PROBLEM 17.89 (Continued)
Solving the quadratic equation for ,
I
0.04965167 0.126590 0.050804 and 0.022179
I
PROBLEM 17.90
A 6-lb collar C is attached to a spring and can slide on rod AB, which in
turn can rotate in a horizontal plane. The mass moment of inertia of rod
AB with respect to end A is 0.35 lb ft s
2
. The spring has a constant
15 lb/in.k and an undeformed length of 10 in. At the instant shown the
velocity of the collar relative to the rod is zero, and the assembly is
rotating with an angular velocity of 12 rad/s. Neglecting the effect of
friction, determine (a) the angular velocity of the assembly as the collar
passes through a point located 7.5 in. from end A of the rod, (b) the
corresponding velocity of the collar relative to the rod.
Kinematics:
Kinetics: Since moments of all forces about shaft at A are zero,
12
()()
AA
HH
101 022
23
11 22
() ()
RC RCC
RC RC
ImvrI mvr
Imr Imr
1
1920 in. lb
160 ft lb
V
2
46.875 in. lb
3.91ft lb
V
PROBLEM 17.90 (Continued)
Data: 2
6lb
0.35 lb ft s , 32.2
7.5
RC
Im
22
32.2 32.2 12
Kinetic energy. 222
11 1 1
11 1
() ()
22 2
2232.2
ACDCr
T I mv mv
1
2
78.865 ft lb
ft (31.089 rad/s) ( )
r
T
v
Recall: 12
160 ft lb and 3.91ft lbVV
2
2
2
2
78.865 160 204.32 0.09317( ) 3.91
30.638 0.09317( )
r
r
v
v
PROBLEM 17.91
A small 4-lb collar C can slide freely on a thin ring of weight 6 lb and radius 10 in.
The ring is welded to a short vertical shaft, which can rotate freely in a fixed
bearing. Initially the ring has an angular velocity of 35 rad/s and the collar is at the
top of the ring ( 0)
when it is given a slight nudge. Neglecting the effect of
friction, determine (a) the angular velocity of the ring as the collar passes through
the position
90 ,
(b) the corresponding velocity of the collar relative to the ring.
2
RC
mm
PROBLEM 17.91 (Continued)
Potential energy. Datum is the center of the ring.
12
0
C
VmgRV
222
22
4
11
22
RCxy
TI mvv
1
35 rad/s
(a) Angular velocity.
From Eq. (1),
6 lb
g
215.00 rad/s
From Eq. (2),
222
ft (35 rad/s) (4 lb) ft
432.2 12 12
4 32.2 2 32.2 12 2 32.2 y
2
2
39.629 3.3333 16.984 0.062112
y
v
PROBLEM 17.92
Rod AB has a weight of 6 lb and is attached to a 10-lb cart C.
Knowing that the system is released from rest in the position
shown and neglecting friction, determine (a) the velocity of
point B as rod AB passes through a vertical position, (b) the
corresponding velocity of the cart C.
PROBLEM 17.92 (Continued)
Conservation of energy. 11 2 2
:TV T V
2
0 7.5 0.63492 15.0 5.9529 ft/s
CC
vv
16 5.9529 31.749 ft/s
PROBLEM 17.93
In Prob. 17.82, determine the velocity of rod AB relative to cylinder
DE as end B of the rod strikes end E of the cylinder.
PROBLEM 17.82
A 3-kg rod of length 800 mm can slide freely in
the 240-mm cylinder DE, which in turn can rotate freely in a
horizontal plane. In the position shown the assembly is rotating with
an angular velocity of magnitude 40 rad/s
and end B of the rod is
moving toward the cylinder at a speed of 75 mm/s relative to the
cylinder. Knowing that the centroidal mass moment of inertia of the
cylinder about a vertical axis is
2
0.025 kg m
and neglecting the
effect of friction, determine the angular velocity of the assembly as
end B of the rod strikes end E of the cylinder.
PROBLEM 17.93 (Continued)
Conservation of energy ( ) 0.075 m/s
r
v
12
22 22
22
0
2222
11
(0.025 kg m )(40 rad/s) (0.16 kg m )(40 rad/s)
22
11
(3 kg)(1.6 m/s) (3 kg)(0.075 m/s)
22
VV
1
22
22
22
20 J 128 J 3.84 J 0.008 J 151.85 J
(0.28 m) (0.28 m)(18.068 rad/s) 5.059 m/s
2222
1(0.025 kg m )(18.068 rad/s)
21(0.16 kg m )(18.068 rad/s)
2
22
T
v
2
r
2
22
4.081J 26.116 J 38.391 J 1.5( )
r
Tv
112 2 2
r
2
2
83.263 1.5( )
r
v
Velocity of rod relative to cylinder. 2
( ) 7.45 m/s
r
v
PROBLEM 17.94
In Problem 17.83 determine the velocity of the tube relative to the rod as the
tube strikes end E of the assembly.
PROBLEM 17.83
A 1.6-kg tube AB can slide freely on rod DE which in turn
can rotate freely in a horizontal plane. Initially the assembly is rotating with an
angular velocity
5 rad/s
and the tube is held in position by a cord. The
moment of inertia of the rod and bracket about the vertical axis of rotation is
2
0.30 kg m
and the centroidal moment of inertia of the tube about a vertical axis
is
2
0.0025 kg m .
If the cord suddenly breaks, determine (a) the angular
velocity of the assembly after the tube has moved to end E, (b) the energy lost
during the plastic impact at E.
2
22
(0.30875)(5) 0.60875 2.5359 rad/s