Spiderwebs are quite elastic, so when an insect gets caught in the web, its stru

Question

Spiderwebs are quite elastic, so when an insect gets caught in the web, its struggles cause the web to vibrate. This alerts the spider to a potential meal. The frequency of vibration of the web gives the spider an indication of the mass of the insect.

A) Suppose that a 30-mg insect lands on a horizontal web and depresses it 3.5 mm. If we model the web as a spring, what would be its effective spring constant?

B) At what rate would the web in previous part vibrate, assuming that its mass is negligible compared to that of the insect?

Explanation / Answer

A)

mass = 30*10^-6 kg

Fg = weight of the spider = mg = 30*10^-6*9.8

x = 3.5 mm = 3.5*10^-3

effective spring constant = Fg/x = 30*10^-6*9.8/(3.5*10^-3) = 0.084 N/m

B)

frequency f = w/2pi = (1/2pi)*sqrt(k/m)

f = (1/(2pi))*sqrt(0.084/(30*10^-6)) = 8.42 Hz

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