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

• metalmagik
In summary, the conversation discusses a small fly caught in a spider's web and the vibration of the web with a frequency of 1.0 Hz. The question arises about the effective spring constant k for the web and the expected frequency if a heavier insect of mass 0.54 g were trapped. The calculations result in values of 194.8 N/m and 46.9 Hz for (a) and (b) respectively. The speaker also requests someone to verify their work and offers to share their equations if needed.
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.

metalmagik said:
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

(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!

## 1. What is a spider's web vibration?

A spider's web vibration refers to the movement or oscillation of a spider's web caused by external forces such as wind, prey caught in the web, or the spider's own movements.

## 2. How is the mass of a spider's web related to its vibration?

The mass of a spider's web affects its vibration because the heavier the web, the more force is required to create a significant vibration. This means that a heavier web will vibrate less than a lighter web.

## 3. What is the frequency of a spider's web vibration?

The frequency of a spider's web vibration refers to the number of oscillations or cycles per unit of time. It is typically measured in Hertz (Hz) and can vary depending on the strength and speed of the external force causing the vibration.

## 4. How does the spring constant of a spider's web affect its vibration?

The spring constant of a spider's web refers to the stiffness of the web. A higher spring constant means that the web is stiffer and requires more force to create a significant vibration. On the other hand, a lower spring constant means that the web is more flexible and can vibrate more easily.

## 5. What factors can affect the vibration of a spider's web?

The vibration of a spider's web can be affected by various factors such as the strength and direction of the external force, the mass and spring constant of the web, humidity, temperature, and the size and shape of the web. The overall health and condition of the spider and its web can also play a role in the web's vibration.

### Similar threads

• Introductory Physics Homework Help
Replies
14
Views
8K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
4K
• Introductory Physics Homework Help
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
1K