3. Calculate the work done by a particle moving from 0 to B, following the path...
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C. F(x, y) = (3x2+y)i + 3xy2jC: boundary of the region lying between the graphs of y = √x. y = 0, and x = 1
(b) Find the work done in moving a particle along the path x-cos y, z 0 from y-0 to y 2m, in the field F(x, y, z)-c" cosy i-xe® sínyi + 2xe2: cos y k. (10 Marks) EvaluatelFdA for surface S: x-z2,0 F(x, y, z)--Зугі + zer cosyj + 3xz2k. (c) y 2,-1 251and (7 Marks) (b) Find the work done in moving a particle along the path x-cos y, z 0 from y-0 to y 2m, in the field...
Calculate the work done by the force F= (x-2y)i+(x+y)j in a) 2. moving from point A at (0,2) to point B at (2,18) along the path y 4x2+2. [5 marks] - Evaluate the line integral(xdy+ydx) along a path C that is b) [5 marks] to t described by x= cos(f), y=2sin(t)+5, from t =: 2 Calculate the work done by the force F= (x-2y)i+(x+y)j in a) 2. moving from point A at (0,2) to point B at (2,18) along the...
The force acting at a point (x, y) in a coordinate plane is F(x, y)- r-xit yj. Calculate the work done by E along the upper half of the circle x2 ya from (a, 0) to (-a, 0). where Irl The force acting at a point (x, y) in a coordinate plane is F(x, y)- r-xit yj. Calculate the work done by E along the upper half of the circle x2 ya from (a, 0) to (-a, 0). where Irl
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path F(x,y) = (ex – 4y)i + (ey + 7x)j C: r = 2 cos(0) -11 POINTS LARCALC11 15.4.028.MI. MY NOTES ASK YOUR TEACHER Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path F(x, y) = (5x2 + y)i + 3xy?j C: boundary of...
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...
Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi + 4yj C: x = t, y = 13 from (0, 0) to (2,8)
Please solve these three questions! (1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
A force acting on a particle moving in the xy-plane is given by F = (2x3y4i+x2y3j), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x=5.00 m and y = 5.00 m as shown in the figure. Calculate the work W = F(r) dr done by F on the particle as it moves along a) The purple path b) The red path
4. Use Green's Theorem to calculate the work done by force F on a particle that is moving counterclockwise around the closed path C. Determine whether the vector field is conservative. C boundary of the triangle with vertices (0,0), (V5,0), (0,15). F(x,y) = (x3 - 3y)i + (6x +5/7);.