Physics Problem involving Young's Modulus *copper wire*?

Question

A copper wire (with a Young's modulus of 120 x 109 Pa) of length 3.08 m is observed to stretch by 2.25 mm when a weight of 136 N is hung from one end. What is the diameter of the wire? 

I need some help setting up the equation. I'm assuming I need to use Hook's Law

F/A=y*(Delta L/L) 
(I break the Area up into (D/2)^2 to find the diameter and then i start having problems isolating the Diameter
 

any help would be great

Answer 1

The Young's Modulus of copper wire is 120 * 109 Pa.

Length of the wire is 3.08m

The wire is stretched by Δl = 2.25 mm = 0.00225 m.

Force = 136 N.

We know that Youngs Modulus = Stress / strain.

Stress = Force / Area = F / A.

Strain = Change in Length / Original Length

Youngs Modulus Y = (F / A) / (Δl / l)

F / A = Y * (Δl / l)

136 / Area = 120 * 109 * (0.00225 / 3.08)

136 / Area = 10.6

Area = 136 / 10.6

Area = 12.80 m²

We know that area of the wire with radius r = πr²

πr² = 12.8

r² = 4.077

r = 2.019 m.

Diameter = 2*r = 2 *2.019 = 4.038 m

Therefore the Diameter of the wire is 4.038 m.

Comments

thanks for the help. Though I will note that the first part of your equation does not come out to be 10.6 because its 120*10^9. But I reasoned out how to work it out so thank you :)

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Please check the updated answer.

Answer 2

The Young's Modulus of copper wire is 120 * 10^9 Pa.

Length of the wire is 3.08m

The wire is stretched by Δl = 2.25 mm = 0.00225 m.

Force = 136 N.

We know that Youngs Modulus = Stress / strain.

Stress = Force / Area = F / A.

Strain = Change in Length / Original Length

Youngs Modulus Y = (F / A) / (Δl / l)

F / A = Y * (Δl / l)

136 / Area = 120 * 10^9 * (0.00225 / 3.08)

136 / Area = 87662337.66

Area = 136 / 87662337.66

Area = 1.55 * 10^-6 m²

We know that area of the wire with radius r = πr²

πr² = 1.55 * 10^-6

r² = 4.9 * 10^-7

r =7.027 * 10^-4 m.

r =7.027 * 10^-4 * 10^3 mm.

r =7.027 * 10^-1 mm.

r =0.7027 mm.

Diameter = 2*r = 2 *0.7027 = 1.405 mm

Therefore the Diameter of the wire is 1.4054 mm.