(a)As shown in Figure 2.1, an architect with an artistic flair designs a gateABC to trap liquid of density pin a canal. The gate is hinged at A and is ofunit width into the plane of the page. Section AB of the gate correspondsto a circular quadrant of radius R centred at O. Section BC of the gate isvertical with a height of 2R. The height of the liquid in the canal is R.Neglect the weight of the gate and friction in the hinge. Some geometricproperties of a rectangle and a circular quadrant are provided in Figure2.2, where the symbols have their usual meanings.(i) Determine the magnitude and direction of the horizontal componentof the hydrostatic pressure force exerted on the gate by the liquid inthe canal.(ii)(iii)Determine the magnitude and direction of the vertical component ofthe hydrostatic pressure force exerted on the gate by the liquid inthe canal.Determine the minimum force F applied at B to prevent the gatefrom opening (i.e. turning anticlockwise about the hinge A).2RBAir(a) RectangleсGateRa A = ba4:381xx.c=Figure 2.1AirLiquid p-Hinge1 ba³12 yy,c= -ab³Figure 2.2TR²4xxc=y.c=0.05488 R¹A =(b) Quadrant

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(a) As shown in Figure 2.1, an architect with an artistic flair designs a gate ABC to trap liquid of density pin a canal. The gate is hinged at A and is of unit width into the plane of the page. Section AB of the gate corresponds to a circular quadrant of radius R centred at O. Section BC of the gate is vertical with a height of 2R. The height of the liquid in the canal is R. Neglect the weight of the gate and friction in the hinge. Some geometric properties of a rectangle and a circular quadrant are provided in Figure 2.2, where the symbols have their usual meanings. (i) (ii) Determine the magnitude and direction of the horizontal component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. Determine the magnitude and direction of the vertical component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. (iii) Determine the minimum force F applied at B to prevent the gate from opening (i.e. turning anticlockwise about the hinge A). 2R Air (a) Rectangle с Gate B OX R A = ba 14:48 Figure 2.1 Air Liquid p -Hinge !xx,c= -ba³ ¹yy.c= -ab³ Figure 2.2 xc=y.c=0.05488 R4 (b) Quadrant

(a) As shown in Figure 2.1, an architect with an artistic flair designs a gate ABC to trap liquid of density pin a canal. The gate is hinged at A and is of unit width into the plane of the page. Section AB of the gate corresponds to a circular quadrant of radius R centred at O. Section BC of the gate is vertical with a height of 2R. The height of the liquid in the canal is R. Neglect the weight of the gate and friction in the hinge. Some geometric properties of a rectangle and a circular quadrant are provided in Figure 2.2, where the symbols have their usual meanings. (i) (ii) Determine the magnitude and direction of the horizontal component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. Determine the magnitude and direction of the vertical component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. (iii) Determine the minimum force F applied at B to prevent the gate from opening (i.e. turning anticlockwise about the hinge A). 2R Air (a) Rectangle с Gate B OX R A = ba 14:48 Figure 2.1 Air Liquid p -Hinge !xx,c= -ba³ ¹yy.c= -ab³ Figure 2.2 xc=y.c=0.05488 R4 (b) Quadrant

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

Center of Gravity and Centroid

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

(a)
As shown in Figure 2.1, an architect with an artistic flair designs a gate
ABC to trap liquid of density pin a canal. The gate is hinged at A and is of
unit width into the plane of the page. Section AB of the gate corresponds
to a circular quadrant of radius R centred at O. Section BC of the gate is
vertical with a height of 2R. The height of the liquid in the canal is R.
Neglect the weight of the gate and friction in the hinge. Some geometric
properties of a rectangle and a circular quadrant are provided in Figure
2.2, where the symbols have their usual meanings.
(i) Determine the magnitude and direction of the horizontal component
of the hydrostatic pressure force exerted on the gate by the liquid in
the canal.
(ii)
(iii)
Determine the magnitude and direction of the vertical component of
the hydrostatic pressure force exerted on the gate by the liquid in
the canal.
Determine the minimum force F applied at B to prevent the gate
from opening (i.e. turning anticlockwise about the hinge A).
2R
B
Air
(a) Rectangle
с
Gate
R
a A = ba
4:38
1xx.c=
Figure 2.1
Air
Liquid p
-Hinge
1 ba³
12 yy,c= -ab³
Figure 2.2
TR²
4
xxc=y.c=0.05488 R¹
A =
(b) Quadrant

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