Alfonso, Noel – Homework 1 – Due: Sep 13 2007, 9:00 am – Inst: Dale Gary
1
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The due time is Central
time.
001
(part 1 of 2) 15 points
Consider three force vectors
~
F
1
,
~
F
2
, and
~
F
3
.
The vector
~
F
1
has magnitude
F
1
= 52 N and
direction
θ
1
= 160
◦
; the vector
~
F
2
has mag
nitude
F
2
= 35 N and direction
θ
2
=

140
◦
;
and the vector
~
F
3
has magnitude
F
3
= 30 N
and direction
θ
3
= 120
◦
. All the direction an
gles
θ
are measured from the positive
x
axis:
counterclockwise for
θ >
0 and clockwise for
θ <
0.
What is the magnitude
F
of the net force
vector
~
F
=
~
F
1
+
~
F
2
+
~
F
3
?
Correct answer: 93
.
1364 N.
Explanation:
In components, each force vector is
F
1
,x
=
F
1
×
cos
θ
1
=

48
.
864 N
,
F
1
,y
=
F
1
×
sin
θ
1
= 17
.
785 N
,
F
2
,x
=
F
2
×
cos
θ
2
=

26
.
8116 N
,
F
2
,y
=
F
2
×
sin
θ
2
=

22
.
4976 N
,
F
3
,x
=
F
3
×
cos
θ
3
=

15 N
,
F
3
,y
=
F
3
×
sin
θ
3
= 25
.
9808 N
,
and therefore the net force is
F
x
=
F
1
,x
+
F
2
,x
+
F
3
,x
=

90
.
6756 N
,
F
y
=
F
1
,y
+
F
2
,y
+
F
3
,y
= 21
.
2682 N
.
Consequently, the magnitude