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PROBLEM 16.141 (Continued)
Rod AE:
/
,
AE AE P AE u= =α αk a j
//
2
P P P AE P AE
′
=+ +×aaa ωv
2
PROBLEM 16.141 (Continued)
Inertial terms at mass centers.
Rod AE:
(0.049689)( 230.93 133.33 ) (11.475 lb) (6.625 lb)
AE G
m= −+ =− +a ij i j
AE AE
Rod BP:
0
BP BP
I=α
Kinetics.
eff / /
A A P A G A AE G AE AE
54
( ) ( 11.475 16.625 ) 1.2750
12 12
53.8249 1.2750 12.240 lb
12
P
PP
− ×− = − ×− + −
−=− − =
ji j i j k
k kk
PROBLEM 16.142
Two rotating rods in the vertical plane are connected by a slider
block P of negligible mass. The rod attached at A has a mass of
0.8 kg and a length of 160 mm. Rod BP has a mass of 1 kg and
is 200 mm long and the friction between block P and AE is
negligible. The motion of the system is controlled by a couple
M applied to bar AE. Knowing that at the instant shown rod BP
has an angular velocity of 20 rad/s clockwise and an angular
acceleration of 80 rad/s2 clockwise, determine (a) the couple M,
(b) the components of the force exerted on AE by block P.
PROBLEM 16.142 (Continued)
Rod AE:
AE AE
a
=α
,
/P AE
u=
a
2
=++×αaa ω v
//P AE P A AE P A
[(0.100 m)
AE
a
=
2
] [(20 rad/s )(0.100 m)+
]
[0.100
AE
a
=
2
] [40 m/s+
]
and
/
2 [(2)(20 rad/s)(3.4641 m/s)
AE P AE
×=ωv
2
] 138.564 m/s=
AE
AE
Masses, weights, and moments of inertia.
2
2
0.8 kg (0.8 kg)(9.81 m/s ) 7.848 N
1.0 kg (1.0 kg)(9.81 m/s ) 9.81 N
AE AE AE
BP BP BP
m W mg
m W mg
= = = =
= = = =
//G AE G A AE G A
2
(772.82 rad/s )(0.08 m)=
2
(20 rad/s )(0.08 m)+
2
[61.826 m/s=
2
] [32 m/s+
]
2
//H BP H A BP H B
ω
=×−aαr r
2
2
2
[8 m/s=
2
60 ] [40 m/s°+
30 ]°
PROBLEM 16.142 (Continued)
Inertial terms at mass centers.
Rod AE:
[49.460 N
AE G
m=a
] [25.6 N+
]
[8 N
m=a
60 ] [40 N°+
30 ]
°
AE AE
Rod BP:
0.2667 N m
BP BP
I= ⋅α
Kinetics:
( ) : 0.10 (0.08)(49.460) 1.3189
MM P
Σ=Σ − =− −
PROBLEM 16.143
Two disks, each of mass m and radius r are connected as shown by a continuous chain
belt of negligible mass. If a pin at point C of the chain belt is suddenly removed,
determine (a) the angular acceleration of each disk, (b) the tension in the left-hand
portion of the belt, (c) the acceleration of the center of disk B.
PROBLEM 16.143 (Continued)
From (1) and (2) we note that
AB
aa
=
( ) ( )
:
M M Wr I ma r
a
Σ=Σ = +
PROBLEM 16.144*
A uniform slender bar AB of mass m is suspended as shown from a uniform
disk of the same mass m. Neglecting the effect of friction, determine the
accelerations of Points A and B immediately after a horizontal force P has
been applied at B.
PROBLEM 16.144* (Continued)
Substitute from (1):
3
22
53
24
AB AB AB
AB AB
L
P m a ma
a
+ −=
Multiply by
:
9
L
2
15 1
9 18 12
AB AB
L
PL ma mL
a
= −
(4)
10 1 5 7
PROBLEM 16.145
A uniform rod AB, of mass 15 kg and length 1 m, is attached to the 20-kg
cart C. Neglecting friction, determine immediately after the system has been
released from rest, (a) the acceleration of the cart, (b) the angular acceleration
of the rod.
