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Answer :
Sure! Let's go through the solution step by step.
To find the increase in length of the wire, we need to use the formula related to Young's modulus, which describes how a material stretches under a force:
[tex]\[
\Delta L = \frac{F \cdot L}{A \cdot Y}
\][/tex]
where:
- [tex]\(\Delta L\)[/tex] is the increase in length,
- [tex]\(F\)[/tex] is the force applied to the wire,
- [tex]\(L\)[/tex] is the original length of the wire,
- [tex]\(A\)[/tex] is the cross-sectional area of the wire,
- [tex]\(Y\)[/tex] is Young's modulus of the material.
Here's how we calculate it:
1. Calculate the Force ([tex]\(F\)[/tex]):
The force is due to the weight of the load. So, it's given by [tex]\(F = mg\)[/tex], where:
- [tex]\(m = 200\, \text{kg}\)[/tex] is the mass of the load,
- [tex]\(g = 9.81\, \text{m/s}^2\)[/tex] is the acceleration due to gravity.
[tex]\[
F = 200 \times 9.81 = 1962\, \text{N}
\][/tex]
2. Use the Young's Modulus formula to find [tex]\(\Delta L\)[/tex]:
- The initial length [tex]\(L\)[/tex] of the wire is 4.00 meters.
- The cross-sectional area [tex]\(A\)[/tex] is [tex]\(0.20 \times 10^{-5}\, \text{m}^2\)[/tex].
- Young's modulus [tex]\(Y\)[/tex] is [tex]\(8.00 \times 10^{10}\, \text{N/m}^2\)[/tex].
Plug these values into the formula to find the increase in length:
[tex]\[
\Delta L = \frac{1962 \times 4.00}{0.20 \times 10^{-5} \times 8.00 \times 10^{10}}
\][/tex]
[tex]\[
\Delta L = \frac{7848}{1.6 \times 10^6} = 0.04905\, \text{m}
\][/tex]
So, the increase in length of the wire is approximately 0.04905 meters.
To find the increase in length of the wire, we need to use the formula related to Young's modulus, which describes how a material stretches under a force:
[tex]\[
\Delta L = \frac{F \cdot L}{A \cdot Y}
\][/tex]
where:
- [tex]\(\Delta L\)[/tex] is the increase in length,
- [tex]\(F\)[/tex] is the force applied to the wire,
- [tex]\(L\)[/tex] is the original length of the wire,
- [tex]\(A\)[/tex] is the cross-sectional area of the wire,
- [tex]\(Y\)[/tex] is Young's modulus of the material.
Here's how we calculate it:
1. Calculate the Force ([tex]\(F\)[/tex]):
The force is due to the weight of the load. So, it's given by [tex]\(F = mg\)[/tex], where:
- [tex]\(m = 200\, \text{kg}\)[/tex] is the mass of the load,
- [tex]\(g = 9.81\, \text{m/s}^2\)[/tex] is the acceleration due to gravity.
[tex]\[
F = 200 \times 9.81 = 1962\, \text{N}
\][/tex]
2. Use the Young's Modulus formula to find [tex]\(\Delta L\)[/tex]:
- The initial length [tex]\(L\)[/tex] of the wire is 4.00 meters.
- The cross-sectional area [tex]\(A\)[/tex] is [tex]\(0.20 \times 10^{-5}\, \text{m}^2\)[/tex].
- Young's modulus [tex]\(Y\)[/tex] is [tex]\(8.00 \times 10^{10}\, \text{N/m}^2\)[/tex].
Plug these values into the formula to find the increase in length:
[tex]\[
\Delta L = \frac{1962 \times 4.00}{0.20 \times 10^{-5} \times 8.00 \times 10^{10}}
\][/tex]
[tex]\[
\Delta L = \frac{7848}{1.6 \times 10^6} = 0.04905\, \text{m}
\][/tex]
So, the increase in length of the wire is approximately 0.04905 meters.
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