SOLUTION
6–89.
Determine the horizontal and vertical components of force
which pin C exerts on member CDE. The 600-N load is
applied to the pin.
1.5 m
2 m2 m
3 m
A
C
D
E
B
600 N
6–90.
The pipe cutter is clamped around the pipe P.If the wheel
at Aexerts a normal force of on the pipe,
determine the normal forces of wheels Band Con
the pipe.The three wheels each have a radius of 7 mm and
the pipe has an outer radius of 10 mm.
F
A
=80 N
10 mm
10 mm
P
C
B
A
SOLUTION
u=sin
–1
a10
17 b=36.03°
6–91.
Determine the force created in the hydraulic cylinders EF
and AD in order to hold the shovel in equilibrium. The
shovel load has a mass of 1.25 Mg and a center of gravity at
G. All joints are pin connected.
0.5m
0.25 m 0.25 m 1.5m
30fi
10fi
H
G
D
E
C
F
60fi2m
A
SOLUTION
*6–92.
Determine the horizontal and vertical componentsof force
at pin Band the normal force the pin at Cexertson the
smooth slot. Also, determine the moment and horizontal
and vertical reactionsof force at A.There isa pulley at E.
SOLUTION
BCE:
a
Ans.
Ans.
Ans.
ACD:
B
y
=62 lb
+c©F
y
=0;B
y
–20a3
5b–50 =0
B
x
=34 lb
:
+©F
x
=0;B
x
+20a4
5b–50 =0
N
C
=20 lb
+©M
B
=0;–50(6) –N
C
(5) +50(8) =0
3ft3ft
4ft
4ft
A
B
C
DE
50 ft
+
6–93.
The constant moment of is applied to the crank
shaft. Determine the compressive force Pthat is exerted on
the piston for equilibrium asafunction of Plot the results
of P(ordinate) versus (abscissa) for 0° …u…90°.u
u.
50 N #m
SOLUTION
Piston:
(1)
(2)
Select , solve for in Eq. (2), then Pin Eq. (1).
Ans.=250 22.252–cos2u
sin ucos u+22.252–cos2u#cos u
P(u)=
250 cos csin–1acos u
2.25 bd
sin ucos u
2.25 +cos csin–1acos u
2.25 bd#cos u
fu
f=sin–1acos u
2.25 b
d=0.2 cos u=0.45 sin f
P=250 cos f
(sin fsin u+cos fcos u)
:
+©Fx=0; FBC cos f–P=0
FBC =250
(sin fsin u+cos fcos u)
P
0.45 m
0.2m
u
A
B
C
50 N fim
6–94.
Five coins are stacked in the smooth plastic container
shown. If each coin weighs 0.0235 lb, determine the normal
reactions of the bottom coin on the container at points A
and B.
SOLUTION
3
4
3
3
5
5
5
5
4
4
3
4
6–95.
The nail cutter consists of the handle and the two cutting
blades. Assuming the blades are pin connected at Band the
surface at Dis smooth, determine the normal force on the
fingernail when a force of 1 lb is applied to the handles as
shown. The pin AC slides through a smooth hole at Aand is
attached to the bottom member at C.
Top blade:
a
Ans.
Or bottom blade:
a
Ans.FN=5.25 lb
+©MB=0; FN(2) –6 (1.75) =0
FN=5.25 lb
+©MB=0; 7(1.5) –FN(2) =0
ND=7lb
+c©Fy=0; ND–1–6=0
FA=6lb
1.5 in.
A
B
1lb
0.25in.0.25 in.
*6–96.
A man having a weight of 175 lb attempts to hold himself
using one of the two methods shown. Determine the total
force he must exert on bar AB in each case and
the normal reaction he exerts on the platform at C.Neglect
the weight of the platform.
CC
AB
AB
SOLUTION
6–97.
Aman having a weight of 175 lb attempts to hold himself
using one of the two methods shown. Determine the total
force he must exert on bar AB in each case and the normal
reaction he exerts on the platform at C.The platform has a
weight of 30 lb.
CC
AB
AB
SOLUTION
6–99.
SOLUTION
Equations of Equilibrium: From the free – body diagram of segment CAEin Fig. a,
a
Ans.
Ans.
Using the results for Axand Ayobtained above and applying the moment equation
of equilibrium about point Bon the free – body diagram of segment BAD,Fig. b,
a
Ans.ND=1045.14 N =1.05 kN
+©MB=0; 12 743.56(60) –2943(100) –ND(450) =0
Ay=2943 N =2.94 kN
+c©Fy=0; 300(9.81) –Ay=0
Ax=12 743.56 N =12.7 kN
+©MA=0;
300(9.81)(600 cos 30°) –NC(120) =0
If the 300-kg drum has a center of mass at point G,
determine the horizontal and vertical components of force
acting at pin Aand the reactions on the smooth pads C
and D.The grip at Bon member DABresists both
horizontal and vertical components of force at the rim of
the drum.
P
390 mm
100 mm
60 mm
60 mm
600 mm
30fi
B
A
C
DG
E
*6–100.
Operat
i
on of ex
h
aust an
d
i
nta
k
e va
l
ves
i
n an automo
bil
e
engine consists of the cam C, push rod DE, rocker arm EFG
which is pinned at F, and a spring and valve, V. If the
compression in the spring is 20 mm when the valve is open
as shown, determine the normal force acting on the cam
lobe at C. Assume the cam and bearings at H,I, and Jare
smooth. The spring has a stiffness of .300 N>m
SOLUTION
a
Ans.T=9.60 N
+©MF=0;
–6(40) +T(25) =0
FG=6N
+c©Fy=0; –FG+6=0
Fs=kx;Fs=300 (0.02) =6N
25 mm
40 mm
E
F
G
H
I
J
V
D
C
6–101.
If a clamping force of is required at A, determine the
amount of force Fthat must be applied to the handle of the
toggle clamp.
300 N
275 mm
30
30
235 mm
30 mm
30 mm
70 mm
F
C
E
B
D
A
SOLUTION
6–102.
If a force of is applied to the handle of the toggle
clamp, determine the resulting clamping force at A.
F
=350 N
275 mm
30
30
235 mm
30 mm
30 mm
70 mm
F
C
E
B
D
A
SOLUTION
SOLUTION
5b
6–103.
Determine the horizontal and vertical components of force
that the pins at A and B exert on the frame.
2 m
2 m 2 m
3 m
2 kN
3 kN
4 kN
C
B