Q3:A force described by -xx yŷ zz F- x2+y 2+z 2 x 2+y 2 +y²+z 1- Express Fin circular cylindrical coordinates. 2- Calculate the curl of F F is conservative or not. 3- Calculate the divergence of F. 4- Calculate the potential of F.

Q3:A force described by -xx yŷ zz F- x2+y 2+z 2 x 2+y 2 +y²+z 1- Express Fin circular cylindrical coordinates. 2- Calculate the curl of F F is conservative or not. 3- Calculate the divergence of F. 4- Calculate the potential of F.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section3.3: Vectors In The Plane

Problem 11ECP

See similar textbooks

Related questions

Q: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If…

Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (ein z + 2y², 6x + tan¬1…

A: Given force field is F→(x,y,z)=esinx+2y2, 6x+tan-1y, xz Now, we will find the Curl(F→).…

Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

A: Here we will use Stokes theorem to calculate flux of curl (F) on surface S bounded by curve C…

Q: Find the workdone in moving a particle in a force field given by f=3xyi-5zj+10xk along the curve…

Q: The given vector function is F(x, y, z) = (2x – y + In(z² + 1))î + (x – 6e²y + 4 cos 4y)ĵ + | 2xz -…

Q: Use the Green's theorem to find the work done by a force F(x, y) = on a particle that moves…

A: find explanation below

Q: 2. Verify that the vector field F(1, y, 2) = sec? y+ -32 2.r tan y + e csc r, 3e -32 cot x + sec z…

Q: Compute the flux of the vector field F(x, y, z) = (2y, 3, –2xz) through the surface S, which is the…

A: Given vector field is, Fx,y,z=2y,3,-2xz. The given surface is, y=x2+z2 and x2+z2≤1. Now for the…

Q: Q#3. Find the work done by the force field 4 1 F(x, y)=- x² +y x'+y? on a particle that moves along…

A: Given- Fx,y=1x2+y2i+4x2+y2j To Find- The work done by the above force field on a particular that…

Q: Use the Divergence Theorem to calculate the flux of the vector fields F1 = -8zi + 8ak and F2 = -8zi…

A: Given vector fields are F1→=−8zi^+8xk^ and F2→=−8zi^+y+2j^+8xk^ We have to calculate the flux of the…

Q: Let v = (x*z, 2 – 4xyz, xz) be the velocity field of a fluid. Compute the flux of v across the…

A: Given, v→=x2z,2-4xyz,xz225x2+16z2=y-202 Then, calculating div v→ div…

Q: Find the work done by the force field F(r, y) = x²i+ xyj on a particle that moves once around the…

Q: (b) Given the force field F(x, y, z) = (z³ – 2xy)i – x²j + 3xz² k (i) Show that F is a conservative…

Q: Evaluate the scalar line integral of the vector held F(z. y. 2) = zi + yj - zk around the closed…

A: Let F(x,y,z)=-yi+xj+zk around a closed circular path c of radius combined at the point(-2,0,3)…

Q: 4. The vector field F(x, y) = (x² – y²)i+ 10-Rj-2zrk represents the velocity of a gas flowing in…

Q: Q3:A force described by -xx zz yŷ 2 x+y2+: + 2 x²+y 2+y 2 2 2+z 1- Express F in circular cylindrical…

A: The given force is:

Q: 2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the…

A: Given that : U=xz3y-x3y=xz3y-x32y12 The gradient will be calculated as :…

Q: 2. Let C be the curve of intersection between the cylinder r2+y = 1 and r-2y+z = 0, oriented…

A: The complete solutions are given below

Q: Find the flux of the vector field F = (y, - z, x) across the part of the plane z = 4+ 2x + 3y above…

A: The given vector field is, F→=y, -z, x. The given part of the plane is z=4+2x+3y And the rectangle…

Q: 1. Let F [ry, -y, 2] be a force field and C be the curve given by the parametrization r(t) = [t,…

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.

Q: A particle starts at the point (-2, 0), moves along the x-axis to (2, 0), and then along the…

Q: Consider the vector of electric field E(x, y, z) = (sinh x)i – (cosh y)j – xyz k a. Compute the…

A: The given vector field is, E(x,y,z) = (sinh x) i - (cosh y) j - (xyz) k the divergence and curl…

Q: 4. Consider the vector field F = (y?2³ + y)i+ (2æyz³ + x – 2)j+ (3xy²z² – y + 3)E. (a) Verify the…

Q: Find the work done by the force field F(x,y) = (-y,x) in moving an object along the path y = V4 – x2…

A: Given force field Fx,y=−y,x and object moving along the path y=4−x2 from 2,0 to -2,0. We have to…

Q: Compute the divergence of the vector field F(r, y, z) = (5x + 12ry)i+ (y + e" sin z)j + (5z + e" cos…

Q: Compute the flux of the vector field F == through the surface S where S is the surface bounded by r…

A: Given thatF→=fr,fθ,fz=r2+sin2θ,rsincosθ,3z∂∂rrfr=∂∂rr22+sin2θ=2r2+sin2θ& ∂∂θfθ=∂∂θr…

Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj…

Q: Find a potential function for the conservative vector field given by y3/2 2T 2 2x sin z F(r, y, 2) =…

A: We will find out the required potential function.

Q: Find the work done by the force field F(x, y) = x* +y? on a particle that moves along the quarter…

Q: Q4(b) Given the force field F(x, y, z) = (z^3 – 2xy)i – x^2j + 3xz^2 k (i) Show that F is a…

Q: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: Let i = (a° cos z, 5 – 3a'y cos z – 3yz? sin æ, 2° sin æ) be the velocity field of a fluid. Compute…

Q: (b) Solve the electric flux through a paraboloid z = x? +y² – 16 that lies below plane %3D z= 0. It…

Q: ul for the through the box [o,8] x[ 0,41 x[0,2]. vector field f=<z,x, y2, calculate the rotalflux S.…

A: We need to calculate divergence . The formula for divergence for F=<P,Q,R> is ,…

Q: A particle starts at the point (-1, 0), moves along the x-axis to (1, 0), and then along the…

Q: Confirm that the force field F(x, y) = yeyi+ xey j is conservative in some open connected region…

A: We have to find the work.

Q: Use Green's theorem to find the work done by the force field F(x.y) %3D хyi + 1 x²+xy]j on a…

Q: Use Green's Theorem to find the work done by the force field F(x,y)= (x3-x2y)i+xy2j on a…

Q: ind the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: The gradient of a function is the rate of change of a function and for a function, f(x,y,z), the…

Q: The moment of inertia of a surface about the z axis is given by the formula I Sls x² + y² dS. Find…

A: (a) We are asked to find the moment of inertia of the surface z=xy lying inside the cylinder…

Q: Q3. Consider the vector of electric field E(x, y, z) = (sinh x)i – (cosh y)j – xyz k a. Compute the…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given : f(x,y,z)=9x2y+5z2 To Find : Conservative Vector field by finding it's gradient

Q: Without using a potential function, find the total work performed by the force field F(x,y) = (2xsin…

Q: b) Show that the force field F(r, y, z) = 3x zi+ 2y ln z j+ is independent of path and find its…

A: F(x,y,z)=3x2zi +2ylnzj+(y2/z +x3)k r(t) =ti +tj+t2k F(t ) =3t4i +4tlnt j +(1+t3)k dr = dt i +dt j…

Q: Calculate the work done by the force field F(x,y, z) = [x² + 10z² i+(y² + 14x² ]j+ z² + 12y² ]k +…

Q: Show that the vector field F(x, y, 2) = (2x cos y – 3)i – (x² sin y + 2²)j – (2yz – 2)kis a…

Q: 5. Compute the flux of F(r, y.2) =zi- 2yj+ 2ak across the surface of the cylinder bounded by a+y =9…

A: Solve the problem as shown below.

Q: Without using a potential function, find the total work performed by the force field F(x, y) =…

A: Work done by vector field while moving a particle along a curve = Line integral of that vector field…

Q: Exercise (3): Find the work done under the influence of the force F = 3xyi – 5zj + 10xk along the…

A: The work done by a force on displacing a object by a certain distance is given by dot product of…

Q: Find the work done by the force field F(z,y,2) = Ir+v,rs, y+:) on a particle that moves along the…

Question

Q3:A force described by
F=-
-xx
vý
+
2
2
2
+y+z
+z
х
+y
+z
1- Express Fin circular cylindrical coordinates.
2- Calculate the curl of FF is conservative or not.
3- Calculate the divergence of F.
4- Calculate the potential of F.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differentiation$

Learn more about

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

Similar questions

A force field is given by the equation. A particle is moved from (1,0,0) to (1,1,1) along a straight line. Calculate the work done by the force field on the particle.
Find the upward flux of F = (14e*, -7e, -6) through the first-octant part of the triangle x+2y+3z = 6. Answer: E
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
Find the work done by a force F = 6ỉ + 57– 3k when a particle moves from point | P(-3, 4, 5) to point Q(2, -3, -1) in space.
Find the work done by the force F= (1,3) in moving an object from A(4, 5) to B(-2, 8).
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y + 9, z?) and the net is decribed by the equation y = V1 - x² – z7, y > 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) v · dS = 10n Incorrect
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by = (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) V. dS =
Find the components of the vertical force F = (0, -6) in the directions parallel to and normal to the plane that makes an angle of the total force is the sum of the two component forces. What is the component of the force parallel to the plane? و اس with the positive x-axis. Show that
4) The force F = 2i-j-5k acts as the point (-5,2,1). Find the torque due to F about the origin and about the line 2x = -4y = -Z. rootor of oving particle be:
Find a unit vector n that is normal to the surface 4z² - x4 - 2y4 = 46 at P = (2, 1, 4) that points in the direction of the xy-plane (in other words, if you travel in the direction of n, you will eventually cross the xy-plane). (Use symbolic notation and fractions where needed.) n =
Show that the force F= (-6x +*yz IS Conservative, hence Find the Potential function to
Q7) The work done by the force F = 2j to move a particle from the origin to the point (3,3,3) is: