In The Amazing Spider-Man game sometime Spider-Man throws his web up in sky and is able to swing. Also he is able to stretch it over long distances. Is there any limit to how long the web can stretch?
You would like to check a link on how Stanford University derives at the elasticity of spider silk scientifically http://engineering.stanford.edu/news/stanford-researcher-sheds-new-light-mysteries-spider-silk This is what http://www.tiem.utk.edu/~gross/bioed/bealsmodules/spider.html says.
In order for a flying insect to be trapped by a web, its motion must be stopped. The force required to stop its motion is inversely proportional to the distance over which the motion must be stopped. In other words, the greater the distance over which the insect is slowed down the smaller the force necessary to stop it. The capture spiral's high extensibility enables spiders to trap insects with a fairly minimal amount of force, and reduces the potential for damage to the web. The extensibility and tensile strength of spider silk in general, combined with its light weight, enable it to resist damage from wind and from being pulled by anchoring points of the web.
So, in real world, the Young 's Modulus of the spiders web is observed to be quite high. And in case of Spider man, swinging from one building to other, you can expect the elasticity to be 10 times higher! But unfortunately, the author haven't gave us a detailed physical properties of the materials that superheroes use!
Using a piece of footage from Spider-Man 2, starring Toby McGuire, we can guess his mechanical web limits (or the limits of brick walls under Spider-Man's webbing) when he tries to stop the train using his webbing.
At seventy miles per hour, his webbing stretches for ten seconds, this means it has the ability to stretch for at least ten times its initial length. 70 miles per hour is 102 feet per second. So let's go with at least 1000 feet of potential stretching capacity when towing extreme weight.
Under his normal weight used for web-slinging it has some degree of resiliency allowing for wide swinging arcs allowing him to reach high velocities and maximize his height through his swing. It may stretch up to three times the initial projected length.
Yes, Spider-Man's webbing does have its limits. What those limits are depend on which version of Spider-Man you're talking about.
Across the various backstories of Spider-Man, there are two different ways that he generates webbing:
Most of the time, Spider-Man relies on mechanical web shooters with liquid webbing cartridges in them. This was the original source of his webbing in the comics, for example. It's also the version seen in the Amazing Spider-Man movie series. Typically, Peter himself invents both the web shooters and the material that goes in them, as seen in this screen-shot:
In this versions of Spider-Man, he can only shoot as much webbing as he can fit into his cartridges. Once they run out, he needs to refill them. This has happened many times, and is one of the things Peter needs to be aware of when he's in a protracted fight.
The physical properties of the webbing are never explained in any great detail; however, it behaves in a way very similar to nylon, only stronger. The material starts out as a fluid in the cartridges, until it's extruded under high pressure through the small openings in the web shooters. This causes the fluid to solidify and stretch. Once it's exposed to air, it only stays sticky and stretchy for a short period of time, though it remains very strong up until it dissolves.
In the comics, Peter invents the formula himself; in The Amazing Spider-Man, it's an Oscorp product called "biocable". Peter watches a video of the cable being used to pull an airplane -- this implies that it doesn't stretch too much, or the cable would stretch instead of pulling.
For a short period of time in the comics, Peter developed the ability to shoot webbing organically from his wrists. This is also the version used in the Spider-Man movie series, as shown here:
The organic version of the webbing lasts much, much longer. For example, soon after getting this organic webbing power, Peter was able to produce enough webbing at one time to completely cover Iron Man:
As far as I know, there was no limit ever shown to how much of this webbing Peter could produce. I assume there would be a practical limit as he exhausted all the nutrients in his body, but he never seemed to come close to that.
Peter doesn't have the organic webbing for very long, so we don't learn very much at all about it. He obtained it after being turned into a spider, so we can conjecture that it's similar to spider silk, which is actually not very stretchy: it's strong, but not elastic.
Several video games include Spider-Man as a character, and his web-swinging power is usually a big part of that. In many cases, it's possible for Peter to swing from "thin air" -- shoot his webbing up in the sky and swing on nothing.
This is basically just a conceit to make the game more fun. The theory usually is that, in NYC where Spider-Man operates, his webbing is likely to hit something eventually (a taller building, a crane, a bridge, etc.), so it's best not to think too hard about it.