MadSci Network: Physics
Query:

Re: At which point on a rubberband is there maximum tension when we stretch it

Date: Mon Aug 4 11:58:59 2008
Posted By: Jay Shapiro, Staff, Engineering, TA Aerospace
Area of science: Physics
ID: 1217462544.Ph
Message:

Our teacher had taught us that when we stretch a rubberband, the tension on it throughout is the same, but I have often seen that when a rubberband is stretched, it always breaks off from th middle.Does this mean there is maximum tension in the middle? Please explain.

Hello Aranyaani,

You made an interesting observation, and asked an important question.
However, your teacher is correct. Let me explain.

First, we need to define a couple of terms:

Tension is equal to the force, or total load applied to the rubber band.

Stress is the total force (or tension) divided by the cross-sectional area of the rubber band.

An object that breaks when pulled apart does not care about the tension, but only about the stress that it experiences. The following example will help clarify this concept.

Imagine that you have a long round piece of rubber with a weight attached at the bottom. (See picture below) The top half of the rubber is 1 cm diameter. Somewhere along the length, the rubber narrows down to .25 cm diameter. Now a small weight is hung from one end of the rubber, while the other end is attached to a holder. Lets say the weight was 1 kg. The rubber piece will stretch, but not break. The tension throughout the entire band, both thin and thick areas will be 1 kg of force (or to be more scientifically correct -- 9.8nt of force). The tension must be constant because every part of the rubber is lifting the same 1 kg weight.

If we increase the weight at the bottom until the rubber breaks, where do you think that the break will occur, in the small or large diameter areas? You probably (correctly) guessed the small diameter area. The reason is that the stress will be much higher in the small section (4 times larger).

Finally, getting back to YOUR rubber band: Your rubber bands break in the middle because that is where the highest STRESS happens to occur. This means that when stretched, the cross-sectional area becomes the smallest at the breakage spot. This is probably a spot on the band that is very slightly smaller than other places, but that causes the highest stress to be produced, and will be the first place for the band to break. This might also be a slightly weaker spot due to tiny flaws that were created when the rubber band was molded.

I hope that this helps you.

Best Regards,

Jay Shapiro


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