Finding mass with given stress, strain, and original area

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SUMMARY

The discussion focuses on calculating the weight of an insect, specifically a bumblebee, that causes a spider-web thread to reach its breaking point. The thread has a stress limit of 8.2 x 108 N/m2, a strain of 2, an initial length of 2 cm, and a cross-sectional area of 8 x 10-12 m2. The initial calculation using the formula for stress (stress = F/A) yields a force of 0.00656 N, indicating that the insect's weight must be just under this force for the thread to break. Further steps include analyzing the equilibrium of forces and geometric relationships in the setup.

PREREQUISITES
  • Understanding of stress and strain concepts in materials science
  • Familiarity with basic physics equations related to force and equilibrium
  • Knowledge of geometric relationships in two-dimensional systems
  • Ability to perform calculations involving units of force (Newtons) and area (m2)
NEXT STEPS
  • Study the principles of stress and strain in materials, focusing on elastic deformation
  • Learn how to apply equilibrium equations in static systems
  • Explore geometric relationships in triangles, particularly in relation to forces
  • Investigate the properties of spider silk and its tensile strength for comparative analysis
USEFUL FOR

This discussion is beneficial for physics students, materials scientists, and anyone interested in understanding the mechanics of materials under stress, particularly in biological contexts such as the strength of spider silk.

Taco John
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Homework Statement



figure whatever represents an insect caught at the midpoint of a spider-web thread. The thread breaks under a stress of 8.2 x 10^8 N/m^2 and a strain of 2. Initially, it was horizontal and had a length of 2cm and a cross-sectional area of 8 x 10^-12 m^2. As the thread was stretched under the weight of the insect, its volume remained constant. If the weight of the insect puts the thread on the verge of breaking, what is the insect's weight?

Homework Equations


I would imagine the different variations of stress and strain


The Attempt at a Solution


I know the answer will be small (as the insect is supposed to be a bumble bee assuming the picture in the book isn't lying to me.

I don't know where to begin exactly.

I did stress = F/A to get F = .00656N, which means the bumble bee would have to apply just under that amount of force, as that is what the web will break at. But I'm unsure on what to do next.
 
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Draw a diagram. Suppose A and B are points where the thread is attached. The midpoint C is now vertically displaced to D. At the point D, the forces acting are the tensions T in the thread, and the weight W.

Write down the eqn for the equilibrium of the vertical forces.
Find the relation between BD and BC, from geometry.
The common thing between these eqns is the angle CBD.

That should be enough to get you started. If you show some work based on this, perhaps we could help you more, if you need it. You can do this.
 
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