Answer to Question #271609 in Physics for jay

Question

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]

Answer 1

(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)

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