Respuesta :
Given:
• Length = 24 m
,• Temperature, T1 = 8°C
,• Expansion coefficient = 11 x 10⁻⁶(°C)⁻¹
Let's solve for the following:
• (a). The increase in length of the rail when the temperature is 36 °C
To find the increase in length, apply the formula:
[tex]L=L_o*\alpha *(T_2-T_1)[/tex]Where:
Lo = 24 m
α = 11 x 10⁻⁶(°C)⁻¹
T2 = 36 °C
T1 = 8°C
Thus, we have:
[tex]\begin{gathered} dL=24*11\times10^{-6}*(36-8) \\ \\ dL=24*11\times10^{-6}*(28) \\ \\ dL=0.0074\text{ m} \end{gathered}[/tex]The increase in length is 0.0074 m.
• (b). Let's calculate the thermal stress.
To find the thermal stress, we have the formula:
[tex]\text{ thermal stress = }Y\frac{dL}{L}[/tex]Where:
Y is the young modulus = 20 x 10¹⁰ N/m
dL is the change in length = 0.0074 m
L is the length = 24 m
Input values in the formula and solve:
[tex]\begin{gathered} \text{ thermal stress = 20}\times10^{10}*\frac{0.0074}{24} \\ \\ \text{ thermal stress = 6.17}\times10^7\text{ N/m}^2 \end{gathered}[/tex]The thermal stress is 6.17 x 10⁷ N/m².
ANSWER:
• (a). 0.0074 m.
• (b). 6.17 x 10⁷ N/m²
