Question

Orb spiders make silk with a typical diameter of 0.15 mm. The Young's modulus of spider silk is 0.2×10^10N/m2 and its tensile strength is 1000×10^6N/m2.

A typical large orb spider has a mass of 0.50 g. If this spider suspends itself from a single 12-cm-long strand of silk, by a) how much will the silk stretch?, and, b) what is the maximum weight that a single thread of this silk could support?

Express your answer using two significant figures.

Answer 1

A) 0.50g = 50*10^-2 g = 50*10^-5kg , x1 = 0.12m
x = mg = 50*9.8*10^-5 = 4.9*10^-3
x = 49*10^-3m = 49mm
so string will stretch = x1+x = 49+120 = 169mm

B)
The tensile strength of spider silk is about 1 x 10^9 N/m².

So given that the diameter of the spider silk is 0.15 mm or 1.5 x 10^-4 m. The cross sectional area is approximately:

A = pr² = (3.14)(1.5 x 10^-4 / 2)² = 1.767 x 10^-8 m²

So this means that the amount of force we can apply before the the silk thread is broken is:

F = PA = (1 x 10^9)(1.767 x 10^-8) = 18N