A small fly of mass 0.143 g is caught in aspider\'s web. The web vibrates predom

Question

A small fly of mass 0.143 g is caught in aspider's web. The web vibrates predominately with a frequency of3.38 Hz.

What is the value of the effective spring constant k for theweb? At what frequency would you expect the web tovibrate if an insect of mass 0.473 g were trapped? A small fly of mass 0.143 g is caught in aspider's web. The web vibrates predominately with a frequency of3.38 Hz.

What is the value of the effective spring constant k for theweb? At what frequency would you expect the web tovibrate if an insect of mass 0.473 g were trapped?

Explanation / Answer

Mass of fly m = 0.143 g
                    = 0.143 x 10-3 kg
We know that the relationship between period, mass and springconstant:

                T = 2Öm/k
                1 / f = 2Öm/k
             k = 42f2 * m                      =4*3.142 * 3.382 * 0.143 x10-3
                     =0.0644 N/m If a mass of 0.473 g = 0.473 x 10-3 kg were trappedin the web, If a mass of 0.473 g = 0.473 x 10-3 kg were trappedin the web, we can turn this spring constant around, and plug into

       f =(1/2)(k/m)          =(1/2*3.14)(0.0644 N/m / 0.473 x 10-3 kg)          =1.8580 Hz

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