stretching makes the rubber strands more aligned, and heating disrupts the
alignment. However, rubber also becomes less resilient when cooled, as its
strands become less mobile. It might be difficult for you to control the
temperature of your rubber bands in your experiment, but if you could,
determining their behavior under different temperatures might make a very
interesting science project.
Richard E. Barrans Jr., Ph.D.
Assistant Director, PG Research Foundation
You have several things going on in your experiments that will make
the results difficult to interpret. Let us look at them:
1. TEMPERATURE RESULTS: A polymer has three types of mechanical behavior
that depends on the specific polymer and the temperature. At sufficiently
low temperature the material is a GLASS (The material is not crystaline, but
is brittle.) Plexiglas (poly-methyl methacrylate) and solid poly-styrene
(not polystyrene foam) are examples of polymers that are glasses at room
temperature, but begin to soften at about 100 C. You may have seen a rubber
hose or a flower shattered by cooling it in liquid nitrogen (boiling point =
77 K) and striking it on the bench top. You may also have read about the
disaster of the space shuttle "Challenger" some years ago. In the
investigation of the cause(s) physicist Richard Feynman demonstrated that a
critical seal most likely failed upon "lift off" because the temperature at
the launch site was cold enough to make the brittle and result in its
As the temperature increases, a polymer becomes elastic (that is, the
polymer deforms (stretches) when a force is applied to it, but returns to
its original shape
(length) when the force is removed. This is called the "rubbery" or
"elastic" region for obvious reasons. At still higher temperatures the
polymer deforms when a force is applied, but it does not return completely to
its original shape (length) when the force is removed, and remains partially
deformed. This is called the
"visco-elastic" temperature range. At yet still higher temperatures the
polymer flows when a force is applied. This is called the "viscous" range.
Keep in mind that these are temperature RANGES, not sharp transitions, and
that they depend upon the composition of the material being tested.
Automobile tires and rubber bands are made of basically the same "stuff" but
have very different mechanical properties, because of how they are
From your description of the behavior of the wet rubber bands that the
glass/elastic temperature range may be about -20 to +15 C. The evaporation
of the water cools the rubber bands to a temperature closer to the
glass/elastic temperature, making them more glassy (and hence harder and
more rigid). This would account for your observation that the wet rubber
bands do not stretch as far as the dry ones. I suspect that if you took a
lunch break and allowed the water to evaporate, and the temperature of the
rubber bands to return to room temperature you would see that their length
had increased when the "normal" value.
2. LOAD: Your load of 450 gm may be too large for the stretching that
the rubber bands undergo. Elastic materials only obey Hooke's Law
(the restoring force = - K * extension) form small changes in length
(extensions). The more accurate formula is: f = K*T*(x- 1/(x^2)) where 'f'
is the restoring force = 450 gm (the acceleration of gravity that converts
weight to mass is absorbed into the experimental constant, 'K', 'T' is the
absolute temperature in kelvins, 'x' is the extension (x=L/Lo), the ratio of
the stretched length and the un-stretched length.
How are you attaching the rubber bands? If you are using a "slip knot"
the length isn't going to be additive (that is, the sum of the lengths of
the individual rubber bands). You should connect each one to the other with
a paper clip and "subtract out" the contribution of the paper clips to the
3. BOUNDARY CONDITIONS ON THE EXTENSION VS. TEMPERATURE: There is a more
fundamental reason for the behavior you are observing, and that is what are
called "boundary conditions". Boundary conditions are just variables that
are held constant, either for experimental or theoretical reasons. The
unusual increase in the restoring force,f, as the temperature,T, increases
in elastic materials (compared to a metal spring where the opposite is
observed) MUST BE MEASURED AT A CONSTANT EXTENSION (x = L/Lo). Adding more
rubber bands changes the extension and obscures this necessary requirement
(boundary condition). To observe the effect you need to modify your
experimental set up.
First, get rid of the 450 gm weight. You might use different weighed amounts
of sand instead. (Glass beads are better because that all weigh about the
same, so you can measure the force by counting the number of beads. You can
find glass beads at most art supply / hobby shops.). Use about 6 rubber
bands (about 2 in. in length each) connected by paper clips. Suspend the
spring setup in a glass tube (or a card board tube with a slit cut into it
so you can see the length of the rubber bands). The purpose of the tube is
to keep drafts of air from interfering with the measurements. Stand a meter
stick or yard stick next to, or in, the tube so that you can measure the
length of the rubber band assembly. Suspend a thermometer inside the tube
about 1/2 way beside the rubber band assembly, to measure the temperature.
Stuff 1 or 2 crumpled coffee filters into the bottom of the tube. Now aim a
hair dryer (on "low", you do not want to start a fire!) at the bottom of the
tube. The hot air will rise up the tube because it is less dense than the
air at room temperature. The crumpled coffee filters are there to deflect
any direct air currents from rising up the tube. Now you can heat the rubber
band assembly to some temperature, and when the temperature stabilizes (You
do not have to pick a particular temperature, just let it stabilize.) add or
remove glass beads until the length of the extension of the rubber bands
is some constant value that you are free to choose so long as it is about
the same value for each measurement. It doesn't have to be exact, just
Now you should see the result you expected. Do not feel bad about not
having done the experiment under the proper boundary conditions. When the
properties of elastic materials first began to be studied, I am sure many
scientists and engineers, who had a lot more experience than you, did the
same thing you did initially. Good Luck.
That sounds like a really interesting experiment! I am tempted to try it
myself. Was the water at room temperature or was it warm or cold? Was
all the work done the same day with the same rubber bands?
If the water was warm it could certainly cause the effect you describe
for a brief period of time but I would expect 60 seconds to be long
enough for the rubber bands to reach thermal equilibrium with the room
air (unless they were very massive). If you waited longer than 60
seconds did you get the same results as before? If the "wet"
experiments were done on a different day it is possible that the room
temperature was warmer the second day.
How long were the rubber bands immersed in the water? Does this time
make a difference in the result? If you just dip them in and do the
measurement do you get the same result as if they are kept in water
overnight? If you get different results it implies that the water is
penetrating the rubber bands and causing different molecular
interactions, possibly by filling any spaces between the randomly coiled
rubber molecules, causing their motion to be slightly restricted.
Click here to return to the Physics Archives
Update: June 2012