Elastic Problem. Aluminum Wire in Horizontal Circle

[XwyhyX]

Homework Statement

An aluminum wire is 0.850 m long and has a circular cross section of diameter 0.780 mm. Fixed at the top end, the wire supports a 1.20-kg object that swings in a horizontal circle. Determine the angular velocity required to produce a strain of 1.00  10–3.

Homework Equations

Y of Aluminum = 7.0x10¹⁰

Y = $\frac{Stress}{strain}$

Stress = $\frac{F}{A}$


F_c = ω²R

The Attempt at a Solution

I use Young's Modulus with the definition of stress and I get the equation

Y = $\frac{F/A}{Strain}$

Then I can solve for F

A = [itex]\frac{∏(0.780)²}{4}[/itex] = 4.77x10^-7

F = Y x Strain x Area

Okay, now I have the force which will give me the strain that is needed. I'll apply it in an object rotating in a horizontal circle, The force that I used will be the one on the X axis. So

F_c = Fsinθ

and also

R = Lsinθ

Using the equation of Centripetal Force I get the equation for angular Velocity

ω = $\sqrt{\frac{Tsinθ}{Lsinθ}}$

Finally I get the value of 6.27 rad/s





I just want to know if I did it right. Because I don't have the correct answer for this. Thanks :D

 

[PhanthomJay]

Fc = mω²R

 

[XwyhyX]

Oops. What a simple mistake :|

So

ω = sqrt(Fsinθ/mLsinθ)

giving an answer of 4.86 rad/s?