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 = 159 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°C to 40.2°C. (The coefficient of linear expansion of copper is

The magnitude and direction are

7.638×10-4m

80.01°

Explanation:

We know that the coefficient of linear expansion for copper = 16.6×10^-6 m/m-C

ΔT = 40.2 - 18.0 = 28.5 C°

The expansion of horizontal pipe length can be calculated as

= (0.28)(16.6×10^-6)(28.5) = 13247×10^-8

= 0.0001325 m

The expansion of vertical pipe length = (1.28)(16.6×10^-6)(28.5) = 60557×10^-8 = 0.000752229 m

horizontal displacement = 0.1325 mm

= 1.356×10^-4m

vertical displacement = 0.75223mm

=7.5223×10-4m

size of total displacement can be calculated as

√(x²+y²)

Where x and y are vertical and horizontal displacement respectively

= √(0.1325)²+(0.75223)² =

= 0.7638 mm

= 7.638×10-4m

Angle below horizontal = arctan Θ

= 0.75223/0.1325

=5.6772

= arctan (5.6772)

= 80.01°

Therefore, the the magnitude and direction of the displacement of the pipe elbow when the water flow is turned at (7.638×10-4m) 0.7638 mm and 80.01°

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