A steel rod 30.0 m long, installed when the temperature was 10°C, is in a bridge that heats up to 40oC on a hot summer day. Steel's coefficient of linear expansion is 1.2 × 10-5 K-1. The bridge is built so the rod has an expansion space of 5 cm. Is this enough space? What is the increase in the length of the rod, in mm?
Expansion in length due to temperature is given by,
dL = L0*alpha*dT
here, L0 = initial length = 30.0 m
alpha = coefficient of linear expansion for steel = 1.2*10^-5 /K
dT = change in temperature = 40 degC - 10.0 degC = 30 degC
So, dL = 30.0*(1.2*10^-5)*30
dL = increase in length of the rod = 0.0108 m = 10.8*10^-3 m
dL = 10.8 mm
During the building of bridge expansion space left is 5 cm, which is greater than increase in length of the steel rod (1.08 cm). So
YES, this is enough space
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