(adsbygoogle = window.adsbygoogle || []).push({}); 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 = 7.0x10^{10}

Y = [itex]\frac{Stress}{strain}[/itex]

Stress = [itex]\frac{F}{A}[/itex]

F_{c}= ω^{2}R

3. The attempt at a solution

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

Y = [itex]\frac{F/A}{Strain}[/itex]

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 = [itex]\sqrt{\frac{Tsinθ}{Lsinθ}}[/itex]

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

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# Elastic Problem. Aluminum Wire in Horizontal Circle

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