roofner (bar784) – Homework 4 – Weathers – (17104)
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001
(part 1 of 2) 10.0 points
Consider four vectors
vector
F
1
,
vector
F
2
,
vector
F
3
, and
vector
F
4
,
where
their
magnitudes
are
F
1
=
41
N,
F
2
= 34 N,
F
3
= 23 N, and
F
4
= 49 N.
Let
θ
1
= 150
◦
,
θ
2
=
−
150
◦
,
θ
3
= 16
◦
, and
θ
4
=
−
66
◦
, measured from the positive
x
axis
with the counterclockwise angular direction
as positive.
What is the magnitude of the resultant vec
tor
vector
F
, where
vector
F
=
vector
F
1
+
vector
F
2
+
vector
F
3
+
vector
F
4
?
Correct answer: 41
.
7695 N.
Explanation:
Basic Concepts:
Vector components fig
ure1
Solution:
The
x
components of the forces
vector
F
1
,
vector
F
2
, and
vector
F
3
are
F
1
x
=
F
1
cos(150
◦
) =
−
35
.
5071 N
F
2
x
=
F
2
cos(
−
150
◦
) =
−
29
.
4449 N
F
3
x
=
F
3
cos(16
◦
) = 22
.
109 N
F
4
x
=
F
4
cos(
−
66
◦
) = 19
.
9301 N
.
and the
y
components are
F
1
y
=
F
1
sin(150
◦
) = 20
.
5 N
F
2
y
=
F
2
sin(
−
150
◦
) =
−
17 N
F
3
y
=
F
3
sin(16
◦
) = 6
.
33966 N
F
4
y
=
F
4
sin(
−
66
◦
) =
−
44
.
7637 N
.
The
x
and
y
components of the resultant vec
tor
vector
F
are
F
x
=
F
1
x
+
F
2
x
+
F
3
x
+
F
4
x
= (
−
35
.
5071 N) + (
−
29
.
4449 N)
+ (22
.
109 N) + (19
.
9301 N)
=
−
22
.
9129 N
F
y
=
F
1
y
+
F
2
y
+
F
3
y
+
F
4
y
= (20
.
5 N) + (
−
17 N)
+ (6
.
33966 N) + (
−
44
.
7637 N)
=
−
34
.
9241 N
Hence the magnitude of the resultant vector
bardbl
vector
F
bardbl
is
bardbl
vector
F
bardbl
=
radicalBig
F
2
x
+
F
2
y
=
radicalBig
(
−
22
.
9129 N)
2
+ (
−
34
.
9241 N)
2
= 41
.
7695 N
002
(part 2 of 2) 10.0 points
What is the direction of this resultant vector
vector
F
?
Note:
Give the angle in degrees, use coun
terclockwise as the positive angular direction,
between the limits of
−
180
◦
and +180
◦
from
the positive
x
axis.
Correct answer:
−
123
.
268
◦
.
Explanation:
(
−
7
.
2, 4
.
2)
(
−
6,
−
3
.
5)
(4
.
5, 1
.
3)
(4
.
1,
−
9
.
1)
−
123
◦
The angle is given by
θ
= arctan
parenleftbigg
F
y
F
x
parenrightbigg
= tan
−
1
parenleftbigg
−
34
.
9241 N
−
22
.
9129 N
parenrightbigg
=
−
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 Fall '08
 Weathers
 mechanics, Acceleration, Work, Velocity, Correct Answer, F3

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