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 a...
1. 5 marks] Find the work done by the force F(x, y) =-ri+yj applied to an object that moves along the quarter circle from (2, 0) to (0, 2) 2. [6 marks Find the volume of the region beneath z (0,0), (1,0), and (1,2) y and the triangle with vertices
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?
3. Calculate the work done by a particle moving from 0 to B, following the path described below. The force acting on the particle is F = x i+yj. y B x 1: parabola, y = x2, II: straight line, y = -3x+27 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 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...
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
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
2. Determine the work done by force F along the path C, that is, compute the line integral SF. dr from point A to point B. You need to find the parameterization of the curve C с and use it to find the line integral: Work = [F-di =[F(F(t).F"(t)dt Use F = (-yx) { +(x²) j in Newtons. and use a = 3 meters in the figure. Parameterization of a circle: Remember that for a circle: r(t) = [rcos(t) rsin(t)...
all questions clearly solved please (2) If the point of application of a force F: R3 R moves along a curve C, then the work done by the force is W F.dr. (a) Find the total work done on an object that traverses the curve c(t) (cos(t), 2 sin(t), (b) Find the total work done on an object that traverses the straight line from (1,0,-2) (c) Explain why the answers in the previous two questions coincide and provide a way...
The plane ABC is hinged along BC. The force F is acting at 90° to the plane. Calculate: NG B(0, 0, Zb) ft F lb →Y C (0, Yc, 0) ft A(Xq, 0, 0) ft R + COLLAPSE IMAGES F = 278 lb Xa = 3 ft Zb= 8 ft Yc = 7 ft The force F in vector form. Oi + @j + OK ENTER 3 tries remaining. 1 point(s) possible The moment around B. Ci + Ok lb.ft...