A spider spins a fine thread of spider silk between two posts a distance L 0 apa

Question

A spider spins a fine thread of spider silk between two posts a distance L0 apart. The thread has a diameter of d = 5 × 10-6 m and an equilibrium length of L0. When the spider (with mass m = 2 milligram) hangs from the center of the thread, the thread sags and stretches to support the weight of the spider, making an angle of ? = 10° below the horizontal, as shown.

a) Why must the thread sag when the spider hangs motionless from it?

b) Calculate the tensile strain ? in the thread and the Young’s modulus Y for the silk.

Explanation / Answer

Part A

thread sag because weight of spider creates tension in the thread and which increase the length of thread. due to elasticity of thread it sags.

Part B

By figure new length of half thread = Lo/2 cos (theta) = 0.5077Lo

so strain

= 0.5077Lo-0.5Lo /( Lo/2)

= 0.0154

youngs modolus Y = stress/strain

Y = F/A /

Y = (mgcos 10 /piR^2)/

Y = (2*10^-6 *9.81*cos10/3.14*2.5*10^-6*2.5*10^-6)/ 0.0154

Y = 6.39x10^6 N/m^2

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