Question:
Suppose the railroad used a single piece of steel from Lansing to Chicago (400 km.) How much would it expand from the coldest winter day (-40° F) to the warmest summer day (110° F)?
Answer:
Because it is the change in temperature that counts, we only need to convertDT = 150·(5/9) = 83.3 °C DL = (12·10-6 m/°C)(400,000 m)(83.3 °C) = 400 m
This is why using a single piece of steel for this project would be a very bad idea. Instead the railroad tracks consist of many individual pieces with expansion joints between them.
Question:
How much force does it take to keep a 5 m piece of track 25 cm2 in cross section from expanding? Here is a case in which we are given the strain and asked to find the stress.
Answer:
strain = DL/L = aDT = (12·10-6 /°C)(83.3°C) = 1.00·10-3 stress = F/A = strain · elastic modulus
F = strain · Y · A = (1.00·10-3)· (20·1010)·(25x10-4) = 500,000 N, independent of length!
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