A small fly of mass 0. 30 g is caught in a spider's web. the web oscillates predominantly with a frequency of 4.3 Hz. The value of the effective spring stiffness constant k for the web is 0.21 N/m
Frequency of the oscillation is the number of oscillation in per unit time. It's SI unit is Hertz or s⁻¹.
Spring stiffness constant k is a measure of the stiffness of spring.
The Frequency of the oscillation is given by the following formula:
f = [tex]\sqrt{k/4\pi m}[/tex]
where, f is the frequency of web
k is the stiffness constant of web
m is the mass of small fly
On rearranging the above equation,
k = 4π²f²m
⇒ k = 4 (3.14)² (4.3)² 0.0003
⇒ k = 0.21 N/m
Hence, the Stiffness constant k for the web is 0.21 N/m
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