Elastic Problem. Aluminum Wire in Horizontal Circle

AI Thread Summary
The discussion revolves around calculating the angular velocity required for an aluminum wire supporting a 1.20-kg object to produce a strain of 1.00 × 10–3. The user correctly applies Young's Modulus to derive the force needed for the specified strain and calculates the cross-sectional area of the wire. Initial calculations yield an angular velocity of 6.27 rad/s, but upon review, a mistake is identified in the centripetal force equation. The corrected formula results in a new angular velocity of 4.86 rad/s. The user seeks confirmation on the accuracy of their revised calculations.
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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}


Fc = 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 = \frac{∏(0.780)<sup>2</sup>}{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
 
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Oops. What a simple mistake :|

So

ω = sqrt(Fsinθ/mLsinθ)

giving an answer of 4.86 rad/s?
 
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