# Perfectly elastic and perfectly inelastic rope behavior

I understand the meaning of transverse and longitudinal waves, but I'm still confused with the edges of elasticity, like perfectly elastic, and perfectly inelastic. Elasticity (to me) has to fulfill 2 conditions as described here, the body must resist a distorting influence and must return to its original size and shape when that influence or force is removed.

So a perfectly elastic object will have a super resistance that it won't bend at all? And in this case the second condition won't have a chance to be applied - thus even if the force is removed?

While a perfectly inelastic object will absolutely deform with no resistance at all, and when the force is removed, will get directly back to its original shape.

Recalling the experiment of a rope, fixed in one end, and in the other end moved up and down fast vertically (back to the original horizontal level). Let's discuss the 2 extreme cases and whether a wave will happen or not in simple terms please without introducing formulae.

The motivation behind my interest in the "elasticity" topic is one sentence I read in my student's book which says that elastic waves can be transverse and longitudinal. I can imagine a longitudinal wave (the horizontal spring example), but was interested in the case of transversal elastic wave, thus started to ask whether the transverse wave can be elastic; which it can. So I thought that understanding the extreme cases of elasticity can help. But we can leave that to another question.

• Re, "A perfectly elastic object will have a super resistance that it won't bend at all?" No. That's not what "elastic" means. A perfectly elastic object does not have to be perfectly stiff, but it does have to give back all of the energy that was used to deform it. A perfectly inelastic object, on the other hand, can resist deformation, but when you do deform it, it gives no energy back. Jan 14, 2020 at 15:25
• Yeah, I felt so, the "must resist" part doesn't have to be infinite. Jan 14, 2020 at 15:28
• I think there is some confusion in that that's not 2 conditions, it's one, and it should be inferred that when they say distorting, they mean permanent.
– user234190
Jan 14, 2020 at 16:06

## 1 Answer

A perfectly elastic object, when deformed, will immediately return to its undeformed shape when the deforming forces are removed. In so doing, it will dissipate zero energy: all the work done in deforming it is returned when it is allowed to relax again. This is true whether the object is stiff (like a cube of steel) or flexible (like a cube of rubber).

A perfectly inelastic object, when deformed, will never return to its undeformed state when the deforming forces are removed. Because of this, all the work performed on it by the deforming forces is dissipated into heat in the object and cannot be (mechanically) recovered when the forces are removed (as in the case of a lump of wet clay).