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

In summary, Young's modulus is the ratio of stress to strain, with stress being force per unit area and strain being the change in dimension over the original dimension. To solve for the change in dimension, we use Hooke's law, which states that F/A = Y * delta L/L. Plugging in the given values, we find that the string must be stretched by 1.9 mm to obtain a tension of 10 N.
  • #1
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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  • #2
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
 
  • #3
so do I use hooks law?

F/A=Y delta L/L

I got it! The answer is 1.9 mm.

Thanks!
 
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  • #4
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.
 

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

What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness of a solid material. It represents the ratio of stress (force per unit area) to strain (change in length per unit length) in a material when it is subjected to tension or compression.

Why is Young's modulus important?

Young's modulus is an important property of materials as it helps determine their strength and ability to deform under stress. It is also used to compare the elasticity of different materials and determine their suitability for various applications.

How is Young's modulus calculated?

Young's modulus is calculated by dividing the stress by the strain in a material. The stress can be measured by applying a known force to a material and measuring the resulting strain using specialized equipment.

What is the unit of Young's modulus?

The unit of Young's modulus is typically measured in pascals (Pa) or newtons per square meter (N/m²). In the imperial system, it is measured in pounds-force per square inch (psi).

What factors affect Young's modulus?

The main factors that affect Young's modulus include the type of material, its composition, and its microstructure. Temperature and strain rate can also have an impact on the modulus of elasticity of a material.

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