Calcuate Elastic Modulus of metal cable

AI Thread Summary
To calculate the Elastic Modulus of a metal cable, a mass of 225 kg causes a stretch of 0.668 mm in a cable of length 1.60 m and diameter 8.20 mm. The force exerted is calculated as 2205 N, and the cross-sectional area is determined to be approximately 5.28 x 10^-5 m². Using the formula E = (F/A) / (change L / orig L), the initial calculation yields an Elastic Modulus of 5.26 x 10^11 N/m². However, the expected value is 100 x 10^9 N/m², indicating potential errors in the calculations, particularly with decimal placements. The discussion emphasizes the importance of double-checking mathematical accuracy in such calculations.
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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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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!
 
Thanks - I'll check them again.
:)
 

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