A 2.00-kg particle moves from the origin to position, having coordinates x = 4.00 m and y = 4.00 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W = FAr cos 0 = F. Ar), calculate the work done by the gravitational force in going from O to the following paths. y (m) (x, y) Z x (m) (a) the purple path (OⓇC) (b) the red path (OⓇC) (c) the blue path (oⒸ) (d) Your results should all be identical. Why? along

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Chapter1: Units, Trigonometry. And Vectors
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A 2.00-kg particle moves from the origin to position, having coordinates x = 4.00 m and y = 4.00 m as shown
in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the
equation (W
FAr cos 0 = F. Ar), calculate the work done by the gravitational force in going from O to
paths.
the following
y (m)
=
(x, y)
A
(a) the purple path (OAC)
(b) the red path (OⓇC)
(c) the blue path (OⒸ)
x (m)
(d) Your results should all be identical. Why?
along
Transcribed Image Text:A 2.00-kg particle moves from the origin to position, having coordinates x = 4.00 m and y = 4.00 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W FAr cos 0 = F. Ar), calculate the work done by the gravitational force in going from O to paths. the following y (m) = (x, y) A (a) the purple path (OAC) (b) the red path (OⓇC) (c) the blue path (OⒸ) x (m) (d) Your results should all be identical. Why? along
The gravitational force is downward with magnitude
F = mg
g
=
2
=
N.
(a) The work on the path OC is the sum of the work on paths OA and
Wo
Wo + W
19.6
=
Wo = F₁ do COS
g
By the definition of work as force times displacement, we have the following, where do and d
lengths of segments OA and OC, respectively.
kg (9.80 m/s²)
=
19.6
= -77.4
o) + F₂d
J.
AC
Substituting the values we know for the gravitational force, the angles, and the lengths of the paths, we have
(
N) (4
m)(0) + (
N) (4
cos(
as follows.
19.6
are the
Transcribed Image Text:The gravitational force is downward with magnitude F = mg g = 2 = N. (a) The work on the path OC is the sum of the work on paths OA and Wo Wo + W 19.6 = Wo = F₁ do COS g By the definition of work as force times displacement, we have the following, where do and d lengths of segments OA and OC, respectively. kg (9.80 m/s²) = 19.6 = -77.4 o) + F₂d J. AC Substituting the values we know for the gravitational force, the angles, and the lengths of the paths, we have ( N) (4 m)(0) + ( N) (4 cos( as follows. 19.6 are the
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