Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
PROBLEM 17.100 (Continued)
Principle of impulse and momentum.
1
Syst. Momenta 12
Syst. Ext. Imp. 2
Syst. Momenta
Moments about A:
79
PROBLEM 17.101
A 45-g bullet is fired with a velocity of 400 m/s at
30
into a 9-kg
square panel of side
200b
mm. Knowing that
150h
mm and that the
panel is initially at rest, determine (a) the velocity of the center of the panel
immediately after the bullet becomes embedded, (b) the impulsive reaction
at A, assuming that the bullet becomes embedded in 2 ms.
2
0
1
cos30 sin 30
24
BGP
b
mv h I mb
(0.045)(400)(0.150cos30 0.100sin 30 )
2
1
0.06 (9)(0.2) 0.15
PROBLEM 17.101 (Continued)
PROBLEM 17.102
A 45-g bullet is fired with a velocity of 400 m/s at
5
into a 9-kg square
panel of side
200b
mm. Knowing that the panel is initially at rest,
determine (a) the required distance h if the horizontal component of the
impulsive reaction at A is to be zero, (b) the corresponding velocity of the
center of the panel immediately after the bullet becomes embedded.
G
PROBLEM 17.103
The uniform rods, each of mass m, form the L-shaped rigid body
ABC which is initially at rest on the frictionless horizontal surface
when hook D of the carriage E engages a small pin at C. Knowing
that the carriage is pulled to the right with a constant velocity
v
0
,
determine immediately after the impact (a) the angular velocity of
the body, (b) the velocity of corner B. Assume that the velocity of
the carriage is unchanged and that the impact is perfectly plastic.
PROBLEM 17.103 (Continued)
Moments about C:
11
00 ( ) ( ) ( )
AB y AB x BC
mv L mv L I mv L I
00
10
B
PROBLEM 17.104
The uniform slender rod AB of weight 5 lb and length 30 in. forms an angle
30
with the vertical as it strikes the smooth corner shown with a vertical
velocity 1
v of magnitude 8 ft/s and no angular velocity. Assuming that the impact
is perfectly plastic, determine the angular velocity of the rod immediately after the
impact.
15
212
G
L
v
Kinetics.
1
Syst. Momenta 12
Syst. Ext. Imp.
2
Syst. Momenta
moments about A: 1sin 0
22
G
LL
mv I mv
(8) sin 30 0 80.875 10
32.2 12 32.2 12 12
PROBLEM 17.105
A bullet weighing 0.08 lb is fired with a horizontal velocity of 1800 ft/s into the 15-lb
wooden rod AB of length L 30 in. The rod, which is initially at rest, is suspended by a
cord of length L 30 in. Determine the distance h for which, immediately after the
bullet becomes embedded, the instantaneous center of rotation of the rod is Point C.
22
2
PROBLEM 17.105 (Continued)
Substitute for 2
v and 2
from Equations (3) and (4).
18 18
PROBLEM 17.106
A prototype of an adapted bowling device is a simple
ramp that attaches to a wheelchair. The bowling ball has
a mass moment of inertia about its center of gravity of
cmr
2
, where c is a unitless constant, r is the radius, and m
is its mass. The athlete nudges the ball slightly from a
height of h, and the ball rolls down the ramp without
sliding. It hits the bowling lane, and after slipping for a
short distance, it begins to roll again. Assuming that the
ball does not bounce as it hits the lane, determine the
angular velocity and velocity of the mass center of the
ball after it has resumed rolling.
,3
22 33
cos
O
Imv Imvr
PROBLEM 17.106 (Continued)
Substitute rolling Kinematics and Mass Moment Equations into Momentum Equation:
v
rm
2
3
rm
3
23
cos 1
rr
cvcr
Substitute in the velocity at position 2 and solve for the angular velocity at position 3:
23
cos 1
cvcr
33
2
1
c
PROBLEM 17.107
A uniform slender rod AB is at rest on a frictionless horizontal
table when end A of the rod is struck by a hammer which
delivers an impulse that is perpendicular to the rod. In the
subsequent motion, determine the distance b through which the
rod will move each time it completes a full revolution.
3
PROBLEM 17.108
A bullet of mass m is fired with a horizontal velocity v
0
and at a height
1
2
hR
into a wooden disk of much larger mass M and radius R. The
disk rests on a horizontal plane and the coefficient of friction between
the disk and the plane is finite. (a) Determine the linear velocity
1
v
and the angular velocity
1
ω
of the disk immediately after the bullet has
penetrated the disk. (b) Describe the ensuing motion of the disk and
determine its linear velocity after the motion has become uniform.
12
MR
1
MR
PROBLEM 17.108 (Continued)
(b) After the motion becomes uniform, the disk rolls without slipping.
Kinematics.
22
vR
0
Syst. Momenta
02
Syst. Ext. Imp.
2
Syst. Momenta
2
3
M
At first the disk slides and rotates , it latter rolls with a constant linear velocity
2
v
and a constant
angular velocity
2
.ω
PROBLEM 17.109
Determine the height h at which the bullet of Problem 17.108 should
be fired (a) if the disk is to roll without sliding immediately after
impact, (b) if the disk is to slide without rolling immediately after
impact.
10
2
MR
PROBLEM 17.110
A uniform slender bar of length L 200 mm and mass m 0.5 kg
is supported by a frictionless horizontal table. Initially the bar is
spinning about its mass center G with a constant angular velocity
1
6rad/s.
ω
Suddenly latch D is moved to the right and is struck
by end A of the bar. Knowing that the coefficient of restitution
between A and D is e 0.6, determine the angular velocity of the
bar and the velocity of its mass center immediately after the
impact.
2
8
2
PROBLEM 17.110 (Continued)
2
1
6
2
21
A
ma
I
va
22
0
PROBLEM 17.111
A uniform slender rod of length L is dropped onto rigid supports at A and
B. Since support B is slightly lower than support A, the rod strikes A with
a velocity
1
v
before it strikes B. Assuming perfectly elastic impact at both
A and B, determine the angular velocity of the rod and the velocity of its
mass center immediately after the rod (a) strikes support A, (b) strikes
support B, (c) again strikes support A.
32 1
22
B
PROBLEM 17.111 (Continued)
Moments about B:
22 33
0
22
LL
mv I mv I
31 1
L
31
2v
33111
() () 3 2
AB
vLv vvv
(c) Second impact at A.
3
Syst. Momenta
34
Syst. Ext. Imp.
4
Syst. Momenta
PROBLEM 17.112
A uniform slender rod AB of mass m and length L is falling freely with a
velocity 0
v when end B strikes a smooth inclined surface as shown.
Assuming that the impact is perfectly elastic, determine the angular
velocity of the rod and the velocity of its mass center immediately after
the impact.
0
24
t
