Tension in a wire, length change

AI Thread Summary
The problem involves calculating the tension in a wire after a chicken lands on it, causing a 0.05% stretch. The original wire length is 10 meters, and the tension was calculated to be 7.2 N based on the geometry of the situation. Some classmates arrived at a tension of 69.8 N, which is deemed incorrect as it would imply an upward force much greater than the chicken's weight. The discussion highlights that the stretching of the wire primarily affects the geometry but does not significantly alter the tension calculation. The conclusion suggests that the tension calculated at 7.2 N is accurate given the parameters provided.
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Homework Statement



3. A flying chicken (m = 450[gram]) lands in the middle of a taught laundry wire of length l=10[m]. The wire has a negligible mass. The chicken causes the wire to stretch by 0.05% from its original length. Find the tension in each segment of the wire.

http://img517.imageshack.us/img517/2922/asdfgggea7.th.jpg http://g.imageshack.us/thpix.php


Homework Equations



Fext = 0

X) Ft1x - Ft2x = 0

Y) Ft1y + Ft2y - Fg = 0


The Attempt at a Solution



Since the length increases by .05% you can make a triangle with lengths 10m ( the origianl length), 5.25m and 5.25m (half of the new length with the chicken in the middle). you can split this into two right triangles with sides 5-5.25-x (doesn't matter right?). Using arccos (5/5.25) you get 17.8 degrees.

Fty1 & Fty2 = Ftx tan 17.8

getting 2 Ftx tan 17.8 = Fg

Ftx = 6.87 N

Ft = Ftx/Cos 17.8 = 7.2 N

The Problem

Students in my class got 69.8 N, and after looking up tension I found that it increases as things stretch. Our teacher never said anything about this (but gave a problem on it). How does the streching of the string play into this? Is there some equation I'm not putting to use?
 
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7.2 N looks fine to me. I doubt the stretching of the string has anything to do with it other than giving you the triangles.

Just by looking at it I would say the other students in your class have done something wrong because of the size of their answer. It would give them about 21N upwards force, much greater than the mass of the bird.
 

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