Determine the location of the horizontal axis ya at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure). The model for ya is attached. Ya = ỹ –hAwhere y is the y-coordinate of the centroid of the gate, Iz is themoment of inertia of the gate about the line y = y, h is the depthof the centroid below the surface, and A is the area of the gate.y = Lhy= yYa=5 -hA yy=Ldab

The y-coordinate of the centroid of the gate is The area of the gate is A = bL And the depth of the…

Ya = ỹ – hA where y is the y-coordinate of the centroid of the gate, Iz is the moment of inertia of the gate about the line y = y, h is the depth of the centroid below the surface, and A is the area of the gate. y = L h y= y Ya=5 - hA y y=L d a b

Ya = ỹ – hA where y is the y-coordinate of the centroid of the gate, Iz is the moment of inertia of the gate about the line y = y, h is the depth of the centroid below the surface, and A is the area of the gate. y = L h y= y Ya=5 - hA y y=L d a b

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 53E

See similar textbooks

Related questions

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

Q: A Click Submit to complete this assessment. Question 15 Using the Divergence Theorem, find the…

Q: ii) A property o(x, y) = ky acts on a region D = {(x, y) = R² | x² + y² ≤ a², y ≥ 0}. Compute the…

Q: Use cylindrical coordinates. Evaluate II Vx2 + y2 dv, where E is the region that lies inside the…

A: Volume using triple integral

Q: Determine the x- and y-coordinates of the centroid of the shaded area. у 0.64 al Answer: (X, ỹ) = (…

A: Answer:----. Date:----20/10/2021

Q: [6 marks] Let Tbe the solid region in the first octant bounded by the circular cylinder Sq:z = V4 –…

A: First, let us find the divergence of the given vector field.…

Q: 2. A thin, flat metal plate is has an area bounded by yx and y- 4x025(units are in meters). The…

A: To determine the required physical parameters using integration

Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = (-5x+ 2y) i + (8x -…

Q: xyj around the square 6. Use Green's Theorem to calculate the circulation of F 0 < x < 1, 0 < y< 1,…

Q: -plane. Use cylindrical coordinates to evaluate the triple integral ///√x² + y²dV, where E is the…

Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

Q: y- 1 Find the centroid and moment of interia woth respext to the axes and the centriod

A: From the diagram R={x,yx2≤y2-1,0≤x≤1} Area of R = ∫01∫x21dydx = ∫011-x2dx = x-x3301 = 23 So, A = 23…

Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

A: Consider the given: The centroid of the region bounded by the function fxand gxis…

Q: Determine the location of the horizontal axis ya at which a vertical gate in a dam is to be hinged…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the centroid of the solid of revolution bounded by the curves x2y = 4, x 1, :4 and y = 0,…

Q: (a) Find the center of mass of a semicircular plate of radius r. (b) Find the centroid of the region…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTIONS AS PER…

Q: a) Find the linearization of the function at the given point. f (x, y) = 1+ e²2=-v, at (1,2). B)…

A: The given problem is to find the linearization of the given function at given point and also to find…

Q: A homogenous solid body is generated by revolving the shaded area, as shown below, through 360°…

A: Given equation is x29+y2a2=1 and its given at a=1+2=3 so, it becomes x29+y232=1x29+y29=1x2+y2=9

Q: f(x, y, z) dV over the solid B. Evaluate the triple integral {(x, y, z) | x2 + y? + z? < 16, y z 0,…

Q: 39.The region enclosed by the curve y= x+- and the lines y= % x, x= 1 and x = 2 is rotated %3D %3!…

A: Note: Since you have posted multiple questions we will solve the first question for you. To get the…

Q: Use a parameterization to find the flux SSF. S plane x+y+z=5a that lies above the square 0≤x≤a,…

A: We have to find the flux

Q: Use the method of cylindrical shell to determ ine the volume of the solid obtained by rotating the…

A: To determine: The volume of the solid obtained by rotating the region bounded by the curves y=4x and…

Q: Let R be the region bounded by y = 4 – x², the x axis and the y axis. 4- 3 2 1 = The solid obtained…

Q: Determine the x- and y-coordinates of the centroid of the shaded area. 11 ייד £ Answers: 10% (X,Y)=…

Q: Find the centroid of the first quadrant area bounded by x = y and x2 − y = 0.

A: In this question we have to find the centroid of the bounded region Note:- As per bartleby…

Q: A solid is formed by revolving about the y-axis, the area bounded by the curve x^3 = y, the y-axis…

A: Given : curve y = x3 & line y =8 To find : Centriod of a solid which is formed by revolving…

Q: Use a parameterization to find the flux The flux is SSF n da of F = 2²1+xj-32k in the outward…

Q: The a and y components of a fluid moving in two dimensions are given by the following functions:…

Q: y y=x³ a Determine the x and y coordinates of the centroids between the curve and the horizonntal…

Q: IV. The area bounded by y = 3, x = 2, y = -3 and x = 0 is revolved about the y-axis. 10. The…

Q: Find the centroid of the solid of revolution bounded by the curves x2y = 4, x = 1, x = 4 and y= 0,…

A: Find your answer below

Q: ASK YOUR TEACHER DETAILS Let F(x, y, z) = z tan-(y2)i + z3 In(x2 + 6)j + zk. Find the flux of F…

Q: Locate the centroid y of the homogeneous solid formed by revolving the shaded area about the y axis.…

A: The solution is given below:

Q: 4. Find the moment of inertia about the origin of a flat, thin metal plate occupying the region D =…

Q: Find the volume V and centroid of the solid E that lies above the cone z = x2 + y2 and below…

A: To determine: the volume V and centroid of the solid E that lies above the cone z = x 2 + y 2 and…

Q: Consider the surface S consisting of the portion the graph of the function z = x2 + y² above the…

A: (A) Given the surface S is z=x2+y2, 64≤x2+y2≤81. In cylindrical coordinates x=rcosθ,y=rsinθ, z=z,…

Q: Let F(x, y, z) = z tan-1(y²)i + z³ In(x² + 1)j + zk. Find the flux of F across S, the part of the…

Q: A) Find the linearization of the function at the given point. f (x, y) = e" cos y, (0. 5). B) Find…

A: Since you have posted the different questions. I am answering the first one. Please post the…

Q: 5) FIND THE CENTROID OF THE SOLID REGION BOUNDED BY THE GRAPHS OF THE FOLLOWING EQUATIONS: y= WHEN…

A: Please see the below picture for detailed solution.

Q: Use cylindrical coordinates. Evaluate II| Vx² + y2 dv, where E is the region that lies inside the…

A: We have to evaluate ∭Ex2+y2dV, where E is the region that lies inside the cylinder x2+y2=1 and…

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: We have to find the hydrostatic force on one end of the trough.

Q: Integrate the given function over the given surface. V15 G(x,y,z) = x over the parabolic cylinder y…

A: Given: The given function is Gx,y,z=x, The equation of the parabolic cylinder y=x2,0≤x≤152 and 0≤z≤2

Q: Find the centroid of the solid formed by revolving about oy the area bounded by y²=2x and the line…

Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

A: We have to find the volume of the solid of revolution generated when the area described is rotated…

Q: Setup a cylindrical or triple integral using. Coordinates Spherical triple integral SSS (x² + y z )…

A: Given ∫∫∫Sx2+yzdV Where S is the solid lying below the cone z=x2+y2 above the plane z=2 and inside…

Q: Let R be the region bounded by y = 4 – x², the x axis and the y axis. 3 2 1 = The solid obtained by…

Q: Find the coordinates of the centroid of the area enclosed by y = 0, x = 0, x = 4, and y = ex.

Q: Using cylindrical coordinates evaluate ʃ ʃ ʃE sqrt ((x2 + y2)) dV where E is the solid bounded by…

A: Consider the triple integral.

Q: Q3-A: Determine the x- and y- coordinates of the centroid of the shaded area. 240 mm 60 mm 120 mm…

Question

Determine the location of the horizontal axis y_a at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure). The model for y_a is attached.

Ya = ỹ –
hA
where y is the y-coordinate of the centroid of the gate, Iz is the
moment of inertia of the gate about the line y = y, h is the depth
of the centroid below the surface, and A is the area of the gate.
y = L
h
y= y
Ya=5 -
hA

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Transformation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

The area bounded by y = 3, x = 2, y = -3 and x = 0 is revolved about the y-axis. a.The x-coordinate of its centroid is… b. The y-coordinate of the centroid of the solid is… c. The moment of inertia of the solid is…
How do I find the centroid of x + y = 1, coordinate axes? Mx = integral(b,a)1/2(y2) dx My = integral(b,a) (xy) dx A = integral(b,a) y dx x = My / A y = Mx / A
y = ex, y = 0, x = 0, x = 3 Find the exact coordinates of the centroid. (x, y) =
The volume of a nose cone is generated by rotating the function y = x – 0.2x2 about the x-axis. What is the volume, in m3, of the cone. The volume of a nose cone is generated by rotating the function y = x – 0.2x2 about the x-axis. What is the volume, in m3, of the cone? What is the x coordinate of the centroid of the volume?
The region in the first quadrant which is bounded by the curves y2 = 4x, x = 4, and y = 0, is revolved about the x-axis. Locate the centroid of the resulting solid of revolution measured from the y-axis. a. 8/3 b. 5/3 c. 11/3 d. 7/3
An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it on display. The artwork has constant density and must be balanced at its centroid. The shape of the artwork was created on a computer program then casted and fabricated. The following equation was put into the computer to generate the shape: y=1sin(πx)+5 bounded by x = 0, x = 2, and y = 0 Draw the Lamina in an x-y plane and put a dot where the centroid should be. Show all work and formulas you are using. The centroid is at (¯x,¯y), where ¯x= ¯y=
3. Find the coordinates of the centroid of the triangle enclosed by x = 1, y = 0,and y = 4x.
a.) Find the centroid of the first quadrant area bounded by x = y and x2 − y = 0. b.) Find the centroid of the area bounded by y2 − x = 0 and x2 + 8y = 0.
Find the centroid of the region R enclosed between the curves y = √ x, y = 1, y = 2, and the y-axis (Figure 6.7.12).
Center of mass of a curved wire A wire of densityd(x, y, z) = 15√y + 2 lies along the curve r(t) = (t2 - 1)j +2t k, -1 … t … 1. Find its center of mass. Then sketch the curveand center of mass together.
Solve the problem with complete solution and draw the figure. Determine the ordinate of the centroid of the area bounded by the curve x2 = 8y and the line 2x – y = 0.
The figure below is a plot of the equation of the line y = A/x where A = 1.1. Determine the length of the line from x = 1 to x = 5. Determine the position of the x-centroid of the line from x = 1 to x = 5. Determine the position of the y-centroid of the line from x = 1 to x = 5. Determine the surface area of revolution when the curve y = 1.1/x from x = 1 to x = 5 is rotated by the x-axis through 232 degrees. Determine the surface area of revolution when the curve y = 1.1/x from x = 1 to x = 5 is rotated by the y-axis through 232 degrees. Determine the position of the y-centroid of the area between the curve y = 1.1/x and the x-axis from x = 1 to x = 5. Determine the volume of the solid of revolution when the area in Q6 is rotated by the x-axis through 232 degrees.