Tension in a wire, length change

Click For Summary
SUMMARY

The discussion focuses on calculating the tension in a laundry wire when a 450-gram chicken lands on it, causing a 0.05% stretch in the wire's length of 10 meters. The correct tension in each segment of the wire is determined to be 7.2 N, derived from the equilibrium of forces and the geometry of the situation. The confusion arises from other students calculating a tension of 69.8 N, which is inconsistent with the mass of the chicken and the principles of tension in a stretched wire. The analysis confirms that the stretching of the wire does not significantly alter the calculated tension in this scenario.

PREREQUISITES
  • Understanding of basic physics principles, particularly equilibrium of forces.
  • Knowledge of trigonometry, specifically the use of right triangles and arccosine.
  • Familiarity with tension in strings and how it relates to mass and force.
  • Ability to apply the concept of percentage change in length to physical scenarios.
NEXT STEPS
  • Study the principles of tension in elastic materials, focusing on Hooke's Law.
  • Learn about the effects of stretching on tension in different types of materials.
  • Explore the application of trigonometric functions in physics problems involving forces.
  • Investigate common mistakes in tension calculations and how to avoid them.
USEFUL FOR

Students in physics courses, educators teaching mechanics, and anyone interested in understanding the dynamics of tension in wires and elastic materials.

CINA
Messages
60
Reaction score
0

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?
 
Last edited by a moderator:
Physics news on Phys.org
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.