How to Calculate Spacing for Bridge Expansion with Linear Expansion Coefficient

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Homework Help Overview

The discussion revolves around calculating the necessary spacing for bridge expansion due to temperature changes, specifically focusing on the linear expansion of concrete. The problem involves a concrete bridge segment of 76 m and a linear expansion coefficient of 1.2 × 10−5(°C)−1, with a temperature increase of 69°F.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the appropriate formula for linear expansion, with one suggesting the formula ΔL = L0αΔT. There is uncertainty regarding the conversion of temperature from Fahrenheit to Celsius, and participants express confusion about the units required for the final answer.

Discussion Status

Some participants have attempted calculations using the suggested formula, but there is a recognition of potential errors in unit conversion and interpretation of the problem's requirements. The discussion is ongoing, with participants seeking clarification on their calculations and the correct approach.

Contextual Notes

Participants note that they have not covered this topic in lecture, leading to uncertainty about the correct methodology. There is also a specific requirement to provide the answer in centimeters, which has caused confusion in the calculations.

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Homework Statement



A bridge is made with segments of concrete 76 m long (at the original temperature). If the linear expansion coefficient is 1.2 × 10−5(◦C)−1, how much spacing is needed to allow for expansion for an increase in temperature of 69◦F? Answer in units of cm.

Homework Equations



I don't know, we never did this in lecture, so I lost as to what to do.

The Attempt at a Solution



What formula am I supposed to use?
 
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DrMcDreamy said:

Homework Statement



A bridge is made with segments of concrete 76 m long (at the original temperature). If the linear expansion coefficient is 1.2 × 10−5(◦C)−1, how much spacing is needed to allow for expansion for an increase in temperature of 69◦F? Answer in units of cm.

Homework Equations



I don't know, we never did this in lecture, so I lost as to what to do.

The Attempt at a Solution



What formula am I supposed to use?
For a formula check
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html
 
Thank you!

So it would be:

\DeltaL=Lo\alpha\DeltaT

\DeltaL= (76 m)(1.2 x 10-5)(◦C)-1(20.5◦C+17.7◦C)

\DeltaL=0.0348 m
 
^It came out to be wrong, so what did I do wrong?
 
DrMcDreamy said:
Answer in units of cm.
ΔL=0.0348 m
That's what's wrong.
 
Oh $h*t! 3.48 cm crap I didnt even realize it had asked in cm!
 

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