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4 2
SOLUTION
x
y
90º
150º
F1 400 N
F2 200 N
F3 300 N
2–21.
Determine the magnitude and direction of the resultant
force, FR measured counterclockwise from the positive x
axis. Solve the problem by first finding the resultant
F′
= F1
+ F2 and then forming FR =
F′
+ F3.
4 3
SOLUTION
2–22.
Determine the magnitude and direction of the resultant force,
measured counterclockwise from the positive x axis. Solve l by
first finding the resultant
F′
= F2 + F3 and then forming
FR =
F′
+ F1.
x
y
90º
150º
F1 400 N
F2 200 N
F3 300 N
2–23.
Two forces act on the screw eye. If and
, determine the angle
between them, so that the resultant force has a magnitude
of .FR=800 N
u(0° …u…180°)F2=600 N
F1=400 N
SOLUTION
F1
u
4 5
*2–24.
SOLUTION
Two forces F
1
and F
2
act on the screw eye. If their lines of
action are at an angle apart and the magnitude of each
force is determine the magnitude of the
resultant force FRand the angle between FRand F1.
F
1=F
2=F,
u
F
1
u
4 6
SOLUTION
2–25.
If F1 = 30 lb and F2 = 40 lb, determine the angles
u
and f so
that the resultant force is directed along the positive x axis
and has a magnitude of FR = 60 lb.
y
x
θ
φ
F1
F2
4 7
2–26.
SOLUTION
Determine the magnitude and direction u of FA so that the
resultant force is directed along the positive x axis and has a
magnitude of 1250 N.
30°
y
x
O
B
A
B
F
= 800 N
FA
θ
4 8
2–27.
SOLUTION
Determine the magnitude and direction, measured
counterclockwise from the positive x axis, of the resultant
force acting on the ring at O, if FA=750 N and u=45°.
30°
y
x
O
B
A
B
F
= 800 N
FA
θ
4 9
SOLUTION
*2–28.
Determine the magnitude of force F so that the resultant FR
of the three forces is as small as possible. What is the
minimum magnitude of FR?.
6 kN
8 kN
F
30
5 0
2–29.
If the resultant force of the two tugboats is , directed
along the positive axis, determine the required magnitude
of force and its direction .uFB
x
3 kN
SOLUTION
x
yA
FB
FA 2 kN
30
C
u
5 1
2–30.
If and , determine the magnitude of the
resultant force of the two tugboats and its direction
measured clockwise from the positive axis.x
u=45°FB=3 kN
SOLUTION
x
yA
FB
FA 2 kN
30
C
u
5 2
2–31.
If the resultant force of the two tugboats is required to be
directed towards the positive axis, and is to be a
minimum, determine the magnitude of and and the
angle .u
FB
FR
FB
x
SOLUTION
x
yA
FB
FA 2 kN
30
C
u
Ans:
5 3
SOLUTION
*2–32.
Determine the magnitude of the resultant force and its
direction, measured counterclockwise from the positive
xaxis.
y
x
30
F1 200 N
F2 150 N
45
5 4
2–33.
Determine the magnitude of the resultant force and its
direction, measured clockwise from the positive x axis.
800 N
400 N
x
y
B
45
30
2–34.
Resolve and into their and components.yxF2
F1
SOLUTION
F1 400 N
x
y
60
30
45
2–35.
Determine the magnitude of the resultant force and its
direction measured counterclockwise from the positive xaxis.
SOLUTION
F1 400 N
y
60
30
5 7
5 8
2–37.
Determine the magnitude of the resultant force acting on
the plate and its direction, measured counterclockwise from
the positive xaxis.
SOLUTION
F2 750 N
F3 650 N
3
4
5
y
5 9
SOLUTION
2–38.
Express each of the three forces acting on the support in
Cartesian vector form and determine the magnitude of the
resultant force and its direction, measured clockwise from
positive x axis.
y
x
F2 80 N
F1 50 N
15
3
4
5
4
F3 30 N
2–39.
SOLUTION
Determine the xand ycomponents of and F
2
.F
1
y
30
F
1
200 N
45
6 1
*2–40.
Determine the magnitudeofthe resultant force andits
direction, measured counterclockwise from the positive
xaxis.
SOLUTION
y
30
F
1
200 N
45
