F
1. The pruning mechanism of a pole saw is shown as it cuts a branch S. For the
particular position drawn, the actuating cord is parallel to the pole and carries a
tension of 120 N. Determine the shearing force P applied to the branch by the cutter
and the total force supported by the pin at E. The force exerted by the light return
spring at C is small and may be neglected.
FTwo-force member: CD
FBD of member EDF
2. The elements of a rear suspension for a front-wheel-drive car are shown in
the figure. Determine the magnitude of the force at each joint if the normal
force F exerted on the tire has a magnitude of 3600 N.
magnitudes of forces at each joint
FCD
Bx
By
ax
y
09.12280
60tan 1
a
NBFBF
NBFBF
NF
FF
M
yCDyy
xCDxx
CD
CDCD
B
400003600sin0
18560cos0
1898
0)70(sin)305(cos)165(3600
0
a
a
aa
NB 441040001856 22
CD
FCDFCD
Wheel + BC
NA
NAFAF
NAFAF
NF
F
M
yEFyy
xEFxx
EF
EF
A
455013844330
138404000sin0
433001856cos0
5920
0)350(4000)260(sin
0
22
Bx
By
x
y
30.65200
435tan 1
FEF
EF
FEF
FEF
Ax
Ay
AEB
3. The linkage shown is used on a garbage truck to lift a 9000 N dumpster. Points A-G are
pins, and member ABC is horizontal. For the position shown, when the dumpster just fully
lifts off the ground, determine the force hydraulic cylinder CF. Roller at G is contact with the
dumpster.
Ax
Ay
FG
FBD of dumpster
NAFAF
NAFAF
NFFM
yGyy
xGxx
GGA
6910045sin90000
15910045cos0
225000)600()1500(90000
Ex
Ey
FCD
FG
FBD of member EDG
NEEF
NEEF
NFFM
yyy
xxx
GCDE
5.79549045sin2250045cos1125000
63640045cos11250045cos225000
1125000)300()1500(225000
Bx
By
FCF
Ex
Ey
From equilibrium of whole system;
NF
FEE
M
CF
CFyx
E
68.118724
0)450(45cos)45cos900900(450)45cos900()1950(900
0
4. A hydraulic lift-table is used to raise a 1000 kg crate. It consists of a platform and two
identical linkages on which hydraulic cylinders exert equal forces. In the figure only one
linkage and one cylinder are shown. Members EDB and CG are each of length 2a and
member AD is pinned to the midpoint of EDB. If the crate is placed on the table, so that
half of its weight is supported by the system shown, determine the force exerted by each
cylinder in raising the crate for =60o, a=0.70 m and L=3.20 m. Show that the result
obtained is independent of the distance d.
FBD of Platform
Two-Force Members: AD, BC, CG, DH.
30o
=60o
FAD
W/2
FCFB
A B C
BCCBCBy
ADADx
FW
FW
FFW
FFF
FFFx
220
20
000
Pulley CFC
C
FCG
30o
FBC
300300
0300
cosFFFcosFF
FsinFF
CGCCCGy
BCCGx
30o
=60o
FBD of CG
C
G
FCG
=60o 30
30
cos
FF
sin
FF
CCG
BCCG
FBD of BC
FCG
FBCFBC
30tanF
F
C
BC
30o
=60o
N.F
FF.F.
.tanF.FF.
.F.F..sinF..cosFM
DH
/W
CBDH
F
CBDH
BCBDHDHE
BC
635124
070670
02113070670
021170350021261002120
2
FBD of EDB
B
E
FB
=60o
Ex
o.sin
.
sin
.
m.DHcosEHDEEHDEDH
021260
91270
912602222
aa
D
H
aEy
FBC
FDH
0.7 m
0.61 m
1.4 m
Cosine theorem:
Sine theorem:
5. The mechanism is designed to keep its load level while raising it. A pin on the rim of the 80 cm
diameter pulley fits in a slot on arm ABC. Arm ABC and DE are each 80 cm long and the package
being lifted weighs 80 kN. The mechanism is raised by pulling on the rope that is wrapped around the
pulley. Determine the force P applied to the rope and all the forces acting on arm ABC when the
package has been lifted 80 cm as shown.
SOLUTION
FBD of Platform Two force member: ED
69.28 mm
FBD of DE
FBD of ABC
FBD of the pulley
6. A simple folding chair comprised of two identical frames, one on each side, is shown in
the figure. The half frame shown carries half the weight of a 70 kg person. Determine all
the forces acting on member BF. Neglect the weights of the connecting elements (not
shown) and the seat, and also the friction at points A, B and F.
Detail of contact at F
Dimensions in “mm”
Geometry of the Chair
SOLUTION
Two force member: EG
Equilibrium of the whole system:
FBD of DC
GE two force member
FBD of BF