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

[DizzyDoo]

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.

 

[PhanthomJay]

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
B) Extension/Original length= 0.85/2.3 = 0.37 Right equation, but again your units are lacking and decimal point is off
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?
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

Any help is greatly appreciated.

see above in red .

 

[ogb p]

As a scientist, it is important to remember that stress and strain are important properties of materials that can help us understand how they behave under external forces. In this case, we are dealing with a wire made of copper, which has a Young's modulus of 1.1 x 10^11. Let's break down the questions one by one to better understand how to approach them.

a) The cross-section of the wire can be calculated using the formula (π)r², where r is the radius of the wire. In this case, r = 0.5mm or 0.0005m. Plugging this into the formula, we get a cross-section of 7.85 x 10^-7 m².

b) Strain is defined as the change in length divided by the original length. In this case, the extension is given as 0.85mm or 0.00085m and the original length is 2.3m. Plugging these values into the formula, we get a strain of 0.00037.

c) Stress is defined as the force applied per unit area. In this case, we do not have the force given, but we can calculate it using the formula stress = Young's modulus x strain. Plugging in the values, we get a stress of 4.07 x 10^7 Pa.

d) Finally, to calculate the force necessary to cause this stress, we can use the formula stress = force/area. Rearranging, we get force = stress x area. Plugging in the values, we get a force of 3.18 x 10^1 N.

I hope this helps clarify the questions and how to approach them. Remember, as a scientist, it is important to always double check your calculations and units to ensure accuracy in your results. Keep up the good work!