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PROBLEM 16.136 (Continued)
Effective couples at mass centers.
Disk AB:
(0.2)(150)
AB AB
I=
α
30 N m= ⋅
Summary of effective
forces and couples.
PROBLEM 16.136 (Continued)
Disk AB and rod BC:
eff
2
( ) : (479.27)(0.4 0.2sin30 ) (147.22)(0.2cos30)
(6 kg)(9.81 m/s )(0.2 0.2sin30 )
(180)(0.2 0.2sin30 ) 11.9719 (179.58)(0.2 0.2sin30 )
(1555.2cos30 )(0.2)
AA
MM MΣ =Σ − − + °+ °
− +°
= +°++ +°
−°
239.635 25.50 17.658
54 11.9719 53.874 269.369
M
−− + −
=+ +−
PROBLEM 16.137
In the engine system shown
250 mml=
and
100 mm.b=
The
connecting rod BD is assumed to be a 1.2-kg uniform slender rod
and is attached to the 1.8-kg piston P. During a test of the system,
crank AB is made to rotate with a constant angular velocity of 600
rpm clockwise with no force applied to the face of the piston.
Determine the forces exerted on the connecting rod at B and D when
180 .
θ
= °
(Neglect the effect of the weight of the rod.)
PROBLEM 16.137 (Continued)
Force exerted on connecting rod at D is:
426.35=D
Kinetics of connecting rod: (neglect weight)
PROBLEM 16.138
Solve Problem 16.137 when
90 .
θ
= °
PROBLEM 16.137 In the engine system shown
250 mml=
and
b
100 mm.=
The connecting rod BD is assumed to be a 1.2-kg
uniform slender rod and is attached to the 1.8-kg piston P. During a
test of the system, crank AB is made to rotate with a constant angular
velocity of 600 rpm clockwise with no force applied to the face of
the piston. Determine the forces exerted on the connecting rod at B
and D when
180 .
θ
= °
(Neglect the effect of the weight of the rod.)
PROBLEM 16.138 (Continued)
Acceleration of mass center G of bar BD
/
2
22
1(0.2291 0.1 )
2
(0.11455 m) (0.05 m)
172.3 ( 1723 ) (0.11455 0.05 ) 0
172.3 197.34 86.15
(86.15 m/s ) (197.34 m/s )
GD
= +
= +
=− +− × + −
=−− +
=−−
r ij
ij
i k ij
i ji
ij
Force on bar BD at P in B.
2
(1.8)( 172.3 )
(310.14 N)
(1.2)( 86.15 197.34 )
(103.38 N) (236.88 N)
1(1.2)(0.25) ( 1723) 10.769 N m
12
DD
BD G
BD BD
m
m
I
a
= −
= −
=−−
=−−
= −=− ⋅
ai
i
a ij
ij
310.14 103.38 413.52 N
xx
BB=−− =−
eff / /
( ): ( ) ( )
B B BD BD D B D D G B BD G
M M xN I m m
a
+Σ = Σ − = + × + ×
k kr a r a
0.2291 10.769 (0.1)( 310.14) ( 0.11455 0.05 )
( 103.38 236.38 )
10.769 31.014 27.038 5.169
86.923 N
N
N
− =− + − +− −
×− −
=−− + −
=
k k k ij
ij
k k kk
eff
( ): ( )
y y y BD G y
F F NB ma+Σ = Σ + =
22
86.923 236.88 323.80 N
413.52 323.80 525.2 N
323.80
tan 38.1
413.52
yy
BB
B
ββ
+=− =−
= +=
= = °
525 N=B
38.1°
PROBLEM 16.138 (Continued)
Force exerted by bar BD as piston D.
PROBLEM 16.139
The 4-lb uniform slender rod AB, the 8-lb uniform slender rod BF, and
the 4-lb uniform thin sleeve CE are connected as shown and move
without friction in a vertical plane. The motion of the linkage is
controlled by the couple M applied to rod AB. Knowing that at the
instant shown the angular velocity of rod AB is 15 rad/s and the
magnitude of the couple M is
5 ft lb,⋅
determine (a) the angular
acceleration of rod AB, (b) the reaction at point D.
PROBLEM 16.140
The 4-lb uniform slender rod AB, the 8-lb uniform slender rod BF, and
the 4-lb uniform thin sleeve CE are connected as shown and move
without friction in a vertical plane. The motion of the linkage is
controlled by the couple M applied to rod AB. Knowing that at the
instant shown the angular velocity of rod AB is 30 rad/s and the
angular acceleration of rod AB is 96 rad/s2 clockwise, determine (a) the
magnitude of the couple M, (b) the reaction at point D.
PROBLEM 16.141
Two rotating rods in the vertical plane are connected by a slider
block P of negligible mass. The rod attached at A has a weight
of 1.6 lb and a length of 8 in. Rod BP weighs 2 lb and is 10 in.
long and the friction between block P and AE is negligible. The
motion of the system is controlled by a couple M applied to rod
BP. Knowing that rod BP has a constant angular velocity of
20 rad/s clockwise, determine (a) the couple M, (b) the
components of the force exerted on AE by block P.
