1. A 54 kg crate rests on the 27 kg pickup tailgate. Calculate the tension T
in each of the two restraining cables, one of which is shown. The centers of
gravity are at G1 and G2. The crate is located midway between the two
cables.
2. As an airplane’s brakes are applied, the nose wheel exerts two
forces on the end of the landing gear as shown. Determine the
horizontal and vertical components of reaction at the pin C and the
force in strut AB.
Solution: Two-force member : link AB
FBD of member CA
Cy
1tan20
0.4tan20
0.6 m
0.4 m
C
A
50o
FAB
M
+
C
0
21  61 tan 20   FAB sin 500.4   FAB cos 500.4 tan 20   0
FAB  0.8637 kN
20o
2 kN
6 kN
Cx
F
x
0
0.8637 sin 50  2  C x  0
F
y

C x  2.66 kN

C y  6.56 kN
0
0.8637 cos 50  6  C y  0
3. The 500-kg uniform beam is subjected to
the three external loads shown. Compute the
reactions at the support point O. The x-y plane
is vertical.
FBD of beam
Wbeam=500(9.81) N
Oy
A
Ox
M
30o
15 kN.m
G
1.4 kN
3 kN
B
2.4 m
+
M
O
0
 1400  1.2   500  9.812.4   15000  3000 cos 304.8  M  0
F
0

F
0

x
y
Ox  3000 sin 30  0


M  7562.766 N  m
(ccw)
Ox  1500 N
O y  1400  5009.81  3000 cos 30  0

O y  6103.07 N
4. The pin A, which connects the 200-kg steel beam with center of gravity at G to the
vertical column, is welded both to the beam and to the column. To test the weld, the 80-kg
man loads the beam by exerting a 300 N force on the rope which passes through a hole in
the beam as shown. Calculate the torque (couple) M supported by the pin.
FBD of beam
Wman=80(9.81) N
Ay
Ax
G
M
300 N
Wbeam=200(9.81) N
M
300 N
+
A
0
80  9.811.8  200  9.811.2   3001.8  3002.1  M  0
M  4937.04 N  m
5. A large symmetrical drum for drying sand is operated by the geared motor
drive shown. If the mass of the sand is 750 kg and an average gear-tooth force of
2.6 kN is supplied by the motor pinion A to the drum gear normal to the
contacting surfaces at B, calculate the average offset x of the center of mass G
of the sand from the vertical centerline. Neglect all friction in the supporting
rollers.
FBD of Drum
Tangent to circle
750 9.81 N
x
2.6 kN
20o
G
+
N1
M
N2
N3
O
0
N4 2.6 103 cos 200.6  750  9.81 x  0
x  0.1992 m  199.2 mm
6. It is desired that a person be able to begin closing the van hatch from the open
position shown with a 40-N vertical force P. As a design exercise, determine the
necessary force in each of the two hydraulic struts AB. The center of gravity of
the 40-kg door is 37.5 mm directly below point A. Treat the problem as twodimensional.
7. The small crane is mounted on one side of the bed of a pickup truck. For
the position q=40o, determine magnitude of the force supported by the pin
at O and the oil pressure p against the 50-mm diameter piston of the
hydraulic cylinder BC.
Two-force member: Hydraulic cylinder BC
FBD of Boom AO
tan a 
360  340 sin 40  110 cos 40
340 cos 40  110 sin 40
a  56.2o
+
 MO  0
120  9.81785  340  cos 40  FBC cos a 360   0
FBC  5065.81 N
Oy
 Fx  0
Ox  5065.81 cos a  0
Ox  2818.09 N
W
Ox  Fy  0
q
C
O
O y  120  9.81  5065.81 sin a  0
O y  3032.41 N
FBC
Oy
360 mm
a
p
B
FBC
d 4
2

5065.81
 50 4
2
 2.58
N
mm
2
MPa 
8. The toggle switch consists of a cocking lever that is pinned to a fixed frame at A and
held in place by the spring which has an unstretched length of 200 mm. The cocking lever
rests against a smooth peg at B. Determine the magnitude of the support force at A and
the normal force on the peg at B when the lever is in the position shown.
300 mm
30o
100 mm
300 mm
k=50 N/m
D
2
CD  3002  4002  2  300  400 cos 150
30o

CD
300
400


sin 150 sin  sin a
300 mm
A

CD  676.4 mm
  12.81o , a  17.19o
D
300 mm
30o
100 mm
l  676.64  200  476.64 mm
Fspring  kl  500.47664  28.832 N
300 mm
a
k=50 N/m
+
FBD of lever
C
MA  0
Fspring  sin  400  FB 100  0

FB  21.136 N
 Fx  0

Ay
A
B
Fspring
30o
FB
Ax
Ax  FB cos 30  Fspring sin30     0

Ax  25.347 N

Ay  12.199 N
 Fy  0
Ay  FB sin 30  Fspring cos 30     0
A  Ax2  Ay2  28.13 N
9. The bracket and pulley assembly has a mass of 40 kg with combined center of
gravity at G. Calculate the magnitude of the force supported by the pin at C and
roller at A when a tension of 400 N is applied in the vertical plane of the cable.
C
375 mm
D
100 mm
G
A
75 mm
B
450 mm
30o
400 N
75 mm
 Fy  0
C y  409.81  400 cos 30  0 
C y  738.81 N
MB  0
 409.81350  40075  C y 450  C x 375  0
FBD of bracket
Cy
C
C x  600 N
Cx
Cx
375 mm
 Fx  0
D
 C x  Ax  400 sin 30  0
W=mg=40(9.81) N
100 mm
G
A
75 mm
B
75 mm
Ax
30o
450 mm
30o
400 N

Ax  800 N
10. Pulley A delivers a steady torque of 100 N.m to a pump through its shaft at C. The
tension in the lower side of the belt is 600 N. The driving motor B has a mass of 100
kg and rotates clockwise. As a design consideration, determine the magnitude of the
force on the supporting pin at O.
FBD of pulley (A)
FBD of motor (B)
mg=100.9.81=981 N
30o
Cy
T
600 N
T=155.6 N
100 N.m
Cx
600 N
Ox
 MC  0
6000.225  T 0.225  100
T  155.6 N
MD  0
FD
Oy
9810.125  155.6 cos 300.2  0.075 cos 30  155.6 sin 300.125  0.075 sin 30  6000.125  O y 0.25  0
O y  906.08 N
 Fx  0
155.6 cos 30  600  Ox  0
Ox  734.75 N
Ro  Ox2  O y2  1166.55 N
70 cm
20 cm
11. The winch consists of a drum
of radius 30 cm, which is pin
60 cm
connected at its center C. At its
outer rim is a ratchet gear having a
mean radius of 60 cm. The pawl
AB serves as a two force member
(short link) and holds the drum
from rotating. If the suspended
30 cm
load is 500 N, determine the
horizontal and vertical components
reaction at the pin C.
70 cm
Two-force member : Pawl AB
20 cm
B
FBD of winch
60 cm
20 cm
FAB
a
a
70 cm
A
30 cm
Cy
Cx
C
+
M
C
 FAB cos a 60  50030  0
FAB  260 N
F
X
500 N
0
0
FAB cos a  C x  0
F
y

0
 FAB sin a  500  C y  0
C x  250 N
Correct sense

C y  571.43 N
12. Determine the support reactions of roller A and the smooth collar B on the
rod. The collar is fixed to the rod AB, but is allowed to slide along rod CD.
Equations of equilibrium;
 Fy  0
N B sin 45  900  0
N B  1272.79 N
 Fx  0
1272.79 cos 45  Ax  0
FBD of rod AB
Ax
Ax  900 N
MB  0
 9001  9002 cos 45  M B  0
45o
NB
MB
M B  227 N  m
13. Plate AB contains a smooth parabolic slot. Fixed pins B and C are
located at the positions shown in the figure. The equation of the parabolic
slot is given as y = x2/160 , where x and y are in mm. If it is known that the
force input P = 4 N, determine the forces applied to the plate by the pins B
and C and also the force output Q.
Q
120 mm
P
y
C
A
20 mm
B
140 mm
46 mm
60 mm 40 mm
x

Q
Tangent to the parabolic slot

120 mm
P=4 kN
C
y
aa
A
C
B
140 mm
 Fx  0

By
60 mm 40 mm
P  C sin a  Q sin   0
x2
60 2
y
y
 22.5 mm
46 mm
160
160
x
dy 2 x
3
y 

tan a 
20 mm
dx 160 x  60
4
tan  
120  46  20
140  60  40

  12.68o
0.6C  0.219Q  4
 Fy  0

B y  C cos a  Q cos   0
B y  0.8C  0.975Q  0
 MC  0

 P22.5  B y 60  Q sin  46  40 tan    22.5  0
60 B y  7.13Q  90
C  4.494 N
Q  5.95 N
By  2.207 N