Young's Modulus

Question

A wire length 2 m, area 2×10⁻⁶ m², Young's modulus 2×10¹¹ Pa stretches 1 mm under load. Force applied?

RankGuru · Accepted Answer

1. **Young's Modulus Formula**: $Y = \frac{	ext{Stress}}{	ext{Strain}} = \frac{F/A}{\Delta L/L} = \frac{F L}{A \Delta L}$.
2. **Isolate F**: $F = \frac{Y A \Delta L}{L}$.
3. **Substitute Values**:
   - $Y = 2 	imes 10^{11} 	ext{ Pa}$
   - $A = 2 	imes 10^{-6} 	ext{ m}^2$
   - $\Delta L = 1 	ext{ mm} = 10^{-3} 	ext{ m}$
   - $L = 2 	ext{ m}$
4. **Calculation**:
   - $F = \frac{(2 	imes 10^{11}) (2 	imes 10^{-6}) (10^{-3})}{2}$
   - $F = \frac{4 	imes 10^{11-6-3}}{2}$
   - $F = \frac{400}{2} = 200$ N.
5. **Conclusion**: The applied force is **$200$ N**.

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