# Elastic Problem. Aluminum Wire in Horizontal Circle

1. Nov 30, 2011

### XwyhyX

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Y of Aluminum = 7.0x1010

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

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

Fc = ω2R
3. 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 = $\frac{∏(0.780)2}{4}$ = 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

Fc = 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

2. Nov 30, 2011

### PhanthomJay

Fc = mω2R

3. Nov 30, 2011

### XwyhyX

Oops. What a simple mistake :|

So

ω = sqrt(Fsinθ/mLsinθ)