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.
PROBLEM 17.118 (Continued)
2
2
33448
13
0321
01233
2
22
V mg c V V mg c V mgh
1(2 1)
232 3
2
1
323
111
(2 1)
hc hc
12sin( 45)
11
216
1
2
(2 1)
sin(45 ) 2
45 46.503
1.50
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.
PROBLEM 17.119 (Continued)
Motion during rising.
Position 2
. Just after the impact.
2
22
22 2
2
22
(datum at level )
2
11
22
2
L
Vmg A
Tmv I
mv
22
(3)(0.0034722) (1100)
1(32.2)(4)
m
gL
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.
PROBLEM 17.120 (Continued)
Motion during rising. Position 2. Just after the impact.
2
22
22 2
2
(datum at level )
2
11
22
L
Vmg A
Tmv I
223 3
Syst. Momenta Syst. Ext. Imp. Syst. Momenta
L
Conservation of energy.
2233
:TVTV
22 2
00
1
2()cos
22 2
m
LL
mv mg m v mg
1(1 cos )
3
6.5524 ft/s
vgL
0
6.5524
v
0
1887 ft/sv
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.
PROBLEM 17.121 (Continued)
From Equation (1) 1(2)(9.81)(2.5)
7.0036 m/s
v
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.
PROBLEM 17.122 (Continued)
Data:
55 kg
70 kg
EA
CB
mm
mm