Spider's Web Vibrations: Mass, Freq., & Spring Const.

[metalmagik]

A small fly of mass 0.13 g is caught in a spider's web. The web vibrates predominately with a frequency of 1.0 Hz.
(a) What is the value of the effective spring constant k for the web?

(b) At what frequency would you expect the web to vibrate if an insect of mass 0.54 g were trapped?

I received 194.8 N/m and 46.9 Hz for (a) and (b), respectively. Could someone check this work for me quick and confirm this is correct? If it is not and you wouldn't mind helping me out, I'll post all the work/equations I have done.

 

[ehild]

I received 194.8 N/m and 46.9 Hz for (a) and (b), respectively. Could someone check this work for me quick and confirm this is correct? If it is not and you wouldn't mind helping me out, I'll post all the work/equations I have done.

Show your work.

ehild

 

[kyle8921]

(a) To calculate the effective spring constant k for the spider's web, we can use the equation for the frequency of a vibrating spring:

f = 1/2π √(k/m)

Where f is the frequency, k is the spring constant, and m is the mass of the object attached to the spring.

We know that the frequency is 1.0 Hz and the mass of the fly is 0.13 g. Plugging these values into the equation, we get:

1.0 Hz = 1/2π √(k/0.13 g)

Rearranging the equation, we get:

k = (1.0 Hz)^2 * 0.13 g * 4π^2

k = 194.8 N/m

Therefore, the value of the effective spring constant k for the spider's web is 194.8 N/m.

(b) To calculate the frequency at which the web would vibrate if an insect of mass 0.54 g were trapped, we can use the same equation as above:

f = 1/2π √(k/m)

We know that the mass of the insect is now 0.54 g. Plugging this value into the equation and using the value of k calculated in part (a), we get:

f = 1/2π √(194.8 N/m / 0.54 g)

f = 46.9 Hz

Therefore, the frequency at which the web would vibrate with an insect of mass 0.54 g trapped is 46.9 Hz.

Your calculations are correct. Great job!