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 $\cdot$ (5/9) = 83.3 °CDL = (12
$\cdot$ 10-6 m/°C)(400,000 m)(83.3 °C) = 400 mThis 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 $\cdot$ 10-6 °C-1)(83.3°C) = 1.00$\cdot$ 10-3stress = F/A = strain
$\cdot$ elastic modulusF = strain
$\cdot$ Y$\cdot$ A = (1.00$\cdot$ 10-3)$\cdot$ (20$\cdot$ 1010)$\cdot$ (25$\cdot$ 10-4) = 500,000 N, independent of length!
© MultiMedia Physics, 1999