с 1. Determine the work done by force F along the path C, that is, compute...
Problem 1 1. Determine the work done by force F along the path C, that is, compute the line integral Si di from point A to point B. You need to find the parameterization of the curve C and use it to find the line integral: Work = [ Fudi =[F(F(t)."(t)dt Use F = (- y) { +(x)ì in Newtons. and use a = 4 and b = 5 meters in the figure. Parameterization of a straight line: Remember that...
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)...
Problem 2 2. Determine the work done by force along the path C, that is, compute the line integral SF.df from point A to point B. You need to find the parameterization of the curve C and use it to find the line integral: Work = [F.dř =[F(F(t)). F"(t)dt с Use F = (-yx) { +(x²) j in Newtons. and use a = 3 meters in the figure. Parameterization of a circle: Remember that for a circle: F(t)=[rcos(t) rsin(t) 0);...
Problem 6 Using Stokes' Theorem, we equate F dr curl F dA. Find curl F- PreviousS us Problem ListNext Noting that the surface is given by (1 point) Calculate the circulation, Fdr7in z - 16-x2 - y2, find two ways, directly and using Stokes' Theorem. dA The vector field F = 6y1-6y and C is the boundary of S, the part of the surface dy dx With R giving the region in the xy-plane enclosed by the surface, this gives...
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...
(2 pts) Calculate the circulation, rF dr, in two ways, directly and using Stokes' Theorem. The vector field F (8x-8y+62)(i + j) and C is the triangle with vertices (0,0,0), (8, 0, 0), (8,2,0), traversed in that order. Calculating directly, we break C into three paths. For each, give a parameterization r (t) that traverses the path from start to end for 0sts 1 On Ci from (0,0, 0) to (8,0,0), r(t) = <8t,0,0> On C2 from (8, 0, 0)...
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...
4. Parameterization a) Find the parameterization of the trajectory from A to B. b) Determine the length of the trajectory using L= =jVP.F dt and compare to the distance between the points around the section of the circle. у B С r Radius =r=3m ༽ 0 A x Use t as the angle: F(t)=( sts F'(t)=[ __ L = dt
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...