Chapter 10, Problem 51AP

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# Inside the wall of a house, an L-shaped section of hot-water pipe consists of three parts: a straight horizontal piece h = 28.0 cm long, an elbow, and a straight, vertical piece ℓ = 134 cm long (Fig. P10.51). A stud and a second- story floorboard hold the ends of this section of copper pipe stationary. Find the magnitude and direction of the displacement of the pipe elbow when the water flow is turned on, raising the temperature of the pipe from 18.0°C to 46.5°C.Figure P10.51

To determine
The magnitude and direction of displacement of the pipe.

Explanation

Section 1:

To determine: The magnitude of displacement of the pipe.

Answer: The magnitude of displacement of the pipe is 0.66 mm.

Explanation:

Given info: Length of the straight horizontal piece is h=28.0â€‰cm . Length of the vertical piece is l=134â€‰cm. The temperature is raised from T1=18Î¿C to T2=46.5Î¿C . The co-efficient of linear expansion ( Î± ) of copper is 17Ã—10âˆ’6/Î¿C .

Formula to calculate the expansion along the horizontal direction is,

Î”Lh=Î±h(T2âˆ’T1) (I)

Formula to calculate the expansion along the vertical direction is,

Î”Lv=Î±l(T2âˆ’T1) (II)

Formula to calculate the total expansion is,

Î”L=(Î”Lh)2+(Î”Lv)2 (III)

Substitute Equations (I) and (II) in (III).

Î”L=[Î±h(T2âˆ’T1)]2+[Î±l(T2âˆ’T1)]2=Î±(T2âˆ’T1)h2+l2

Substitute 17Ã—10âˆ’6/Î¿C for Î± , 18Î¿C for T1 , 46.5Î¿C for T2 , 28.0 cm for h and 134 cm for l in the above equation to get Î”L .

Î”L=(17Ã—10âˆ’6/Î¿C)[(46.5Î¿C)âˆ’(18Î¿C)](28.0â€‰cm)2+(134â€‰cm)2=(17Ã—10âˆ’6/Î¿C)(28

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started