Question

Orb spiders make silk with a typical diameter of 0.15 mm. The Young's modulus of spider silk is 0.2×1010N/m2 and its tensile strength is 1000×106N/m2.Part A: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 how much will the silk stretch? (answer in mm)Part B:What is the maximum weight that a single thread of this silk could support? (answer in N)

Answer 1

Answer:

(a) 1.66 x 10^-3 cm

(b) 17.66 N

Explanation:

diameter, d = 0.15 mm

radius, r = 0.075 mm = 0.075 x 10^-3 m

Young's modulus, Y = 0.2 x 10^10 N/m^2

Tensile strength = 1000 x 10^6 N/m^2

mass of spider, m = 0.50 g

length of the strand, L = 12 cm

(a) Let the silk strand be stretch by ΔL.

Use the formula for Young's modulus

Y = stress /strain

strain = Stress / Y

stress = force / area

Area, A = πr² = 3.14 x 0.075 x 10^-3 x 0.075 x 10^-3 = 1.766 x 10^-8 m^2

stress = mg / A

stress = 0.5 x 10^-3 x 9.8 / (1.766 x 10^-8) = 277423.92 N/m^2

strain = 277423.92 / (0.2 x 10^10) = 1.387 x 10^-4

ΔL = 1.387 x 10^-4 x L

ΔL = 1.387 x 10^-4 x 12 = 1.66 x 10^-3 cm

Thus, the stretch in length is 1.66 x 10^-3 cm .

(b) Tensile strength = maximum force / area

maximum weight = 1000 x 10^6 x 1.766 x 10^-8

maximum weight = 17.66 N

Thus, the maximum weight is 17.66 N.