6 2
SOLUTION
2–41.
Determine the magnitude of the resultant force and its
direction, measured counterclockwise from the positive
xaxis.
y
x
F2 5 kN
F1 4 kN
F3 8 kN
60
45
2–42.
SOLUTION
Express ,,and as Cartesian vectors.F3
F2
F1
y
x
30
45
F1 850 N
F3 750 N
5
4
3
2–43.
Determine the magnitude of the resultant force and its
direction measured counterclockwise from the positive xaxis.
SOLUTION
y
x
30
45
F1 850 N
F3 750 N
5
4
3
6 5
SOLUTION
*2–44.
Determine the magnitude of the resultant force and its
direction, measured clockwise from the positive xaxis.
x
y
3
5
5
4
30 lb
40 lb
6 6
2–45.
SOLUTION
Determ
i
ne t
h
e magn
i
tu
d
e an
d
di
rect
i
on
u
of t
h
e resu
l
tant
force Express the result in terms of the magnitudes of
the components and and the angle f.F2
F1
FR.
F
6 7
2–46.
SOLUTION
Determine
the magnitude and orientation u of FB so that
the
resultant force is directed along the positive y axis and
has a magnitude of 1500 N.
y
x
30
BA
u
FA 700 N
FB
6 8
2–47.
SOLUTION
Determine the magnitude and orientation, measured
counterclockwise from the positive y axis, of the resultant
force acting on the bracket, if FB=600 N and u=20°.
y
x
30
BA
u
FA 700 N
FB
6 9
*2–48.
SOLUTION
Three forces act on the bracket. Determine the
magnitude and direction of so that the resultant
force is directed along the positive axis and has a
magnitude of 800 N.
x¿
F1
u
F
2
200N
F
3
180N
y
x¿
5
13
60F
1
u
2–49.
If and determine the magnitude and
direction, measured counterclockwise from the positive
axis,of the resultant force acting on the bracket.x¿
u
=10°,F
1
=300 N
SOLUTION
F
2
200N
F
3
180N
y
x¿
5
13
60F
1
u
7 1
2–50.
Express ,,and as Cartesian vectors.F
3
F
2
F
1
y
x
F2 26 kN
5
12
13
F1 15 kN
40
7 2
2–51.
SOLUTION
Determine the magnitude of the resultant force and its
orientation measured counterclockwise from the positive
xaxis.
30
y
x
F2 26 kN
5
12
13
F1 15 kN
40
7 3
SOLUTION
*2–52.
Determine the x and y components of each force acting on
the gusset plate of a bridge truss. Show that the resultant
force is zero.
y
x
3
4
53
4
5
F1 8 kN
F2 6 kN
F3 4 kN
F4 6 kN
7 4
2–53.
Express and as Cartesian vectors.F
2
F
1
SOLUTION
F2=26kN
12
5
13
x
y
7 5
2–54.
SOLUTION
Determine the magnitude of the resultant force and its
direction measured counterclockwise from the positive
xaxis.
F2=26kN
12
5
13
x
y
7 6
2–55.
Determine the magnitude of force so that the resultant
force of the three forces is as small as possible.What is the
magnitude of the resultant force?
F
SOLUTION
F
8 kN
14 kN
45
30
7 7
*2–56.
If the magnitude of the resultant force acting on the bracket
is to be 450 N directed along the positive uaxis, determine
the magnitude of F1and its direction .f
SOLUTION
y
x
u
F
2
200 N
F
1
f
30
7 8
2–57.
SOLUTION
If the resultant force acting on the bracket is required to be
a minimum, determine the magnitudes of F1and the
resultant force. Set .f=30°
y
x
u
F
2
200 N
F
1
f
30
Ans:
FR=380
N
F1=57.8
N
7 9
SOLUTION
2–58.
Three forces act on the bracket. Determine the magnitude
and direction
u
of
F
so that the resultant force is directed
along the positive
x′
axis and has a magnitude of8kN.
6 kN
4 kN
x’
x
y
F
15
30
u
8 0
2–59.
If F = 5 kN and
u
= 30°, determine the magnitude of
the resultant force and its direction, measured counter–
clockwise from the positive x axis.
SOLUTION
6 kN
4 kN
x’
x
y
F
15
30
u
8 1
*2–60.
The force Fhas a magnitude of 80 lb and acts within the
octant shown. Determine the magnitudes of the x,y,
zcomponents of F.
SOLUTION
y
F 80 lb
z
Fz
b 45