3. A board whose width changes as w(x) = 2(√I-√) (0≤x≤ L), as shown is fixed on the left edge. Here L is the length of the board. The material has an area mass density (per unit area) of pkg/m² dA w(x) = 2(√L-√) L F(x,y) a) What is the weight of the board? Derive it by integrating weight of a differential element, dA located at z and that has a width w(a) as shown. b) What is the moment of the weight of the board about the y-axis. Derive it by integrating the moment applied by the differential element, dA, located at distance z away from the fixed edge. c) An additional distributed load, that is constant along the width but changes with distance as F(x, y) = kæ² N/m², is applied on the board (the gray surface in the figure is the force function). What is the moment applied by this external load on the fixed edge. Solve this using a similar approach as step (b).

3. A board whose width changes as w(x) = 2(√I-√) (0≤x≤ L), as shown is fixed on the left edge. Here L is the length of the board. The material has an area mass density (per unit area) of pkg/m² dA w(x) = 2(√L-√) L F(x,y) a) What is the weight of the board? Derive it by integrating weight of a differential element, dA located at z and that has a width w(a) as shown. b) What is the moment of the weight of the board about the y-axis. Derive it by integrating the moment applied by the differential element, dA, located at distance z away from the fixed edge. c) An additional distributed load, that is constant along the width but changes with distance as F(x, y) = kæ² N/m², is applied on the board (the gray surface in the figure is the force function). What is the moment applied by this external load on the fixed edge. Solve this using a similar approach as step (b).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

3. A board whose width changes as w(x) = 2(√I-√√) (0 ≤ x ≤ L), as shown is fixed on the left edge. Here L is the length of
the board. The material has an area mass density (per unit area) of pkg/m²
dA
w(x) = 2(√L-√x)
L
F(x,y)
a) What is the weight of the board? Derive it by integrating weight of a differential element, dA located at z and that has a
width w(r) as shown.
b) What is the moment of the weight of the board about the y-axis. Derive it by integrating the moment applied by the
differential element, dA, located at distance r away from the fixed edge.
c) An additional distributed load, that is constant along the width but changes with distance as F(x, y) = kx² N/m², is
applied on the board (the gray surface in the figure is the force function). What is the moment applied by this external
load on the fixed edge. Solve this using a similar approach as step (b).

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