PROBLEM 2.19
Two forces P and Q are applied to the lid of a storage bin as shown.
Knowing that P = 48 N and Q = 60 N, determine by trigonometry
the magnitude and direction of the resultant of the two forces.
SOLUTION
Using the force triangle and the laws of cosines and sines:
We have
PROBLEM 2.20
Two forces P and Q are applied to the lid of a storage bin as shown.
Knowing that P = 60 N and Q = 48 N, determine by trigonometry the
magnitude and direction of the resultant of the two forces.
SOLUTION
Using the force triangle and the laws of cosines and sines:
We have
180 (20 10 )
150
γ
= °− °+ °
= °
PROBLEM 2.21
Determine the x and y components of each of the forces shown.
SOLUTION
Compute the following distances:
PROBLEM 2.22
Determine the x and y components of each of the forces shown.
SOLUTION
Compute the following distances:
PROBLEM 2.23
Determine the x and y components of each of the forces shown.
SOLUTION
80-N Force:
(80 N) cos 40
x
F=+°
61.3 N
x
F=
41.0 N
x
F=
PROBLEM 2.24
Determine the x and y components of each of the forces shown.
SOLUTION
40-lb Force:
(40 lb) cos 60
x
F=+°
20.0 lb
x
F=
PROBLEM 2.25
Member BC exerts on member AC a force P directed along line BC. Knowing
that P must have a 325-N horizontal component, determine (a) the magnitude
of the force P, (b) its vertical component.
SOLUTION
22
(650 mm) (720 mm)
970 mm
BC = +
=
PROBLEM 2.26
Member BD exerts on member ABC a force P directed along line BD.
Knowing that P must have a 300-lb horizontal component, determine (a) the
magnitude of the force P, (b) its vertical component.
SOLUTION
PROBLEM 2.27
The hydraulic cylinder BC exerts on member AB a force P
directed along line BC. Knowing that P must have a 600-N
component perpendicular to member AB, determine (a) the
magnitude of the force P, (b) its component along line AB.
SOLUTION
180 45 90 30
180 45 90 30
15
α
α
°= °+ + °+ °
= °− °− °− °
= °
PROBLEM 2.28
Cable AC exerts on beam AB a force P directed along line AC. Knowing
that P must have a 350-lb vertical component, determine (a) the magnitude
of the force P, (b) its horizontal component.
SOLUTION
PROBLEM 2.29
The hydraulic cylinder BD exerts on member ABC a force P directed
along line BD. Knowing that P must have a 750-N component
perpendicular to member ABC, determine (a) the magnitude of the force
P, (b) its component parallel to ABC.
SOLUTION
PROBLEM 2.30
The guy wire BD exerts on the telephone pole AC a force P directed along
BD. Knowing that P must have a 720-N component perpendicular to the pole
AC, determine (a) the magnitude of the force P, (b) its component along line
AC.
SOLUTION
(a)
PROBLEM 2.31
Determine the resultant of the three forces of Problem 2.21.
PROBLEM 2.21 Determine the x and y components of each of the
forces shown.
SOLUTION
Components of the forces were determined in Problem 2.21:
Force x Comp. (lb) y Comp. (lb)
29 lb
+21.0 +20.0
PROBLEM 2.32
Determine the resultant of the three forces of Problem 2.23.
PROBLEM 2.23 Determine the x and y components of each of the
forces shown.
SOLUTION
Components of the forces were determined in Problem 2.23:
Force x Comp. (N) y Comp. (N)
80 N +61.3 +51.4
PROBLEM 2.33
Determine the resultant of the three forces of Problem 2.24.
PROBLEM 2.24 Determine the x and y components of each of
the forces shown.
SOLUTION
Force x Comp. (lb) y Comp. (lb)
40 lb +20.00 –34.64
PROBLEM 2.34
Determine the resultant of the three forces of Problem 2.22.
PROBLEM 2.22 Determine the x and y components of each of the
forces shown.
SOLUTION
Components of the forces were determined in Problem 2.22:
Force x Comp. (N) y Comp. (N)
800 lb +640 +480
PROBLEM 2.35
Knowing that
α
= 35°, determine the resultant of the three
forces shown.
SOLUTION
100-N Force:
(100 N) cos 35 81.915 N
(100 N)sin 35 57.358 N
x
y
F
F
=+ °=+
=− °=−
PROBLEM 2.36
Knowing that the tension in rope AC is 365 N, determine the
resultant of the three forces exerted at point C of post BC.
SOLUTION
Determine force components:
Cable force AC:
960
(365 N) 240 N
1460
1100
(365 N) 275 N
1460
=−=−
=−=−
x
y
F
F
PROBLEM 2.37
Knowing that
α
= 40°, determine the resultant of the three
forces shown.
SOLUTION
60-lb Force:
(60 lb) cos 20 56.382 lb
(60 lb)sin 20 20.521 lb
x
y
F
F
= °=
= °=
PROBLEM 2.38
Knowing that
α
= 75°, determine the resultant of the three
forces shown.
SOLUTION
60-lb Force:
(60 lb) cos 20 56.382 lb
(60 lb)sin 20 20.521 lb
x
y
F
F
= °=
= °=