A tensile test is the most basic, yet one of the most important tests in structural mechanics. Using the given load and elongation of the material throughout the test, you can create a stress-strain curve for the material which gives you pertinent information such as the material's proportional limit, yield strength, elastic modulus, ultimate strength, rupture strength, strain hardening ratio (if any), ductility, etc. This basic information helps a structural engineer use this material in a proper manner when designing a structure.

to find out the tensile strength of the specimen.

So you know how much weight your structure can take so you don't design more than that into it so that everyone doesn't die horribly and it's all your fault.

To see if the tree will look good covered in it. ;)

for fun