PROBLEM 17.89 (Continued)
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.
23
11 22
RC RC
Imr Imr
PROBLEM 17.90 (Continued)
6lb
r
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
111
1
6 lb
10 in. 0.83333 ft
35 rad/s
C
R
W
R
(a) Angular velocity.
6 lb
24lb
6 lb (35 rad/s)
2
g
gg
(b) Velocity of collar relative to ring.
2
2
16lb 10 10
y
y
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.
2 32.2 2 32.2 3 2 12 32.2
vv L
2
PROBLEM 17.92 (Continued)
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.
SOLUTION
Kinematics and geometry.
1
1.6 m/s
v
Initial position Final position
Conservation of angular momentum about C.
22
1(3 kg)(0.8 m) 0.16 kg m
PROBLEM 17.93 (Continued)
Conservation of energy ( ) 0.075 m/s
r
v
12
22 2 2
11 1 1 1
0
1111
()
DE AB AB AB r
VV
TI I mv mv
r
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.
SOLUTION
Let Point C be the intersection of axle C and rod DE. Let Point G be the mass center of tube AB.
Masses and moments of inertia about vertical axes.
22
22
(0.30875)(5) 0.60875 2.5359 rad/s
PROBLEM 17.94 (Continued)
Kinetic energy.
222
11 1
AB DCE AB
TI I mv
11
2
r
PROBLEM 17.95
The 6-lb steel cylinder A and the 10-lb wooden cart B are at rest in
the position shown when the cylinder is given a slight nudge,
causing it to roll without sliding along the top surface of the cart.
Neglecting friction between the cart and the ground, determine the
velocity of the cart as the cylinder passes through the lowest point
of the surface at C.
SOLUTION
Kinematics (when cylinder is passing C)
BC A
vvr v
AB
vv
r
Principle of impulse and momentum.
Syst. of Momenta
1
Syst. Ext. Imp.
12
Syst. Momenta
2
PROBLEM 17.96
At what height h above its center G should a billiard ball of radius r be
struck horizontally by a cue if the ball is to start rolling without sliding?
22
5
PROBLEM 17.97
A bullet weighing 0.08 lb is fired with a horizontal velocity of 1800 ft/s into the
lower end of a slender 15-lb bar of length 30 in.L Knowing that 12 in.h and
that the bar is initially at rest, determine (a) the angular velocity of the bar
immediately after the bullet becomes embedded, (b) the impulsive reaction at C,
assuming that the bullet becomes embedded in 0.001 s.
SOLUTION
2
15
2
G
Kinetics.
PROBLEM 17.97 (Continued)
PROBLEM 17.98
In Problem 17.97, determine (a) the required distance h if the impulsive reaction
at C is to be zero, (b) the corresponding angular velocity of the bar immediately
after the bullet becomes embedded.
PROBLEM 17.97
A bullet weighing 0.08 lb is fired with a horizontal velocity of
1800 ft/s into the lower end of a slender 15-lb bar of length 30 in.L Knowing
that 12 in.h and that the bar is initially at rest, determine (a) the angular
velocity of the bar immediately after the bullet becomes embedded, (b) the
impulsive reaction at C, assuming that the bullet becomes embedded in 0.001 s.
SOLUTION
2
15
2
Kinetics.
PROBLEM 17.98 (Continued)
PROBLEM 17.99
A 16-lb wooden panel is suspended from a pin support at A and is initially at
rest. A 4-lb metal sphere is released from rest at B and falls into a hemispherical
cup C attached to the panel at a point located on its top edge. Assuming that the
impact is perfectly plastic, determine the velocity of the mass center G of the
panel immediately after the impact.
SOLUTION
112
C
Impact analysis.
Kinematics: Immediately after impact in terms of 2
22
22
9
12
7
() 12
C
v
v
Principle of impulse and momentum.
Syst. Momenta1 Syst. Ext. Imp.12 Syst. Momenta2
PROBLEM 17.99 (Continued)
Moments about A:
1222
779
() ft 0 () ft ft
12 12 12
4lb 7 4lb 7 7 16lb 9 9
(6.9498 ft/s) ft ft 0.18634 ft
sC sC P
mv mv I mv
PROBLEM 17.100
An 16-lb wooden panel is suspended from a pin support at A and is initially at
rest. A 4-lb metal sphere is released from rest at B and falls into a hemispherical
cup C attached to the panel at the same level as the mass center G. Assuming
that the impact is perfectly plastic, determine the velocity of the mass center G
of the panel immediately after the impact.
SOLUTION
Mass and moment of inertia.
4lb
s
W
1
218
12
2(32.2 ft/s ) ft
9.8285 ft/s
C
Impact analysis.
Kinematics: Immediately after impact in terms of 2.
22
12