# Spider web?

An orb weaver spider with a mass of 0.21 grams hangs vertically by one of its threads. The thread has a Young's modulus of 4.7 x 109 N/m2 and a radius of 9.8 x 10-6 m.

1)What is the fractional increase in the thread's length caused by the spider?

fs =

x 10-3

2)Suppose a 71 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? (The Young's modulus for nylon is 3.7 x 109 N/m2)

R =

### 1 Answer

- FiremanLv 74 weeks ago
1) By E = (F/A)/(ΔL/L)

=>E = (mg/πr^2)/(ΔL/L)

=>(ΔL/L) = {mg/(E x πr^2)}

=>(ΔL/L) = [(0.21 x 10^-3 x 9.8)/{4.7 x 10^9 x 3.14 x (9.9 x 10^-6)^2}]

=>(ΔL/L) = 1.42 x 10^-3 m OR 1.42 mm

2) By E = (F/A)/(ΔL/L)

=>E = (mg/πr^2)/(ΔL/L)

=>r^2 = [mg/{E x π x (ΔL/L)}]

=>r = √[mg/{E x π x (ΔL/L)}]

=>r = √[(71 x 9.8)/{3.7 x 10^9 x 3.14 x 1.42 x 10^-3}]

=>r = 6.49 x 10^-3 m OR 6.49 mm