A steel beam is used in the construction of a skyscraper. By what fraction (change in L)/(Lo) does the length of the beam increase when the temperature changes from that on a cold winter day (-15 F) to that on a summer day (+105 F)?
Can anyone please give me some hints to do it?THANKS A LOT!
http://en.wikipedia.org/wiki/Coefficient_of_thermal_expansion
but i got .00144 for the answer...
the correct answer should be 8.0*10^-4
how come?
To find the fraction by which the length of the steel beam increases, we can use the coefficient of linear expansion. The formula for linear expansion is:
ΔL = α * Lo * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
Lo is the initial length of the beam
ΔT is the change in temperature
The coefficient of linear expansion (α) for steel is typically around 0.000012 per degree Celsius.
To calculate the fraction change in length (ΔL/Lo), we need to determine ΔL and Lo.
Given:
ΔT = 105°F - (-15°F) = 120°F
α = 0.000012 per degree Celsius
Hint 1:
First, convert the temperature change from Fahrenheit to Celsius, as the coefficient of linear expansion is typically given in terms of degrees Celsius.
Hint 2:
Next, calculate the change in length (ΔL) by substituting the values of α, Lo, and ΔT into the formula.
Hint 3:
Finally, calculate the fraction change in length (ΔL/Lo) by dividing ΔL by Lo.
Let me know if you need any further assistance!
T= ((105-32)*5/9)-((-15-32)*5/9)
= 40.55-(-26.11)
= 66.66
L/Lo = (12*10^-6)(66.66)
= 8.00*10^-4
= .0008