I have a fifty foot long chain consisting of 300 two-inch links. If I pull on the chain until it breaks, will the chain 'snap back' to it's tie points; as a cable certainly would. Or, would each of the links absorb 1/300th of the total potential energy of the stretched chain; leaving the chain to fall relatively harmlessly to the ground?

I think chains have a lot less stretch than cables, so there would be some recoil, but much less than a cable. (neither of which has as much stretch as a nylon rope)

If the total stretch of a three hundred link chain is three inches, then each of the links has been stretched approximately 1/100th of an inch. The energy released by the breaking of the chain will be divided between the links, relative to the amount that each link has been stretched; but not equal to the total energy required to break the chain. Most of the energy spent stretching each of the links is lost; as the chain will not return to it's original length, before stretching. Hence, only a small fraction of the energy required to break the chain will be released upon breakage. The rest of the energy will have been used to stretch each of 299 unbroken links.

I've driven a farming tractor in my youth. To pull something real heavy, chains are used. It had happened pretty often that a chain detached from the object I pulled (e.g. a log) and the chain crashed into my tractor as if it was made of rubber!

That is incredible! It seems to defy physics laws. In fact, this principle is precisely why chains are used; for their dispersion of energy, if broken!

Not so incredible. While a chain is better for reducing whiplash, it still has some. Tension on a chain will deform each link. If the elastic limit is not reached, it will regain its original shape, very quickly, the same as a cable will. Since one end is still attached to the tractor or whatever, it will energetically rebound in that direction.

Gee, when something is strained, the stored strain energy goes somewhere if fracture occurs??? Wow. Really "defies physics".

Whether the chain snaps back, or drops to the ground is entirely based upon tensil strength and elasticty; mostly elasticity. Elasticity being the capability of a strained body to recover its size and shape after deformation. Therefore,the higher the elasticity of the chain the greater it's properties dictate the chain returning to it's original length; or, 'snapping back'. The bottom line is this. The more expensive the chain, the lower the chain's elasticity; as the 'snapping back' syndrome is the least desirable property of any pulling medium.

The issue isn't the Young's modulus of the steel, per se... it's the total amount of excess strain energy when fracture occurs.

This is also why firing an "empty" bow or catapult is a major no-no and leads to damage -- the stored energy needs to go somewhere, and usually goes to fracturing the bow or catapult.

Bend a piece of spaghetti. You're storing strain energy. Look at how far the piece(s) from the center flies when the spaghetti finally breaks. Very little strain energy went into new fracture surfaces and quite a bit went into kinetic energy of the flung piece.

Something ductile, with a high work of fracture, will absorb more of the strain energy leading up to/at fracture, but there is still strain energy to be released. If the steel had a lower work of fracture, the snap-back would be considerably more violent.

Theoretical and empirical considerations of the work-of-fracture are irrelavent.The energy principle of the work-of-fracture provides a modified Irwin
similarity relationship in the nonlinear fracture mechanics regime. Various microscopic
deformation and fracture processes in the crack wake and the crack-face contact regions
contribute to the rising ^?-curve behavior of brittle materials, and then significantly
affect the work-of-fracture, resulting in the work-of-fracture that is dependent on the
dimension and geometry of test specimens as well as test methods. The requisite for
the work-of-fracture to be a material characteristic resistance to failure is discussed in
relation to the R-curvc behavior. Some examples of the work-of-fracture test results
demonstrate the usefulness of the work-of-fracture for designing brittle materials with
improved toughness. This leads to the elasticity explanation seemingly being the most viable.

Reading the responses, i believe that the mythbusters team should investigate this. there seems to be alot of contradictory physics theories involved.

I do believe, however, that the "weakest link" will have enough potential energy to cause a "snapback reaction", but the amount of snapback is ultimately determined by the chemical and metrological makeup of the "steel" used in making the chain.

No contradictory physic here. When the chain just get loose while its still in its elastic loading it will spring back because the metal regain its shape fast. When it breaks it won't do the same thing because the metal went beyond its elasticity point and don't want to regain its original shape.

steel will have a springback force on it, the weakest link will have the most springback force, but the combined potential energy of the stretched links releasing at the same time, I believe, will have a "whipping" reaction.

quote:

Theoretical and empirical considerations of the work-of-fracture are irrelavent.

So, whether up to a million times more energy is used up in creating new fracture surfaces and thus isn't available for things like "snap-back" is "irrelavent" to how much snap-back something has???

How exactly do you figure that?

with all do respect "roofingguy" i'm not that familiar with empirical physics. WTF are you talking about?

The chain does not have to fracture, in order to obtain results in an experiment of this nature; a relinquishment of one end of the chain is all that is necessary to obtain calculable results.

quote:

The chain does not have to fracture, in order to obtain results in an experiment of this nature

Um... didn't you ask

quote:

If I pull on the chain until it breaks, will the chain 'snap back' to it's tie points; as a cable certainly would.

in your original post?


So you want to test what happens when the chain breaks by not breaking it?

In this case the term 'breaking' is a metaphor for a sudden release of holding power. It really doesn't matter whether or not the chain breaks; only that potential energy has been stored in the chain, and then that energy is suddenly released, by whatever means. Breaking the chain seems the easiest way to express a sudden release.

Empirical physics is that which is capable of being verified or disproved by observation or experiment.