Young's modulus of a hanging wire

In summary, Young's modulus is a measure of the stiffness of a material and is defined as the ratio of stress to strain. For a hanging wire, this means that the Young's modulus determines how much the wire will stretch or deform under a given weight or load. It is an important factor to consider in engineering and construction, as materials with a higher Young's modulus are more resistant to deformation and can support heavier loads.
  • #1
Westin
87
0

Homework Statement


A hanging wire made of an alloy of titanium with diameter 0.5cm is initially 6m long. When a 60kg mass is hung from it, the wire stretches an amount 1.44cm. A mole of titanium has a mass of 48g, and its density is 4.54g[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngcm3.

Based on these experimental measurements, what is Young's modulus for this alloy of titanium?

Y=


As you've done before, from the mass of one mole and the density you can find the length of the interatomic bond (diameter of one atom). This is 2.60×10-10m for titanium. The micro quantity ks[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3B.pngi (the stiffness of one interatomic bond) can be related to the macro property Y. Determine the interatomic spring stiffness:

ks[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3B.pngi =

Homework Equations

Y=(FT/A) / (ΔL/L)

The Attempt at a Solution



A=pir^2
A=pi(.25)^2
Stress = (60)(9.8)/.1963
Y= (588/.1963) / (600/1.44)

I thought everything was set up right.. Need assistance on part 2 also, thanks.
[/B]
 
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  • #2
Watch those units. Also, arithmetic error.

Chet
 

FAQ: Young's modulus of a hanging wire

What is Young's modulus?

Young's modulus is a measure of the stiffness or elasticity of a material. It is the ratio of stress (force per unit area) to strain (change in length per unit length) in a material under tension or compression.

How is Young's modulus calculated?

You can calculate Young's modulus by dividing the stress by the strain. The formula is E = σ/ε, where E is Young's modulus, σ is stress, and ε is strain.

Why is Young's modulus important for a hanging wire?

Young's modulus is important for a hanging wire because it determines how much the wire will stretch or deform when a weight is hung on it. A higher Young's modulus means the wire will have less stretch and be more rigid, while a lower Young's modulus means the wire will have more stretch and be more flexible.

What factors can affect the value of Young's modulus for a hanging wire?

The value of Young's modulus for a hanging wire can be affected by factors such as the material the wire is made of, the diameter and length of the wire, the temperature, and the amount of weight applied to the wire.

How is Young's modulus used in engineering and material science?

Young's modulus is an important property that is used in engineering and material science to determine the strength and stiffness of a material. It helps engineers and scientists understand how materials will behave under different types of stress and can be used to design and select materials for specific applications.

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