Please do on paper and upload 3. A board whose width changes as w(r) = 2(√L-√x) (0 ≤ x ≤ L), as shown is fixed on the left edge. Here L is the length ofthe board. The material has an area mass density (per unit area) of pkg/m²dAw(x) = 2(√L-√x)LF(x,y)a) What is the weight of the board? Derive it by integrating weight of a differential element, dA located at x and that has awidth 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 thedifferential 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) = kr² N/m², isapplied on the board (the gray surface in the figure is the force function). What is the moment applied by this externalload on the fixed edge. Solve this using a similar approach as step (b).

Answered: Image /qna-images/answer/7a9a3fea-b304-4e1d-ad47-3a30bc503d16.jpg

3. A board whose width changes as w(x) = 2(√L-√) (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

3. A board whose width changes as w(x) = 2(√L-√) (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

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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The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.

Question

Please do on paper and upload

3. A board whose width changes as w(r) = 2(√L-√x) (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 x 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 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) = kr² 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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