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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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