Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
PROBLEM 17.106 (Continued)
Substitute rolling Kinematics and Mass Moment Equations into Momentum Equation:
v
rm
23
rm
3
rr
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.
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.
PROBLEM 17.108 (Continued)
(b) After the motion becomes uniform, the disk rolls without slipping.
Kinematics.
22
vR
022
Since
1
2
hR
is given:
2
11
22
0
2
3
mv
MR
22
vR
0
2
3
mv
M
v
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.
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.
PROBLEM 17.110 (Continued)
2
1
6
2
21
3
A
ma
I
va
ma ma
45 linear components: 0
22
0
22
A
mv mv mb
21225
23226
32
v
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.
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.
44414
A
Moments about A:
33 44
0
22
LL
mv I mv I
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.
