Thermal Expansion Concrete Problem

[Mr. Goosemahn]

Homework Statement

A highway is made of concrete slabs that are 15 m long at 20.0 degrees Celsius.

(a) If the temperature range at the location of the highway is from -20.0degrees Celsius to +40.0degrees Celsius, what size expansion gap should be left (at 20.0degrees Celsius) to prevent buckling of the highway?

1. 3.8 mm
2. 1.6 mm
3. 3.6 mm
4. 4.2 mm
5. 2.6 mm

(b) How large are the gaps at -20.0 degrees Celsius?

1. 9.5 mm
2. 11.7 mm
3. 11.0 mm
4. 12.7 mm
5. 10.8 mm

Homework Equations

L=L₀*a*T

The Attempt at a Solution

I plugged in the values I have and I got:

L=15*(12*10^-6)*40 and got .0072 meters, or 7.2 millimeters, but that isn't one of the options.

I can't do 'B' until I have A.

Am I plugging in the values incorrectly?

Help?

 

[Mr. Goosemahn]

Anybody?

 

[Mr. Goosemahn]

I tried the problem again and still get 7.2 millimeters. Does anybody know what exactly I'm doing wrong?

 

[Mr. Goosemahn]

Do I have to divide the 7.2 by 2? That's the only possible relation that I see between what I'm getting and the possible answers, being 3.6.

 

[ideasrule]

Why did you use 40 for the temperature difference? The hottest it gets is 40 degrees, so the maximum possible temperature difference is 20 degrees.

 

[Mr. Goosemahn]

Why did you use 40 for the temperature difference? The hottest it gets is 40 degrees, so the maximum possible temperature difference is 20 degrees.

But wouldn't it be 40 since the difference between -20 and 20 is 40?

 

[ideasrule]

But the concrete contracts when temperature is lowered, so you wouldn't need to leave a gap. You'd need to leave a gap when it expands.

 

[Mr. Goosemahn]

But the concrete contracts when temperature is lowered, so you wouldn't need to leave a gap. You'd need to leave a gap when it expands.

Ooohhhh, that makes sense. Yeah, 3.6 worked. Thanks for the help, I really appreciate it.