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The worlds longest suspension bridge is the Akashi Kaikyo Bridge in Japan. The bridge is 3910 m long and is constructed of steel. How much longer is the bridge on a warm summer day (30.0 °C) than on a cold winter day (-5.00 °C)?

Respuesta :

Answer:1.642 m

Step-by-step explanation:

Given

Initial Length of bridge [tex]L_0=3910 m[/tex]

temperature on cold day [tex]t_1=-5^{\circ}C[/tex]

temperature on hot day [tex]t_2=30^{\circ}C[/tex]

Change in temperature is [tex]\Delta T=30-(-5)=35^{\circ}C[/tex]

Coefficient of linear expansion of steel [tex]\alpha =12\times 10^{-6}/^{\circ}C[/tex]

and length after change in temperature is given by

[tex]L=L_0(1+\alpha \cdot \Delta T)[/tex]

[tex]\Delta =L_0\cdot \alpha \Delta T[/tex]

[tex]\Delta L=3910\cdot 12\times 10^{-6}\cdot 35[/tex]

[tex]\Delta L=1.642 m[/tex]

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