How Do You Calculate Stress and Strain in a Stretched Copper Wire?

AI Thread Summary
To calculate stress and strain in a stretched copper wire, first determine the cross-sectional area using the formula πr², which results in 7.8 x 10^-7 m². The strain is calculated as the extension (0.85 mm) divided by the original length (2.3 m), yielding a strain of approximately 0.37. Stress can be derived from Young's modulus, which relates stress and strain, allowing for the calculation of stress once strain is known. Finally, the force required to produce that stress can be calculated using the stress formula, where force equals stress multiplied by area. Understanding these relationships is crucial for solving the problem effectively.
DizzyDoo
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The last question on my homework (always the hardest).

Homework Statement


A wire of diameter 1.0mm and length 2.3m is made of copper. Young modulus is 1.1 x 10^11. Find:
a) The cross-section of the wire in m²
b) The strain if the wire is stretched by 0.85mm
c) The stress
d) The force necessary to cause the stress

Homework Equations


(Pie)r²
strain = extension/original length
stress = Force/area

The Attempt at a Solution


Here is my attempt, I get stuck at C, but please check what I've done so far.

A) if (pie)r² then stick that into the calculator, and I get 7.8 x 10 ^7
B) Extension/Original length= 0.85/2.3 = 0.37
c) Hmm, they ask for stress but there is no force given, so how do I work that out?
d) Now they ask the force needed to cause the stress, but I need that to work out the stress. Very confusing

Any help is greatly appreciated.
 
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DizzyDoo said:
The last question on my homework (always the hardest).

Homework Statement


A wire of diameter 1.0mm and length 2.3m is made of copper. Young modulus is 1.1 x 10^11. Find:
a) The cross-section of the wire in m²
b) The strain if the wire is stretched by 0.85mm
c) The stress
d) The force necessary to cause the stress

Homework Equations


(Pie)r²
strain = extension/original length
stress = Force/area

The Attempt at a Solution


Here is my attempt, I get stuck at C, but please check what I've done so far.

A) if (pie)r² then stick that into the calculator, and I get 7.8 x 10 ^7 you mean 7.8 x 10^-7 m^2[/color]
B) Extension/Original length= 0.85/2.3 = 0.37 Right equation, but again your units are lacking and decimal point is off[/color]
C) Hmm, they ask for stress but there is no force given, so how do I work that out? You have Young's modulus and you have calculated the strain...what is the formula that relates stess and strain?[/color]
d) Now they ask the force needed to cause the stress, but I need that to work out the stress. Very confusing once you have the stress, the force should be easy to calculate[/color]

Any help is greatly appreciated.
see above in red [/color].
 
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