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PROBLEM 17.132 (Continued)
Add Equations (1) and (2) to eliminate .Pdt
11
or
AB BA
mv mv mv v v v
(3)
1
0,
AB
vvv
Moments about G:
00 0
BB
I
1
v
Condition of rolling without slipping:
AA
vr
1
7
2
7
A
r
vv
Motion after impact. Sphere B.
1
Syst. Momenta
12
Syst. Ext. Imp.
2
Syst. Momenta
PROBLEM 17.132 (Continued)
Condition of rolling without slipping: BB
vr
PROBLEM 17.133
In a game of pool, ball A is rolling without slipping with a velocity
0
v
as it hits
obliquely ball B, which is at rest. Denoting by r the radius of each ball and by
k
the coefficient of kinetic friction between a ball and the table and assuming
perfectly elastic impact, determine (a) the linear and angular velocity of each ball
immediately after the impact, (b) the velocity of ball B after it has started rolling
uniformly.
PROBLEM 17.133 (Continued)
Moments about y axis:
00 cos
B
I
(7)
or
0
() () cos
Bx Ax
vvv
(9)
From Equations (2) and (6),
0
() sin,() 0
Ay By
vv v
0
(sin)
A
vv
j
0
0
A
r
0
A
r
From Equations (7) and (8) simultaneously,
0
B
0
B
(b) Subsequent motion of ball B.
Moments about C:
0
BBB
mv r I mv r
1
5cos
7
B
vv
0
5(cos)
7
B
v
vi
PROBLEM 17.134
Each of the bars AB and BC is of length
400 mmL
and mass 1.2 kg.m Determine the
angular velocity of each bar immediately after the impulse Q (1.5 N s)
i
t is applied at C.
PROBLEM 17.134 (Continued)
Moments about A:
0( ) 2
12 2 2
xABAB
L
BtLI mv
1
3
x
AB
Bt mL
(3)
A
BBC
5
BC AB
(5)
Substitute for BC
in Eq. (1): 11
(5 )
23
7
A
BAB
Qt mL mL
Qt
mL
30
7
BC
Qt
mL
(7)
Given data: 0.400 m
L
7 (7)(1.2)(0.4)
Qt
mL
Angular velocity of bar BC. 30 (30)(1.5)
7(7)(1.2)(0.4)
BC
Qt
mL
13.39 rad/s
BC ω
PROBLEM 17.135
A uniform disk of constant thickness and initially at rest is placed in
contact with the belt shown, which moves at a constant speed v
80 ft/s. Knowing that the coefficient of kinetic friction between the
disk and the belt is 0.15, determine (a) the number of revolutions
executed by the disk before it reaches a constant angular velocity,
(b) the time required for the disk to reach that constant angular velocity.
PROBLEM 17.135 (Continued)
(b) Principle of impulse-momentum.
PROBLEM 17.136
The 8-in.-radius brake drum is attached to a larger flywheel that is not
shown. The total mass moment of inertia of the flywheel and drum is
2
14 lb ft s
and the coefficient of kinetic friction between the drum and
the brake shoe is 0.35. Knowing that the initial angular velocity of the
flywheel is 360 rpm counterclockwise, determine the vertical force
P
that
must be applied to the pedal C if the system is to stop in 100 revolutions.
PROBLEM 17.137
Charpy impact test pendulums are used to determine the amount of
energy a test specimen absorbs during an impact (see ASTM
Standard E23). The hammer weighs 71.2 lbs and has a mass moment
of inertia about its center of gravity G
H
of 20.9 slug·in
2
. The arm
weighs 19.5 lbs and has a mass moment of inertia about its own
center of gravity G
A
of 47.1 slug·in
2
. The pendulum is released from
rest from an initial position of
θ
= 39°. Knowing that the friction at
pin O is negligible, determine (a) the impact speed when the hammer
hits the test specimen, (b) the force on the pin O just before the
hammer hits the test specimen, (c) the amount of energy that the test
specimen absorbs if the hammer swings up to a maximum of
= 70°
after the impact.
Free Body Diagram at Position 2:
12
