the figure shows a vector
force field F(x,y) mapped in the x-y plane. (It depicts a vector
quantity whose magnitude and direction varies only with x and y,
Not z). Several points (A, B, and C) are indicated, and a (dashed)
path from A to B is shown.
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the figure shows a vector
force field F(x,y) mapped in the x-y plane. (It depicts a...
Find a formula F⃗ =〈 F1(x,y), F2(x,y) 〉 for the vector field in the plane that has the properti...
Find a formula F⃗ =〈 F1(x,y), F2(x,y) 〉 for the vector field in the plane that has the properties that F⃗ (0,0)=〈0,0〉 and that at any other point (a,b)≠(0,0) the vector field F⃗ is tangent to the circle x^2+y^2=a^2+b^2 and points in the counterclockwise direction with magnitude ∥F⃗ (a,b)∥=2sqrt(a^2+b^2)
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a...
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a gradient field, which means F is a conservative field and the work of F is path independent? Show all your work. a) Find f(x,y,z) whose gradient is equal to F. Is the line integral ſi. · di path independent? b) Find the line integral, or work of the force F along any trajectory from point Q:(-10, 2,5) to point P: (7,-3, 12).
Assignment # 2 (40 Points] (Page 1/2) A force of magnitude F is on the r-y...
Assignment # 2 (40 Points] (Page 1/2) A force of magnitude F is on the r-y plane (see Figure 2) and is known. Assuming that the angle a is a known quantity, calculate the coordinate direction angles and express the force as cartesian vector F Figure 2. Force vector of assignment # 2. You need to find the coordinate direction angles and express the force as cartesian vector.
Sketch the vector field at the given points marked in the xy-plane. (a) =< 0, y > (b) F =
please answer asap
Sketch the vector field at the given points marked in the xy-plane. (a) =< 0, y > (b) F =<-x,y >
Sketch the vector field at the given points marked in the xy-plane. (a) = (b) F =
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); +...
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); + (x+y); + (4y2Z) K and the curve C defined by the intersection Counter clockwise as viewed from above. Evaluate the Work- SF. dr done by F along in the following ways (a) Directly, using parametrization of C (b) Using stakes theorem
212 (a) Visualize the vector field on R2\{(0,0)}. More precisely, draw F in the x-y plane...
212 (a) Visualize the vector field on R2\{(0,0)}. More precisely, draw F in the x-y plane by clearly indicating the vector Fr,y) for at least ten points (x,y) in each quadrant. Your drawing should be at scale, following the specifications in the preamble, using clear coordinates and making use of a clearly indicated unit. (b) Find the equations of the flow lines of F, carefully documenting your work out. (c) In a separate diagram, but still following the specifications above,...
(1 point) Compute the flux of the vector field F(x, y, z) = 3 + 2+...
(1 point) Compute the flux of the vector field F(x, y, z) = 3 + 2+ 2k through the rectangular region with corners at (1,1,0), (0,1,0), (0,0,2), and (1,0, 2) oriented in the positive Z-direction, as shown in the figure. 2.0 1.5 Flux = 0.0 12.0 11.5 2 1.0 0.5 0.0 2.94. god. og 9.500.00 [Enable Java to make this image interactive] (Drag to rotate) (1 point) Compute the flux of the vector field F(t, y, z) = 31 +23...
The magnitude of the force vector F is 75.6 newtons. The x component of this vector...
The magnitude of the force vector F is 75.6 newtons. The x component of this vector is directed along the +x axis and has a magnitude of 67.2 newtons. The y component points along the +y axis. Find the direction of F relative to the +x axis in degrees.Find the component of F (in Newtons), in the previous question, that points along the +y axis.
This next figure shows a conducting loop as we pull it with a constant force from...
This next figure shows a conducting loop as we pull it with a constant force from a region of uniform magnetic field. Example 30.2.1 Figure 1 Assume that the field cuts off sharply along the vertical dashed line (this is, of course, very unrealistic but useful if we are going to avoid spending a long time working this problem). The speed of the loop is a constant v = 2.00 mm/s. The loop height is L = 3.00 cm, and...
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1)...
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1) to B(0,3) depicted in Figure 1 Figure 1. Rectangular path of the particle. Compute the work done by the force in this field; Using line integral (if the integral is difficult to evaluate, then use Matlab) b. Also using Green's Theorem without computer aid. Compare your results. a.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the...
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a gradient field, which means F is a conservative field and the work of F is path independent? Show all your work. a) Find f(x,y,z) whose gradient is equal to F. Is the line integral ſi. · di path independent? b) Find the line integral, or work of the force F along any trajectory from point Q:(-10, 2,5) to point P: (7,-3, 12).
Assignment # 2 (40 Points] (Page 1/2) A force of magnitude F is on the r-y plane (see Figure 2) and is known. Assuming that the angle a is a known quantity, calculate the coordinate direction angles and express the force as cartesian vector F Figure 2. Force vector of assignment # 2. You need to find the coordinate direction angles and express the force as cartesian vector.
please answer asap
Sketch the vector field at the given points marked in the xy-plane. (a) =< 0, y > (b) F =<-x,y >
Sketch the vector field at the given points marked in the xy-plane. (a) = (b) F =
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); + (x+y); + (4y2Z) K and the curve C defined by the intersection Counter clockwise as viewed from above. Evaluate the Work- SF. dr done by F along in the following ways (a) Directly, using parametrization of C (b) Using stakes theorem
212 (a) Visualize the vector field on R2\{(0,0)}. More precisely, draw F in the x-y plane by clearly indicating the vector Fr,y) for at least ten points (x,y) in each quadrant. Your drawing should be at scale, following the specifications in the preamble, using clear coordinates and making use of a clearly indicated unit. (b) Find the equations of the flow lines of F, carefully documenting your work out. (c) In a separate diagram, but still following the specifications above,...
(1 point) Compute the flux of the vector field F(x, y, z) = 3 + 2+ 2k through the rectangular region with corners at (1,1,0), (0,1,0), (0,0,2), and (1,0, 2) oriented in the positive Z-direction, as shown in the figure. 2.0 1.5 Flux = 0.0 12.0 11.5 2 1.0 0.5 0.0 2.94. god. og 9.500.00 [Enable Java to make this image interactive] (Drag to rotate) (1 point) Compute the flux of the vector field F(t, y, z) = 31 +23...
This next figure shows a conducting loop as we pull it with a constant force from a region of uniform magnetic field. Example 30.2.1 Figure 1 Assume that the field cuts off sharply along the vertical dashed line (this is, of course, very unrealistic but useful if we are going to avoid spending a long time working this problem). The speed of the loop is a constant v = 2.00 mm/s. The loop height is L = 3.00 cm, and...
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1) to B(0,3) depicted in Figure 1 Figure 1. Rectangular path of the particle. Compute the work done by the force in this field; Using line integral (if the integral is difficult to evaluate, then use Matlab) b. Also using Green's Theorem without computer aid. Compare your results. a.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the...
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