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
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A force acting on a particle moving in the xy-plane is given by F = (2x3y4i+x2y3j)
A force acting on a particle moving in the x-y plane is given by F=2yi+x^2j N. The particle...
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?
A force acting on a particle in the xy plane at coordinates (x, y) is given...
A force acting on a particle in the xy plane at coordinates (x, y) is given by vector F = (F_0/r) (y hat i - x hat j), where F_0 is a positive constant and r is the distance of the particle from the origin. Show that the magnitude of this force is F_0. Show that the direction of vector F is perpendicular to vector r = x hat i + y hat j.
(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...
A force in the xy plane is given by = where F is a constant and...
A force in the xy plane is given by = where F is a constant and r=. a.) Find the magnitude of the force. b.)Show that is perpendicular to =x c.) Find the work done by this force on a particle that moves once around a circle of radius 5 m centered at the origin. A force in the xy plane is given by hat{i}+yhat{j} c.) Find the work done by this force on a particle that moves once around...
A force } = (5xy3 î + 5x2y2ſ), where F is in newtons and x and...
A force } = (5xy3 î + 5x2y2ſ), 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=5.00 m. Find the force W = $. F(r). dr done on the object.
A particle in the xy plane travels along a spiral path C beginning at a point...
A particle in the xy plane travels along a spiral path C
beginning at a point P that is 8 units from the origin and ending
at a point Q that is 2 units from origin.
The particle makes 2.5 revolutions aroung the origin along the
way.
What is work done by the gravitational field
F(x, y) =
i +
j in moving the particle along its path?
(x2 + y2) 3/2)
Consider a particle conned to the xy-plane under the inuence of the force given by: Fx...
Consider a particle conned to the xy-plane under the inuence of the force given by: Fx = -ky Fy = kx where k is a constant and x & y are the coordinates of the particle. Assume the particle is initially at the origin. We wish to move the particle in a closed counter-clockwise loop, consisting of four straight segments: Segment A - { [0,0] to [a,0] } B - { [a,0] to [a,b] } C = { [a,b] to...
In each of the following exercises, you are given a force field F = F(x, y),...
In each of the following exercises, you are given a force field F = F(x, y), in Newtons, and a oriented, closed curve C in the xy-plane, where x and y are in meters. Use Green's Theorem to calculate the work done by F along C. 9. F(x, y) = (2,5 – yº, x3 – y5), and C is the curve which starts at (0,0), moves along a line segment to (1/V2,1/V2), moves counterclockwise along the circle of radius 1,...
The force on a particle is directed along an x axis and given by F =...
The force on a particle is directed along an x axis and given by F = F0(x/x0 - 1) where x is in meters and F is in Newtons. If F0 = 1.6 N and x0 = 2.0 m, find the work done by the force in moving the particle from x = 0 to x = 2x0 m.
The position ModifyingAbove r With right-arrow of a particle moving in an xy plane is given...
The position ModifyingAbove r With right-arrow of a particle
moving in an xy plane is given by ModifyingAbove r With right-arrow
equals left-parenthesis 4 t cubed minus 3 t right-parenthesis
ModifyingAbove i With caret plus left-parenthesis 6 minus 2 t
Superscript 4 Baseline right-parenthesis ModifyingAbove j With
caret with ModifyingAbove r With right-arrow in meters and t in
seconds.
In unit-vector notation, calculate
(a)ModifyingAbove r With right-arrow,
(b)v Overscript right-arrow EndScripts, and
(c)a Overscript right-arrow EndScripts for t = 2...
A force acting on a particle in the xy plane at coordinates (x, y) is given by vector F = (F_0/r) (y hat i - x hat j), where F_0 is a positive constant and r is the distance of the particle from the origin. Show that the magnitude of this force is F_0. Show that the direction of vector F is perpendicular to vector r = x hat i + y hat j.
(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...
A force } = (5xy3 î + 5x2y2ſ), 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=5.00 m. Find the force W = $. F(r). dr done on the object.
A particle in the xy plane travels along a spiral path C
beginning at a point P that is 8 units from the origin and ending
at a point Q that is 2 units from origin.
The particle makes 2.5 revolutions aroung the origin along the
way.
What is work done by the gravitational field
F(x, y) =
i +
j in moving the particle along its path?
(x2 + y2) 3/2)
In each of the following exercises, you are given a force field F = F(x, y), in Newtons, and a oriented, closed curve C in the xy-plane, where x and y are in meters. Use Green's Theorem to calculate the work done by F along C. 9. F(x, y) = (2,5 – yº, x3 – y5), and C is the curve which starts at (0,0), moves along a line segment to (1/V2,1/V2), moves counterclockwise along the circle of radius 1,...
The position ModifyingAbove r With right-arrow of a particle
moving in an xy plane is given by ModifyingAbove r With right-arrow
equals left-parenthesis 4 t cubed minus 3 t right-parenthesis
ModifyingAbove i With caret plus left-parenthesis 6 minus 2 t
Superscript 4 Baseline right-parenthesis ModifyingAbove j With
caret with ModifyingAbove r With right-arrow in meters and t in
seconds.
In unit-vector notation, calculate
(a)ModifyingAbove r With right-arrow,
(b)v Overscript right-arrow EndScripts, and
(c)a Overscript right-arrow EndScripts for t = 2...
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