The force field F (x, y) = (x + 4y)i + (x^2 − 3)j acts on an object traveling from (0, 0) to (0, 1). The object moves along the path x = c(y − y^2 ) with 0 ≤ y ≤ 1. Determine the value of c that minim...
The force field F (x, y) = (x + 4y)i + (x^2 − 3)j acts on an object traveling from (0, 0) to (0, 1). The object moves along the path x = c(y − y^2 ) with 0 ≤ y ≤ 1. Determine the value of c that minimizes the work done on the object by the force field. Please use the line work integral, and optimization
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The force field F (x, y) = (x + 4y)i + (x^2 − 3)j acts on an object traveling from (0, 0) to (0, 1). The object moves along the path x = c(y − y^2 ) with 0 ≤ y ≤ 1. Determine the value of c that minim...
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...
Please help solve the following question with steps. Thank you! 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine t...
Please help solve the following question with steps. Thank
you!
3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
force field: find the work done by F in moving object from (0,1) to (1,2) along the path from x=0 to x=1 We were una...
force field: find the work done by F in moving object from (0,1) to (1,2) along the path from x=0 to x=1 We were unable to transcribe this imagey = 1 + sin(π·r/2)
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 3: A force F = 4x2 - 3x acts on an object as it moves...
Problem 3: A force F = 4x2 - 3x acts on an object as it moves along the x-axis. a) How much work is done by the force as the object moves from x = 2.0 m to x = 7.0 m? b) If the mass of the object is 5.0 kg and it started at rest, what is it's speed at x = 7.0 m? Please show step-by-step.
(a) A force F = (5xî + 4yĵ), where F is in newtons and x and...
(a)
A force
F =
(5xî +
4yĵ),
where
F
is in newtons and x and y are in meters, acts
on an object as the object moves in the x-direction from
the origin to
x = 5.21 m.
Find the work W =
F ·
dr done by the force on the object (in
J).
J
(b)
What If? Find the work W
=
F ·
dr done by the force on the object (in J)
if it moves...
Problem 1 1. Determine the work done by force F along the path C, that is,...
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...
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...
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);...
(1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C...
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]...
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...
Please help solve the following question with steps. Thank
you!
3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
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)...
(a)
A force
F =
(5xî +
4yĵ),
where
F
is in newtons and x and y are in meters, acts
on an object as the object moves in the x-direction from
the origin to
x = 5.21 m.
Find the work W =
F ·
dr done by the force on the object (in
J).
J
(b)
What If? Find the work W
=
F ·
dr done by the force on the object (in J)
if it moves...
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...
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...
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);...
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]...
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