Continue but use power 11 not 13 for the young modulus

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Given:

• Length of copper wire ($L_c$) = 1.5 m
• Length of steel wire ($L_s$) = 1.5 m
• Diameter ($d$) = 2.0 mm = $2.0 \times 10^{-3}$ m
• Load ($F$) = 200 N
• Young's Modulus for Copper ($E_c$) = $1.1 \times 10^{11} \text{ Pa}$
• Young's Modulus for Steel ($E_s$) = $2.0 \times 10^{11} \text{ Pa}$

1. Calculate the stress in each wire.

Step 1: Calculate the cross-sectional area of the wire. The diameter of the wire is $d = 2.0 mm = 2.0 \times 10^{-3} \text{ m}$. The radius is $r = d/2 = 1.0 \times 10^{-3} \text{ m}$.

$A = \pi r^2$ $A = \pi (1.0 \times 10^{-3} m)^2$ $A = \pi (1.0 \times 10^{-6} m^2)$ $A \approx 3.14159 \times 10^{-6} m^2$

Step 2: Calculate the stress in each wire. Since the wires are joined end-to-end and the same load is applied, the stress in each wire is the same. Stress ($\sigma$) = Force ($F$) / Area ($A$)

$\sigma = \frac{200 N}{3.14159 \times 10^{-6} m^2}$ $\sigma \approx 6.366 \times 10^{7} Pa$ The stress in each wire is $\boxed{6.37 \times 10^{7} Pa}$.

2. Calculate the total extension of the composite wire.

Step 3: Calculate the extension of the copper wire ($\Delta L_c$). Young's Modulus ($E$) = Stress ($\sigma$) / Strain ($\epsilon$) Strain ($\epsilon$) = Extension ($\Delta L$) / Original Length ($L$) So, $E = \frac{F/A}{\Delta L/L} = \frac{FL}{A \Delta L}$. Rearranging for extension: $\Delta L = \frac{FL}{AE}$.

For copper wire: $\Delta L_c = \frac{F L_c}{A E_c}$ $\Delta L_c = \frac{(200 N)(1.5 m)}{(3.14159 \times 10^{-6} m^2)(1.1 \times 10^{11} Pa)}$ $\Delta L_c = \frac{300 N\cdotm}{3.45575 \times 10^{5} N}$ $\Delta L_c \approx 8.681 \times 10^{-4} m$

Step 4: Calculate the extension of the steel wire ($\Delta L_s$). For steel wire: $\Delta L_s = \frac{F L_s}{A E_s}$ $\Delta L_s = \frac{(200 N)(1.5 m)}{(3.14159 \times 10^{-6} m^2)(2.0 \times 10^{11} Pa)}$ $\Delta L_s = \frac{300 N\cdotm}{6.28318 \times 10^{5} N}$ $\Delta L_s \approx 4.774 \times 10^{-4} m$

Step 5: Calculate the total extension ($\Delta L_{total}$). $\Delta L_{total} = \Delta L_c + \Delta L_s$ $\Delta L_{total} = 8.681 \times 10^{-4} m + 4.774 \times 10^{-4} m$ $\Delta L_{total} = 13.455 \times 10^{-4} m$ $\Delta L_{total} \approx 1.346 \times 10^{-3} m$ The total extension of the composite wire is $\boxed{1.35 \times 10^{-3} m}$.

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