The Most Elastic Object

Classical Mechanics Level 2

The Oxford English Dictionary defines elasticity as

the ability of an object to resume its normal shape after being stretched or compressed.

Which of the following objects is the most elastic?

Steel wire Rubber band Modelling clay Wooden toothpick

Pranshu Gaba by Pranshu Gaba , 22, India

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2 solutions

Michael Mendrin
Sep 11, 2016

Try making a piano using any of the other three.

10 Helpful 0 Interesting 0 Brilliant 0 Confused

Perfect analogy (if it can be called that)!

Sharky Kesa - 4 years, 9 months ago
Pranshu Gaba
Sep 19, 2016

Every object behaves as elastic upto a certain level of stress; that is the ratio of stress to strain of the object remains constant. When stress is released, the object resumes its original size and shape.

If stress is increased further, the object becomes plastic. The object can now be deformed and does not return to its original shape and size even after the stress is released. If sufficient stress is applied, it is possible to even break the object. The stress level at which it changes from elastic to plastic is called the yield point of the object. Out of the given objects, the steel wire has the highest yield point.

A steel wire can withstand stress as high as \SI{6e8}{\newton \per \meter^{-2}} and still return to its original length when released. When this same amount of stress is applied on the other objects, they either break, or are permanently deformed.

Thus, steel is the most elastic object out of the given ones.

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Alright. I get that a steel wire can withstand the most stress applied on it. But was that really the object we're looking for? According to the dictonary elasticity is the ability of an object to resume its normal shape after being stretched or compressed. So the most elastic object is the object which can be stretched the most. In my opinion that could also mean having the greatest ratio between the lengths of the stretched object and the normal shape. And in that case I think the rubber band would be the desired object.. thanks for any explanation

Kai Ott - 4 years, 8 months ago

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Steel can stretch a lot too. Since the Young's modulus of steel is so high, we can hardly notice its change in length when we apply small amounts of stress. If we apply greater stress, we see that steel can extend up to three times its original length. (Young's modulus = 200 Gpa, Yield stress = 600 Gpa). It would not be right to say that rubber band stretches the most.

Since the steel wire can withstand more stress and still return to its original length, it can be called more elastic, and therefore yield point is a good way to measure elasticity.

Pranshu Gaba - 4 years, 8 months ago

I feel like it would be the modeling clay. After a certain amount of stress, the other 3 objects will all break. But in the case of the clay, it can still resume it's original shape, it just takes some work to get it back :P I guess you could say that for any object, though, it's just that it would take more work. Perhaps a more apt description, then, would be "the ability of an object to naturally resume its normal shape after being stretched or compressed."

Alex Li - 4 years, 8 months ago

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Yes, we want the object to resume its original shape and size on its own, without requiring any external help. Clay would be the least elastic, or the most plastic, of the given objects, since its deforms even at minimum amounts of stress. How easy it is for us to get the original shape back by doing some work is another matter altogether :)

Pranshu Gaba - 4 years, 8 months ago

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