   # A steel beam being used in the construction of a skyscraper has a length of 35.000 m when delivered on a cold day at a temperature of 15.000°F. What is the length of the beam when it is being installed later on a warm day when the temperature is 90.000°F? ### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399

#### Solutions

Chapter
Section ### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399
Chapter 19, Problem 19.46AP
Textbook Problem
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## A steel beam being used in the construction of a skyscraper has a length of 35.000 m when delivered on a cold day at a temperature of 15.000°F. What is the length of the beam when it is being installed later on a warm day when the temperature is 90.000°F?

To determine
The length of the beam when it is being installed later on a warm day.

### Explanation of Solution

Given information: The initial length of beamis 35.000m , the initial temperature is 15.000°F and the final temperatureis 90.000°F .

The formula to convert temperature from Fahrenheit to Celsius is,

T=59(TF32)°C

• TF is the temperature in Fahrenheit.

Convert initial temperature from Fahrenheit to Celsius.

Ti=59(TFi32)°C

Here,

TFi is the initial temperature in Fahrenheit.

Substitute 15.000°F for Ti in above equation.

Ti=59(15.000°F32)°C=9.44°C

Convert final temperature from Fahrenheit to Celsius.

TF=59(TFF32)°C

Here,

TFF is the final temperature in Fahrenheit.

Substitute 90.000°F for TF in above equation.

Tf=59(90.000°F32)°C=32.22°C

The coefficient of the linear expansion of the steel is 11×106°C1 .

The formula for the coefficient of the linear expansion is,

α=ΔLLi(TfTi)ΔL=αLi(TfTi)

Here,

ΔL is the change in the length

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