Inside the wall of a house, an L-shaped section of hot-water pipe consists of th

Question

Inside the wall of a house, an L-shaped section of hot-water pipe consists of three parts: a straight, horizontal piece 28.0 cm long, an elbow, and a straight vertical piece = 150 cm long. 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

Inside the wall of a house, an L-shaped section of hot-water pipe consists of three parts: a straight, horizontal piece 28.0 cm long, an elbow, and a straight vertical piece l = 150 cm long. 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 degree C to 44.0 degree C. (The coefficient of linear expansion of copper is 1.7 10-5( degree C-1).)

Explanation / Answer

change in vertical length of l = 150 * 1.7 * 10^(-5 ) * ( 44-18 ) = 0.0663 cm = 0.663 mm

change in horizontal length = 28 * 1.7 * 10^(-5 ) * ( 44-18 ) = 0.012376 cm = 0.12376 mm


so... total displacement ... a) magnitude = sqrt ( 0.12376^2 + 0.663^2 ) = 0.674452 mm


b) direction = tan inverse ( change in vertical / change in horizontal ) = tan inverse ( 0.663/ 0.12376)

= 79.426477 degree below +ve x-axis

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