How Much Must You Stretch a Guitar String to Obtain a Tension of 10 N?

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Homework Help Overview

The discussion revolves around determining the amount a guitar string must be stretched to achieve a specific tension of 10 N. The problem involves concepts from material science, specifically Young's modulus, and its application in understanding stress and strain in materials.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of Young's modulus and its relationship to stress and strain. Questions arise regarding the initial steps to take in solving the problem, including the application of Hooke's Law.

Discussion Status

Some participants have provided insights into the relationship between force, area, and Young's modulus, suggesting the use of formulas to isolate the unknown variable. There is an indication of progress as one participant claims to have reached an answer, although the validity of that answer is not confirmed by others.

Contextual Notes

Participants note that all necessary values are provided except for the change in dimension, which is the primary unknown in the problem. There is also a mention of uncertainty regarding the application of the relevant equations.

kavamo
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Homework Statement



A 0.46 m long guitar string, of cross-sectional area 1.1 10-6 m2, has Young's modulus Y = 2.20 109 N/m2. By how much must you stretch the string to obtain a tension of 10 N?

Homework Equations



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The Attempt at a Solution



I don't know how to begin this problem. What is Young's modulus, and how is it used?
 
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youngs modulus is the ratio of stress to strain

stress is given in force/unit area

strain change in dimension/original dimension (no units)

all values are given except change in dimension
 
so do I use hooks law?

F/A=Y delta L/L

I got it! The answer is 1.9 mm.

Thanks!
 
Last edited:
kavamo said:
so do I use hooks law?

F/A=Y delta L/L

Yep. That's using the definition of Young's Modulus!

Isolate your unknown variable, [tex]\Delta \ell[/tex] as a function of all your known variables, [tex]F, A, \ell, Y[/tex] and just stick all the values into the formula you get.
 

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