6 2
Ans:
SOLUTION
Scalar Notation. Summing the force components along x and y axes algebraically by
referring to Fig. a,
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
6 3
2–42.
SOLUTION
Express ,,and as Cartesian vectors.F3
F2
F1
y
x
30
45
F1 850 N
F3 750 N
5
4
3
Ans:
6 4
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
Ans:
6 5
SOLUTION
Scalar Notation. Summing the force components along x and y axes algebraically by
referring to Fig. a,
*2–44.
Determine the magnitude of the resultant force and its
direction, measured clockwise from the positive xaxis.
x
y
12
3
5
5
13
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
1
Ans:
6 7
2–46.
SOLUTION
Scalar Notation:
Suming the force components algebraically, we have
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
Ans:
6 8
2–47.
SOLUTION
Scalar Notation: Suming the force components algebraically, we have
The magnitude of the resultant force FR is
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
Ans:
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
Ans:
7 0
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
Ans:
7 1
2–50.
Express ,,and as Cartesian vectors.F
3
F
2
F
1
SOLUTION
y
x
F2 26 kN
5
12
13
F1 15 kN
40
Ans:
2–51.
SOLUTION
Also,
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
Ans:
7 3
SOLUTION
Scalar Notation. Referring to Fig. a, the x and y components of each forces are
Thus,
*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
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
Ans:
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
Also, from the figure require
Ans:
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
Rectangular Components: By referring to Fig. a, the xand ycomponents of F1,F2,
F3, and FRcan be written as
Resultant Force:Summing the force components algebraically along the xand yaxes,
5
12 13
y
x
u
F
2
200 N
F
1
f
30
Ans:
7 8
2–57.
SOLUTION
Rectangular Components: By referring to Fig. a, the xand ycomponents of F1,F2,
and F3can be written as
Resultant Force:Summing the force components algebraically along the xand yaxes,
The magnitude of the resultant force FRis
Thus,
The first derivative of Eq. (2) is
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°
5
12 13
y
x
u
F
2
200 N
F
1
f
30
Ans:
7 9
Ans:
SOLUTION
Scalar Notation. Equating the force components along the x and y axes algebraically
by referring to Fig. a,
Divide Eq (1) by (2)
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
Ans:
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
Scalar Notation. Summing the force components along x and y axes algebraically
by referring to Fig. a,
And its directional angle
u
measured counterclockwise from the positive
x axis is
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
Fy
z
Fz
b 45
Ans: