Calc Min Steel Wire Diameter for 323kg Load

[iamtrojan3]

Homework Statement

Find the minimum diameter of an l = 17.2 m long steel wire that will stretch no more than 7.38 mm when a mass of 323 kg is hung on the lower end. (Hint: The Young's modulus of steel is 200.0 GPa.)

Homework Equations

Youngs = (Force / Area) / (change L / L)
= (mg / pi*r^2) / (change L / L)

The Attempt at a Solution

Simple enough... just plug and chug right?
just to clarify, 200.0GPa = 2x10^11 N/m^2 correct?
and 7.38mm = 0.00738m
If so,

Then after solving for r... i got .006853m, which is wrong. And i did multiply by 2 for the diameter. 0.0685 is also wrong, so is .685m

What am i doing wrong?? or am i just way off??

Thanks

 

[Jobrag]

What value of g did you use?

 

[method_man]

I used the same formula as you did and I get 0.0069 m. Do you know the correct answer?

 

[iamtrojan3]

Sorry for not replying earlier... fell asleep.
I used 9.81 as g, and idk what the right answer is... =(

 

[Redbelly98]

You have the right answer. Maybe you have the wrong number of significant figures, or are rounding incorrectly.

g=9.81 gives 6.86 mm, and g=9.80 gives 6.85 mm for the diameter.