# What Mass Can a Bug Have to Maximize Stress on a Spider Web?

• dimpledur
In summary, Spider Silk can withstand a maximum stress of 1.4x10^9 N/m^2 and has a Young Modulus of 4.0x10^9 N/m^2. A single webstrand has a cross sectional area of 1.0x10^-11 m^2 and a web is made up of 50 radial strands. To exert this maximum stress, a bug should have a mass of 48 grams. The tension can be expressed as T*sinθ = m*g, where θ is the angle the web makes with the horizontal.
dimpledur

## Homework Statement

Spider Silk has a Young Modulus of 4.0x10^9 N/m^2 and can withstand stresses of up to 1.4x10^9 N/m^2. A single webstrand has a cross sectional area of 1.0x10^-11 m^2, and a web is made up of 50 radial strands. A bug lands in the centre of a horizontal web. With what mass should the bug be to exert this maximum stress?

## Homework Equations

F/A = 1.4x10^9 N/m^2

## The Attempt at a Solution

F/A = 1.4x10^9 N/m^2
mg / A = 1.4x10^9 N/m^2

A = 50 strands * 1.0x10^-10 N/m^2 = 5.0x10^-10

so m = (1.4x10^9 N/m^2)(5.0x10^-10) / 9.8
m = 71.4g

HOWEVER, the answer is 48 grams. I am unsure of what to do with the area. Like, I'm pretty sure that I am messing that portion up.

Since the web is horizontal, won't the strands stretch?

It seems like the angle of that stretch will be Cosθ = L/(L +ΔL).

Then it's a matter of tension, with the vertical m*g being the Tmax*Sinθ isn't it?

Now if only there was some way to figure the stretch at Tmax?

LowlyPion said:
Since the web is horizontal, won't the strands stretch?

It seems like the angle of that stretch will be Cosθ = L/(L +ΔL).

Then it's a matter of tension, with the vertical m*g being the Tmax*Sinθ isn't it?

Now if only there was some way to figure the stretch at Tmax?

Wouldn't it be Tension = sin theta * mg ?

I'm having a hard time visualizing the problem...

Draw a diagram.

The web is horizontal. Looking in cross-section it will look like a weight supported by 2 lines in Tension sagging down. (Ignore for a moment the other 24 pairs of strands.) The angle θ it makes with the horizontal can be used to express the vertical component of the tension which I think you should see is T*sinθ = m*g.

LowlyPion said:
Draw a diagram.

The web is horizontal. Looking in cross-section it will look like a weight supported by 2 lines in Tension sagging down. (Ignore for a moment the other 24 pairs of strands.) The angle θ it makes with the horizontal can be used to express the vertical component of the tension which I think you should see is T*sinθ = m*g.

I totally see it now thank you!

## 1. What is maximum stress in a spider web?

The maximum stress in a spider web refers to the amount of force or weight that can be applied to the web before it breaks or becomes damaged. This is an important measure of the strength and durability of the web.

## 2. How is maximum stress calculated in a spider web?

Maximum stress is typically calculated by dividing the force applied to the web by the cross-sectional area of the web. This gives the maximum stress in units of force per unit area, such as pounds per square inch or newtons per square meter.

## 3. What factors affect the maximum stress in a spider web?

The maximum stress in a spider web can be affected by several factors, including the type of spider that created the web, the thickness and composition of the web strands, the humidity and temperature of the environment, and the placement and geometry of the web.

## 4. Is the maximum stress the same for all spider webs?

No, the maximum stress can vary greatly between different spider webs. This is due to the many factors that can influence the strength and durability of a web, as well as the different species of spiders that create them.

## 5. Why is understanding the maximum stress in a spider web important?

Understanding the maximum stress in a spider web can provide valuable insights into the design and construction of webs, as well as the behavior and survival of spiders. It can also have practical applications in engineering and biomimicry, as spider webs are known for their impressive strength and resilience.

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