What is the Tension and Stretching of Spider Silk in Equilibrium?

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Homework Help Overview

The discussion revolves around the tension and stretching of spider silk in equilibrium, specifically focusing on a spider's silk with a given force constant and the weight of the spider. Participants are tasked with calculating the tension in the strands of silk and the distance each strand stretches beyond its normal length.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the application of equations related to tension and forces, with some attempting to derive relationships between the tensions in the strands. Questions arise regarding the accuracy of calculated tensions and the interpretation of angles in the setup.

Discussion Status

Some participants have provided calculations and expressed uncertainty about the correctness of their results, particularly regarding significant figures and potential rounding errors. Others have suggested re-evaluating the angles used in the calculations, indicating a productive exploration of the problem.

Contextual Notes

There is mention of significant figures and the need for precise calculations, as well as a potential misinterpretation of the angles involved in the tension setup. Participants are navigating through these constraints while attempting to arrive at accurate values.

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Homework Statement


The stretchy silk of a certain species of spider has a force constant of 1.50 . The spider, whose mass is 15mg, has attached herself to a branch as shown in the figure.
Figure:
http://session.masteringphysics.com/problemAsset/1348379/2/5-70.jpg
a)Calculate the tension in each of the three strands of silk.
b) Calculate the distance each strand is stretched beyond its normal length.

Homework Equations


Worked with the equations: Tc=Tacos(30) + Tbcos(40) for vertical components where Tc=mg=147 mN. And for the horizontal Tasin(30) = Tbsin(40). Found the ratio and plugged back into the equations to find Tb and then Ta.


The Attempt at a Solution


Using the relevant equations, I derived Ta = Tb x 1.286 and ultimately got answers:
Ta=100mN, Tb=78.2mN, and Tc=147mN.
 
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re tensions: chech 147mN

re last part: use force = force constant x extension
 
Does that say check* 147 mN, in that it is an incorrect magnitude for Tc?
 
A mass of 15mg = 15/(1000) = 0.015grams = 0.015/(1000) = 0.000015kg and now multiply by 9.81 to give weight in N to give 0.000147N = 0.147mN
 
so it should come to .100mN, .0782mN, .147mN for Ta, Tb, and Tc respectively?
 
the answer needs to be in 2 sig figs. I put in .100, .078, and .15. A message came up and said "Term 2: Not quite. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures."

I cannot find this error. Kept all numbers in my calculator.

Same response for the second part, in which I submitted .067, .052, and .098
 
I think that the angles were interpreted incorrectly.

The angle beteen tension A and tension B looks to me to be more than 90 degrees. So I think that the angles are 30deg and 70deg, together making up 100deg.
 
worked out. Thanks a lot
 

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