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Problem 1 1. Determine the work done by force F along the path C, that is,...
с 1. Determine the work done by force F along the path C, that is, compute...
с 1. Determine the work done by force F along the path C, that is, compute the line integral F.dr 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 = ff.dr =[F(F(t)). 7"(t)dt с с Use F = (-y)ỉ +(x)ì in Newtons. and use a = 4 and b = 5 meters in the figure. Parameterization of a straight line: Remember that for any...
2. Determine the work done by force F along the path C, that is, compute the...
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...
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...
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...
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...
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...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk...
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...
4. Parameterization a) Find the parameterization of the trajectory from A to B. b) Determine 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
Show all required work, Inc AFind the work of force F=-0.470.LX 0.5px Newtons acting on a...
Show all required work, Inc AFind the work of force F=-0.470.LX 0.5px Newtons acting on a particle along the trajectory from A to B. Use b-4 meters and a 3 meters. B) Is the work of F path independent? N 12 0," ROL { (it) & (6) dt r(t) = At the } = [-C Ay Oil 0.5px] ro /4 C OX al x 13,0,) 72 S mix asys Fotosye 7016 Oils -64-0 5 FOC Osy - ANA Wor=??
(2) If the point of application of a force F: R3 R moves along a curve C, then the work done by 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...
Find the work done by a force F-1-1+ 7k that moves an object from the point...
Find the work done by a force F-1-1+ 7k that moves an object from the point (0, 10, 6) to the point (6, 14, 24) along a straight line. The distance is measured in meters and the force in newtons.
с 1. Determine the work done by force F along the path C, that is, compute the line integral F.dr 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 = ff.dr =[F(F(t)). 7"(t)dt с с Use F = (-y)ỉ +(x)ì in Newtons. and use a = 4 and b = 5 meters in the figure. Parameterization of a straight line: Remember that for any...
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...
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...
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...
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
Show all required work, Inc AFind the work of force F=-0.470.LX 0.5px Newtons acting on a particle along the trajectory from A to B. Use b-4 meters and a 3 meters. B) Is the work of F path independent? N 12 0," ROL { (it) & (6) dt r(t) = At the } = [-C Ay Oil 0.5px] ro /4 C OX al x 13,0,) 72 S mix asys Fotosye 7016 Oils -64-0 5 FOC Osy - ANA Wor=??
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...
Find the work done by a force F-1-1+ 7k that moves an object from the point (0, 10, 6) to the point (6, 14, 24) along a straight line. The distance is measured in meters and the force in newtons.
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