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Rubber Band Elasticity and Width
Name: Madison
Status: student
Grade: 6-8
Location: MI
Date: April 2011
Question:
How does the elasticity of a rubber band depend on its width?
Replies:
Madison,
Being a (polymer) chemist, I tend to think in terms of what the
molecules are doing. So in the case of a rubber band, what I
visualize are a bunch of long stiff threads that have formed a loose
ball. When the rubber band is stretched, what happens to the threads
is that they get elongated in the stretch direction - in some cases,
depending on how much the rubber band is pulled, individual strands
start forming a more straight line. Since the elongated form is a
more energetic state, then when the rubber band is released, the
strands snap back to their loose bundle shape. This tendency to snap
back is called "elasticity".
Okay, so how is this picture affected by having a larger
cross-section (when the rubber band is wider)? We know several
things from the first paragraph: (1) rubber tends to be elastic
because the elongated form - with the molecules being in a more
straight line - is more energetic and since molecules tend to go to
a lower energy state, the loose, entangled form is the preferred
form, (2) the amount of stored potential energy that the
straightened strands will have is proportional to the degree of
entanglements (think of the threads wrapping around each other, the
more wrapped into each other they are, the more energy is required
to stretch them out), (3) the more entanglements, the more energy
required to stretch, the more potential energy in the stretched
form, the more energy recovered in the snap back -and the more
elastic the rubber band. ...so the conclusion is, the wider the
rubber band, the more energy will be required to stretch because
there are now more entanglements involved, the more energy is stored
in the stretched form, and so there is more energy recovered in the
snapping back which results in the greater the tendency to snap back
- hence the wider the band the more elastic.
Greg (Roberto Gregorius)
Hi Madison,
The width of an elastic band is only part of the story. Let us say that you
have several different elastic bands that are all the same length and
made of the same material, but which differ only by their width and
thickness, and each is stretched the same distance. You will find that
the tension when stretched will be directly related to the cross
sectional area of the rubber band. Cross sectional area is the width of
the rubber band multiplied by its thickness.
So, from this you can see, if (for example) you double the width of a
rubber band (without changing anything else), or you double its
thickness (without changing anything else), result the result will be
the same either way: you will have to pull twice as hard to stretch it a
given length.
Regards,
Bob Wilson
You need to be careful about both experimental measurements, definitions and
physical concepts. They sometimes are all mixed together. Here goes:
Elasticity (we will define) as the restoring force of an elastic RECTANGULAR
band , where the cross section (width and thickness) of the width and
thickness of the band is negligible compared to the deformation of the band.
Thus the problem becomes only in one directional. Put another way,
stretching the rubber band changes in only one direction -- the direction of
the stretching occurs only in the direction of load (weight applied). If the
applied weight is large enough to change the cross section, the analysis of
that model becomes much more complicated. In addition, if the applied
stretching force is so large that it is not proportional to stretching
--distance, the analysis becomes more complicated. So the restoring force,
given all these pre-conditions is: F = -k (x-xo) x (T x W) and terms of
the order of (x - xo)^2 = 0.
Given all these qualifications, the restoring force is proportional to the
width of the rubber band. This a simplified treatment of the problem.
Vince Calder
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Update: June 2012
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