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PROBLEM 17.112 (Continued)
moments about B:
22 211
L
0
PROBLEM 17.113
The slender rod AB of length L 1 m forms an angle β 30° with the vertical as
it strikes the frictionless surface shown with a vertical velocity
1
2v
m/s and no
angular velocity. Knowing that the coefficient of restitution between the rod and
the ground is e 0.8, determine the angular velocity of the rod immediately after
the impact.
2
1
13sin
L
PROBLEM 17.113 (Continued)
1m
13sin30
6.17 rad/s
PROBLEM 17.114
The trapeze/lanyard air drop (t/LAD) launch is a proposed innovative method for airborne launch of a
payload-carrying rocket. The release sequence involves several steps as shown in (1) where the payload rocket is
shown at various instances during the launch. To investigate the first step of this process where the rocket
body drops freely from the carrier aircraft until the 2-m lanyard stops the vertical motion of B, a trial rocket is
tested as shown in (2). The rocket can be considered a uniform 1-m by 7-m rectangle with a mass of 4000 kg.
Knowing that the rocket is released from rest and falls vertically 2 m before the lanyard becomes taut,
determine the angular velocity of the rocket immediately after the lanyard is taut.
22 2
12
1(4000 kg)[(7 m) (1 m) ] 16.667 kg m
12
PROBLEM 17.114 (Continued)
For impact use the principle of impulse and momentum.
1
(3.5) [ (3.5) ]mv I m
22
PROBLEM 17.115
The uniform rectangular block shown is moving along a
frictionless surface with a velocity
1
v
when it strikes a
small obstruction at B. Assuming that the impact between
corner A and obstruction B is perfectly plastic, determine
the magnitude of the velocity
1
v
for which the maximum
angle
through which the block will rotate is 30.
SOLUTION
Let m be the mass of the block.
22
22 2
122
22
2
2
11
()
212
1()
3
mv b m a b md
ma b
PROBLEM 17.115 (Continued)
3
vb
1
(3)(0.100)
PROBLEM 17.116
The 40-kg gymnast drops from her maximum height of h = 0.5 m
straight down to the bar as shown. Her hands hit the bar and clasp onto
it, and her body remains straight in the position shown. Her center of
mass is 0.75 meters away from her hands, and her mass moment of
inertia about her center of mass is 7.5 kg·m2. Assuming that friction
between the bar and her hands is negligible and that she remains in the
same position throughout the swing, determine her angular velocity
when she swings around to θ = 135°.
SOLUTION
2
42
7.5 40 0.75
PROBLEM 17.117
A slender rod of mass m and length L is released from rest in the position
shown and hits edge D. Assuming perfectly plastic impact at D, determine
for
0.6 ,bL
(a) the angular velocity of the rod immediately after the
impact, (b) the maximum angle through which the rod will rotate after the
impact.
23
11 1 1
12 20 12 100
PROBLEM 17.117 (Continued)
553
14 14 2
g
L
g
L
For analysis of the rotation about Point D after the impact use the principle of conservation of energy.
PROBLEM 17.118
A uniformly loaded square crate is released from rest with its
corner D directly above A; it rotates about A until its corner B
strikes the floor, and then rotates about B. The floor is
sufficiently rough to prevent slipping and the impact at B is
perfectly plastic. Denoting by
0
the angular velocity of the
crate immediately before B strikes the floor, determine (a) the
angular velocity of the crate immediately after B strikes the
floor, (b) the fraction of the kinetic energy of the crate lost
during the impact, (c) the angle
through which the crate will
rotate after B strikes the floor.
100
2
22
00
22
0
22
11 1 1 2
26 2 2
1
3
mc m c
mc
PROBLEM 17.118 (Continued)
2
22 22
11 11 11
2
TI mv mc m c
(
b
) Fraction of energy lost:
11
348
12
1
1
116
TT
15
0321
01233
2
22
V mg c V V mg c V mgh
1(2 1)
232 3
2
3
1
2
(2 1)
12sin( 45)
PROBLEM 17.119
A 1-oz bullet is fired with a horizontal velocity of 750 mi/h into the 18-lb
wooden beam
AB
.
The beam is suspended from a collar of negligible mass that
can slide along a horizontal rod. Neglecting friction between the collar and the
rod, determine the maximum angle of rotation of the beam during its subsequent
motion.
0
L
PROBLEM 17.119 (Continued)
Motion during rising.
Position 2
. Just after the impact.
2
22
0
(datum at level )
2
2212
2
L
Vmg A
mv
PROBLEM 17.120
For the beam of Problem 17.119, determine the velocity of the 1-oz bullet for
which the maximum angle of rotation of the beam will be
90 .
PROBLEM 17.119
A 1-oz bullet is fired with a horizontal velocity of 350 m/s
into the 18-lb wooden beam AB. The beam is suspended from a collar of
negligible weight that can slide along a horizontal rod. Neglecting friction
between the collar and the rod, determine the maximum angle of rotation of the
beam during its subsequent motion.
0
L
PROBLEM 17.120 (Continued)
Motion during rising. Position 2. Just after the impact.
2
22
22 2
(datum at level )
2
11
22
L
Vmg A
Tmv I
0.0034722
PROBLEM 17.121
The plank CDE has a mass of 15 kg and rests on a small pivot at D.
The 55-kg gymnast A is standing on the plank at C when the 70-kg
gymnast B jumps from a height of 2.5 m and strikes the plank at E.
Assuming perfectly plastic impact and that gymnast A is standing
absolutely straight, determine the height to which gymnast A will
rise.
1
2.5 m
P
h
PROBLEM 17.121 (Continued)
PROBLEM 17.122
Solve Problem 17.121, assuming that the gymnasts change places so
that gymnast A jumps onto the plank while gymnast B stands at C.
PROBLEM 17.121
The plank CDE has a mass of 15 kg and rests
on a small pivot at D. The 55-kg gymnast A is standing on the plank
at C when the 70-kg gymnast B jumps from a height of 2.5 m and
strikes the plank at E. Assuming perfectly plastic impact and that
gymnast A is standing absolutely straight, determine the height to
which gymnast A will rise.
SOLUTION
22
11
2
C
PROBLEM 17.122 (Continued)
