PROBLEM 10.20
For the linkage shown, determine the force
Q
required for
equilibrium when
18 in.,l
600 lb in.,M
and
70 .
SOLUTION
PROBLEM 10.21
A 4-kN force
P
is applied as shown to the piston of the engine
system. Knowing that
= 50 mmAB
and BC
200 mm,
determine the couple
M
required to maintain the equilibrium
of the system when (a)
30, (b)
150 .
SOLUTION
Analysis of the geometry:
PROBLEM 10.21 (Continued)
Virtual Work: 0: 0
C
UPxM
sin( ) 0
cos
AB
PM
PROBLEM 10.22
A couple
M
of magnitude 100 N m is applied as shown to the
crank of the engine system. Knowing that AB
50 mm
and
200 mm,BC
determine the force
P
required to maintain the
equilibrium of the system when (a)
60 ,
(b)
120 .
SOLUTION
Analysis of the geometry:
PROBLEM 10.22 (Continued)
Virtual Work:
0: 0
C
UPxM
sin( ) 0
cos
AB
PM
Thus, sin( )
cos
MAB P
(4)
PROBLEM 10.23
Rod AB is attached to a block at A that can slide freely in the vertical
slot shown. Neglecting the effect of friction and the weights of the
rods, determine the value of
corresponding to equilibrium.
SOLUTION
Dimensions in mm.
PROBLEM 10.24
Solve Problem 10.23 assuming that the 800-N force is replaced by a
24-N m
clockwise couple applied at D.
PROBLEM 10.23
Rod AB is attached to a block at A that can slide
freely in the vertical slot shown. Neglecting the effect of friction and
the weights of the rods, determine the value of
corresponding to
equilibrium.
SOLUTION
PROBLEM 10.25
Determine the value of
corresponding to the equilibrium position of the rod
of Problem 10.10 when
30 in.,l
5 in.,a
25 lb,P
and
40 lb.Q
PROBLEM 10.10
The slender rod AB is attached to a collar A and rests on a
small wheel at C. Neglecting the radius of the wheel and the effect of friction,
derive an expression for the magnitude of the force
Q
required to maintain the
equilibrium of the rod.
SOLUTION
For
triangle :AA C
tanAC a
() tan
A
yACa
PROBLEM 10.25 (Continued)
with 30 in., 5 in., 25 lb, and 40 lblaP Q
PROBLEM 10.26
Determine the values of
corresponding to the equilibrium position of the rod
of Prob. 10.11 when l = 24 in., a = 4 in., P = 10 lb, and Q = 18 lb.
PROBLEM 10.11
The slender rod AB is attached to a collar A and rests on a
small wheel at C. Neglecting the radius of the wheel and the effect of friction,
derive an expression for the magnitude of the force
Q
required to maintain the
equilibrium of the rod.
SOLUTION
For
triangle :AA C
tanAC a
() tan
A
yACa
2
cos
A
a
y
PROBLEM 10.26 (Continued)
with 24 in., 4 in., 10 lb, and 18 lblaP Q
PROBLEM 10.27
Determine the value of
corresponding to the equilibrium position
of the mechanism of Problem 10.12 when
= 80 NP
and
100 N.Q
PROBLEM 10.12
Knowing that the line of action of the force
Q
passes through Point C, derive an expression for the magnitude of
Q
required to maintain equilibrium.
SOLUTION
From geometry
2cos , 2sin
2sin , ( ) cos
22
AA
yl y l
CD l CD l
PROBLEM 10.28
Determine the value of
corresponding to the equilibrium position of the
mechanism of Prob. 10.14 when P = 270 N and Q = 960 N.
SOLUTION
Virtual Work:
2 sin , 2 cos
3cos , 3sin
AA
FF
xl xl
yl y l
PROBLEM 10.29
Two rods AC and CE are connected by a pin at C and by a
spring AE. The constant of the spring is k, and the spring is
unstretched when
30 .
For the loading shown, derive an
equation in P,
, l, and k that must be satisfied when the system
is in equilibrium.
SOLUTION
cos
E
yl
sin
E
yl
PROBLEM 10.30
Two rods AC and CE are connected by a pin at C and by a spring
AE. The constant of the spring is 1.5 lb/in., and the spring is
unstretched when 30 .
Knowing that 10 in.l and
neglecting the weight of the rods, determine the value of
corresponding to equilibrium when 40 lb.P
SOLUTION
From the analysis of Problem 10.29 12sin
8tan
P
kl
PROBLEM 10.31
Solve Problem 10.30 assuming that force
P
is moved to C and
acts vertically downward.
PROBLEM 10.30
Two rods AC and CE are connected by a pin
at C and by a spring AE. The constant of the spring is 1.5 lb/in.,
and the spring is unstretched when
30 .
Knowing that
l
10 in.
and neglecting the weight of the rods, determine the
value of
corresponding to equilibrium when
40 lb.P
SOLUTION
cos , sin
CC
yl y l
Spring:
PROBLEM 10.32
Two bars AD and DG are connected by a pin at D and by a spring
AG. Knowing that the spring is 300 mm long when unstretched and
that the constant of the spring is 5 kN/m, determine the value of x
corresponding to equilibrium when a 900-N load is applied at E as
shown.
SOLUTION
1
xx x
PROBLEM 10.33
Solve Prob. 10.32 assuming that the 900-N load is applied at C
instead of E.
Problem 10.32: Two bars AD and DG are connected by a pin at D
and by a spring AG. Knowing that the spring is 300 mm long when
unstretched and that the constant of the spring is 5 kN/m, determine
the value of x corresponding to equilibrium when 900-N load is
applied at E as shown.
SOLUTION
1
66
CC
x
yyx
PROBLEM 10.34
Two 5-kg bars AB and BC are connected by a pin at B and by a
spring DE. Knowing that the spring is 150 mm long when
unstretched and that the constant of the spring is 1 kN/m, determine
the value of x corresponding to equilibrium.
SOLUTION
First note:
2
bar (5 kg)(9.81 m/s ) 49.05 NW
PROBLEM 10.35
A vertical force
P
of magnitude 150 N is applied to end E of cable
CDE, which passes over a small pulley D and is attached to the
mechanism at C. The constant of the spring is k 4 kN/m, and the
spring is unstretched when
0. Neglecting the weight of the
mechanism and the radius of the pulley, determine the value of
corresponding to equilibrium.
SOLUTION
0.2 m
0.1 m
lBC
r