A single railroad stretches from New York to Los Angeles (Li = 2770 mi). Each of

Question

A single railroad stretches from New York to Los Angeles (Li = 2770 mi). Each of the two rails has a cross - sectional area of 64 cm2. As a prank, a mad scientist has welded all the 40-foot section together so that each of the two rails acts as a solid piece of steel.

a) in the year 2050, World War III sends the world into a nuclear winter, loweing the average temperture in the US by 65F. If the ends of the track remained fixed, what is the tensionin each rail?

b) in about one billion years, the sun will be about 10% brighter than it is today, which will increase the average surface temperatrue in the US for 52F to 520F. Steel's melting point is 2750F, so it remains solid. What is change in lenght of the track?

c)How much space would you need to place betweeen each of the 40-foot rail sections so that the rail stays on the ground?

Explanation / Answer

That is, a 1 m length will increase by 12E-6 m if it heats up one degree.

change in temperature = 520-52= 468 F=242.22C

change in length = coefficient of expansion x degrees of change x length
= 12E-6 x 242.22 x 12.92= 0.038m= 3.8 cm

Linear expansion is given by the formula

Change in length = Original Length * constant * change in temperature.

space would you need to place betweeen each of the 40-foot rail sections so that the rail stays on the ground=3.8 cm

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