An orb weaver spider with a mass of 0.26 g hangs vertically by one of its thread

Question

An orb weaver spider with a mass of 0.26 g hangs vertically by one of its threads. The thread has a Young's modulus of 4.7*10^9N/m^2 and a radius of 9.8*10^-6 m. (a) What is the fractional increase in the thread's length caused by the spider? (b) Suppose a 76 kg person hangs vertically from a nylon rope. What radius must the rope have if its fractional increase in length is to be the same as that of the spider's thread?

Answers are (a) 1.8*10^-3 (b) 0.60cm, but I don't know how to get these answers. Can someone explain please, thank you.

Explanation / Answer

Youngs modlulus Y of a material is given Y = FL/ADL

A = area, DL = change of length

L = original length, F = force

so here we apply

a. here we need DL/L = F/AY

DL/L = 0.26 e-3 *9.8 /( 3.14* 9.8 e-6 *9.8 e-6* 4.7 e9 )

DL/L = 0.0017977 m or 1.8 *10^-3 m

---------------------------------

b. Y of Nylon is   = 3.6*10^9 N/m^2

so here as we need Area A = FL/YDL

A = (76 *9.8)/(3.6e9 * 1.8 e-3)

A = pi r^2 = 1.149 *10^-4/

r^2 = 36.66 *10^-6

r = 6.055 mm 0r 0.605 cm

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