Why Does Concrete Contract Differently in Cold Temperatures?

[titusdna]

Got this question wrong on this weeks physics quiz and can't figure out why. I keep getting the same answer - which was wrong - over and over. What am I missing?

By how much will a slab of concrete 18 m long contract when the temperature drops from 24 °C to -16 °C? (The coefficient of linear thermal expansion for concrete is 10-5 per degree C.)
Answers are in centimeters.
Formula:
change in length= a* Lo* change in temp
Lo = 1800cm
A = 10-5
change in T = 24- (-16) = 40
I keep coming up with .7 cm
the answer was .5cm
Where did I go wrong? Any help greatly appreciated
Thank you

 

[inha]

I can't find an error in your calculations. Maybe the result was rounded in the answers or there's a typo somewhere?

 

[thepatientmental]

for reaching out for help with this question. It seems like you have the correct formula and values, so let's go through the steps to see where the error may have occurred.

First, let's check the units. The coefficient of linear thermal expansion is given in 10^-5 per degree C, so we need to make sure that our temperature change is also in degrees Celsius. In this case, 24 °C to -16 °C would be a change of -40 °C, not 40 °C.

Next, let's double check the calculation. Using the formula, we get:
change in length = (10^-5) * 1800cm * (-40 °C) = -0.72 cm
So it looks like the answer should be -0.72 cm, which is close to the answer you were getting. However, the question asks for the change in length in centimeters, so we need to take the absolute value of this answer. This gives us a final answer of 0.72 cm, which is closer to the given answer of 0.5 cm.

It's possible that there was a rounding error at some point in the calculations, or an incorrect unit conversion. Make sure to always double check your units and calculations to avoid any errors. I hope this helps and good luck on your future quizzes!