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]


1
Expert's answer
2021-11-25T16:23:03-0500

(a)

f=12πkm,f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}},f2=14π2km,f^2=\dfrac{1}{4\pi^2}\dfrac{k}{m},k=4π2f2m,k=4\pi^2f^2m,k=4π2×(4.0 Hz)2×2.5×104 kg=0.16 Nm.k=4\pi^2\times(4.0\ Hz)^2\times2.5\times10^{-4}\ kg=0.16\ \dfrac{N}{m}.

(b)

f=12πkm,f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}},f=12π0.16 Nm5×104 kg=2.8 Hz.f=\dfrac{1}{2\pi}\sqrt{\dfrac{0.16\ \dfrac{N}{m}}{5\times10^{-4}\ kg}}=2.8\ Hz.

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