Calcuate Elastic Modulus of metal cable

In summary, the problem involves calculating the Elastic Modulus of a metal based on a mass of 225 kg hung from a 1.60m long and 8.20mm diameter metal cable, causing it to stretch by 0.668mm. The formula used is E = (F/A)/(change L / orig L), and after plugging in the correct values, the result is 5.26 * 10^11 N/M2. However, the correct value given in the book is 100 * 10^9 N/M2, indicating there may be a decimal point error in the calculation.
  • #1
EroAlchemist
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Homework Statement



A mass of 225 kg is hung from a metal cable of length 1.60m and diameter 8.20mm. This causes the cable to stretch by an amount 0.668mm. Calculate the Elastic Modulus of the metal.

Homework Equations



E=(F/A)/(change L / orig L)


The Attempt at a Solution



F = mg = 2205N
A = Pi (r2) = 5.28*10^-5 m2
F/A = 2.2*10^7

Change L = 6.68*10^-4m
Orig L = 1.6m
CL/OL = 4.18*10^-5

(2.2*10^7) / (4.18*10^-5) = 5.26 *10^11 N/M2 = E

The book says the correct value for E = 100*10^9 N/M2. I'm not sure where I went wrong.
Thanks for the help!
 
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  • #2
Oh you have a couple of math or decimal point errors. Your formula is correct. Just recheck the math, it is easy to slip a decimal point or 2 when dealing with decimals or numbers with a lot of 000000000's :smile:

And welcome to PF!
 
  • #3
Thanks - I'll check them again.
:)
 

Related to Calcuate Elastic Modulus of metal cable

1. How is the elastic modulus of a metal cable calculated?

The elastic modulus of a metal cable is calculated by dividing the stress applied to the cable by the strain that results from the stress. This calculation is known as Hooke's Law and is expressed as E = σ / ε, where E is the elastic modulus, σ is the stress, and ε is the strain.

2. What factors affect the elastic modulus of a metal cable?

The elastic modulus of a metal cable can be affected by a variety of factors, including the type of metal used, the thickness and diameter of the cable, the temperature at which it is being tested, and any external forces or stresses acting upon the cable.

3. What is a typical range for the elastic modulus of a metal cable?

The elastic modulus of a metal cable can vary greatly depending on the type of metal used, but in general, most metal cables have an elastic modulus ranging from 1 to 200 GPa (gigapascals). However, some specialized cables, such as carbon nanotube cables, can have much higher elastic moduli.

4. How does the elastic modulus of a metal cable affect its strength?

The elastic modulus of a metal cable is directly related to its strength. A higher elastic modulus means that the cable is more resistant to deformation under stress, which translates to a higher tensile strength. Therefore, a metal cable with a higher elastic modulus will generally be stronger and able to withstand greater forces without breaking or deforming.

5. Can the elastic modulus of a metal cable change over time?

Yes, the elastic modulus of a metal cable can change over time due to a phenomenon called creep. Creep is the gradual increase in strain that occurs when a material is subjected to a constant stress over a long period of time. This can cause the elastic modulus of a metal cable to decrease, making it less resistant to deformation and potentially weakening it over time.

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