4. A planar gate of width Wa = 10 ft and length L = 20 ft is held at an angle by a rope. The rope is attached to an object having a weight W through a pulley placed so that the rope makes an angle 90° with the gate. We seek to find the weight W necessary to hold the gate static at an angle with respect to the horizontal surface. The density of water is p= 1 g/cm³ and the gravitational acceleration is g = 9.8 m/s². air Z water air 0₁ z (a) Find the horizontal and vertical components of the net hydrostatic force exerted on the gate? (b) Find zep and Zep, the coordinates of the center of pressure. (c) Find the tension force required to balance the moment of the hydrostatic forces about the point O₂. (d) What is the weight required to maintain the gate at a static equilibrium at 9 = 30°?
4. A planar gate of width Wa = 10 ft and length L = 20 ft is held at an angle by a rope. The rope is attached to an object having a weight W through a pulley placed so that the rope makes an angle 90° with the gate. We seek to find the weight W necessary to hold the gate static at an angle with respect to the horizontal surface. The density of water is p= 1 g/cm³ and the gravitational acceleration is g = 9.8 m/s². air Z water air 0₁ z (a) Find the horizontal and vertical components of the net hydrostatic force exerted on the gate? (b) Find zep and Zep, the coordinates of the center of pressure. (c) Find the tension force required to balance the moment of the hydrostatic forces about the point O₂. (d) What is the weight required to maintain the gate at a static equilibrium at 9 = 30°?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Transcribed Image Text:4. A planar gate of width Wa = 10 ft and length L = 20 ft is held at an angle by a rope. The rope is attached
to an object having a weight W through a pulley placed so that the rope makes an angle 90° with the gate.
We seek to find the weight W necessary to hold the gate static at an angle with respect to the horizontal
surface. The density of water is p = 1 g/cm³ and the gravitational acceleration is g = 9.8 m/s².
air
Z
water
air
0₁
z
(a) Find the horizontal and vertical components of the net hydrostatic force exerted on the gate?
(b) Find zep and Zep, the coordinates of the center of pressure.
(c) Find the tension force required to balance the moment of the hydrostatic forces about the point 02.
(d) What is the weight required to maintain the gate at a static equilibrium at 0 = 30°?
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Step 1: Given data
VIEWStep 2: Draw FBD of given system and find depth of water from free surface
VIEWStep 3: Calculation of net hydrostatic force acting on the gate
VIEWStep 4: Calculation of centre of pressure and tension in the rope
VIEWStep 5: Calculation of tension in the rope, horizontal and vertical components of hydrostatic force
VIEWStep 6: Calculation of co-ordinates of certre of pressure and weight required to maintain equilibrium
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