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2 Jan Show that the force field given by: F=x?yzi - xyz?k ,is non...
92. Suppose F(x, y, z) (xyz,x2,zy3) describes the velocity field of a flowing fluid a) Show...
92. Suppose F(x, y, z) (xyz,x2,zy3) describes the velocity field of a flowing fluid a) Show that F is not a conservative vector field b) Find a vector which points in the direction of the axis of rotation of the fluid at the point (2,-3,1), if the fluid rotates at the point. Explain c) Determine whether the point (2, -3 1,) is a sink or a source (ie., whether fluid is flowing into the point or out of the point,...
Let F(XYZ) = <2y27, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative,...
Let F(XYZ) = <2y27, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = vfand f(1,2,1) = 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0,0,0) to (3.9, 1.8, 2.3). y2 + x4z2 + 2x4(x3 + y2 + 24)1/2 = K Kis a constant .- Answer:
9. The work done by the force F(x, y) (2at +e) i (4y in moving a...
9. The work done by the force F(x, y) (2at +e) i (4y in moving a particle -re from (0,0) to (1,1) along the curve y =x4 needs to be calculated. a. Show that F is a conservative vector field. b. Describe three different ways to calculate the work. Answer: 3 +1/e c. Calculate the work by a method of your choice.. a. Show that F=(y+yz) i + (x + 32 + xz) j +(9yz2 + y 1) k is...
Find the potential when F =-Vº, a conservative force of field defined by F = (3x’yz...
Find the potential when F =-Vº, a conservative force of field defined by F = (3x’yz – 3yli + (xºz – 3x)j + (x*y+2z)k
(a). Consider the field F(xyz-1 (x + y2) і-1 (x2 + y) j + 1 (x...
(a). Consider the field F(xyz-1 (x + y2) і-1 (x2 + y) j + 1 (x + Y) k. Integrate F around the rectangle defined by the points (21,0), (3.5.1.0). (3.5.3.90), and (2.3.9,0). (b). Consider the field given in Part (a). Integrate F over the surfaces of a rectangular prism defined by the points given in Part (a) and extruded in the positive k direction by a distance 0.6 Give answers to three decimal places. Answer for Part (a): Answer...
A force acting on a particle moving in the x-y plane is given by F=2yi+x^2j N. The particle...
A force acting on a particle moving in the x-y plane is given by F=2yi+x^2j N, where x and y are in meters. The particle moves from the origin to a final position having the coordinates x=5 m and y=5 m and shown in the figure above. Calculate the work done by F along (a) OAC, (b) OBC, and (c) OC. (d) Is F a conservative or non-conservative force? Explain?
Show that the gravitational field F(x)--mMG is conservative with the potential function f(x) mMG(...
Show that the gravitational field F(x)--mMG is conservative with the potential function f(x) mMG(--) and then (on another page) evaluate Jcxds for Ci: y=x2 ,-1〈x 1 xl
Show that the gravitational field F(x)--mMG is conservative with the potential function f(x) mMG(--) and then (on another page) evaluate Jcxds for Ci: y=x2 ,-1〈x 1 xl
Let a, b and c be constants and let the force field be given by F(x,y,z)...
Let a, b and c be constants and let the force field be given by F(x,y,z) = ax i+by j+cz k. If the work done by the force field F on a particle as it moves along a curve given by r(t) = costi +te'sint j+tk 312 .Osts it, is equal to . Find the value of the constant c. 4 Answer:
+ cos(y) is conservative by responding to the 2. Show that the vector field F(x,y) =...
+ cos(y) is conservative by responding to the 2. Show that the vector field F(x,y) = (ye* + sin(y))i + ( following steps: a.) Determine both P(x,y) and Q(x,y) given F. b.) Demonstrate your answers in a.) satisfy Clairaut's theorem. c.) Partially integrate P with respect to r to obtain the potential S(= y) = P(x,y)da = (1.x) + C) where (a,b) is the anti-derivative of P(x,y) with respect to r and C(y) is a function of y such that...
If F is a position dependent force given by F(x) = Ae-kx, where k is a...
If F is a position dependent force given by F(x) = Ae-kx, where k is a positive constant, sketch the graphs showing F(t), v(t) and x(t) for v0 = 0 and x0 = 0. Show all salient points on your graphs and the behavior as x approaches infinity.
92. Suppose F(x, y, z) (xyz,x2,zy3) describes the velocity field of a flowing fluid a) Show that F is not a conservative vector field b) Find a vector which points in the direction of the axis of rotation of the fluid at the point (2,-3,1), if the fluid rotates at the point. Explain c) Determine whether the point (2, -3 1,) is a sink or a source (ie., whether fluid is flowing into the point or out of the point,...
Let F(XYZ) = <2y27, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = vfand f(1,2,1) = 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0,0,0) to (3.9, 1.8, 2.3). y2 + x4z2 + 2x4(x3 + y2 + 24)1/2 = K Kis a constant .- Answer:
9. The work done by the force F(x, y) (2at +e) i (4y in moving a particle -re from (0,0) to (1,1) along the curve y =x4 needs to be calculated. a. Show that F is a conservative vector field. b. Describe three different ways to calculate the work. Answer: 3 +1/e c. Calculate the work by a method of your choice.. a. Show that F=(y+yz) i + (x + 32 + xz) j +(9yz2 + y 1) k is...
Find the potential when F =-Vº, a conservative force of field defined by F = (3x’yz – 3yli + (xºz – 3x)j + (x*y+2z)k
(a). Consider the field F(xyz-1 (x + y2) і-1 (x2 + y) j + 1 (x + Y) k. Integrate F around the rectangle defined by the points (21,0), (3.5.1.0). (3.5.3.90), and (2.3.9,0). (b). Consider the field given in Part (a). Integrate F over the surfaces of a rectangular prism defined by the points given in Part (a) and extruded in the positive k direction by a distance 0.6 Give answers to three decimal places. Answer for Part (a): Answer...
Show that the gravitational field F(x)--mMG is conservative with the potential function f(x) mMG(--) and then (on another page) evaluate Jcxds for Ci: y=x2 ,-1〈x 1 xl
Show that the gravitational field F(x)--mMG is conservative with the potential function f(x) mMG(--) and then (on another page) evaluate Jcxds for Ci: y=x2 ,-1〈x 1 xl
Let a, b and c be constants and let the force field be given by F(x,y,z) = ax i+by j+cz k. If the work done by the force field F on a particle as it moves along a curve given by r(t) = costi +te'sint j+tk 312 .Osts it, is equal to . Find the value of the constant c. 4 Answer:
+ cos(y) is conservative by responding to the 2. Show that the vector field F(x,y) = (ye* + sin(y))i + ( following steps: a.) Determine both P(x,y) and Q(x,y) given F. b.) Demonstrate your answers in a.) satisfy Clairaut's theorem. c.) Partially integrate P with respect to r to obtain the potential S(= y) = P(x,y)da = (1.x) + C) where (a,b) is the anti-derivative of P(x,y) with respect to r and C(y) is a function of y such that...
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