Question #271609

A small fly on mass 0.25 g is caught in a spider’s web. The web oscillates predominantly with a frequency of 4.0 Hz.

a) What is the value of the effective spring stiffness constant k for the web? [ANS = 0.16 N m^{-1}]

b) At what frequency would you expect the web to oscillate if an insect of mass 0.50 g were trapped? [ANS = 2.8 Hz]

Expert's answer

(a)

"f=\\dfrac{1}{2\\pi}\\sqrt{\\dfrac{k}{m}},""f^2=\\dfrac{1}{4\\pi^2}\\dfrac{k}{m},""k=4\\pi^2f^2m,""k=4\\pi^2\\times(4.0\\ Hz)^2\\times2.5\\times10^{-4}\\ kg=0.16\\ \\dfrac{N}{m}."(b)

"f=\\dfrac{1}{2\\pi}\\sqrt{\\dfrac{k}{m}},""f=\\dfrac{1}{2\\pi}\\sqrt{\\dfrac{0.16\\ \\dfrac{N}{m}}{5\\times10^{-4}\\ kg}}=2.8\\ Hz."
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