Spider silk has a Young\'s modulus of 4.0x10^9 N/m^2 and can withstand stresses

Question

Spider silk has a Young's modulus of 4.0x10^9 N/m^2 and can withstand stresses up to 1.4x10^9 N/m^2. A single web strand has a cross-sectional area of 1.0x10^-11 m^2, and a web is made up of 50 radial strands. A bug lands in the center of a horizontal web so that the web stretches downward. (a) If the maximum stress is exerted on each strand, what angle does the web make with the horizontal? (b) What does the mass of a bug have to be in order to exert this maximum stress on the web? (c) If the web is 0.10 m in radius, how far down does the web extend?

Explanation / Answer

F/A = 1.4x10^9 N/m^2 mg / A = 1.4x10^9 N/m^2 A = 50 strands * 1.0x10^-10 N/m^2 = 5.0x10^-10 so m = (1.4x10^9 N/m^2)(5.0x10^-10) / 9.8 m = 71.4g

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