PROBLEM 17.123
A slender rod AB is released from rest in the position shown. It
swings down to a vertical position and strikes a second and
identical rod CD which is resting on a frictionless surface.
Assuming that the coefficient of restitution between the rods is
0.4, determine the velocity of rod CD immediately after the
impact.
33
33
CC
PROBLEM 17.123 (Continued)
Principle of impulse–momentum at impact.
2
Syst Momenta 23
Syst Ext Imp
3
Syst Momenta
LL
3
C
PROBLEM 17.124
A slender rod AB is released from rest in the position shown. It
swings down to a vertical position and strikes a second and
identical rod CD which is resting on a frictionless surface.
Assuming that the impact between the rods is perfectly elastic,
determine the velocity of rod CD immediately after the impact.
2
L
23
B
PROBLEM 17.124 (Continued)
Impact condition:
32
3
CB B
vvev
30.866
C
PROBLEM 17.125
Block A of mass m is attached to a cord which is wrapped around a uniform disk of mass
M. The block is released from rest and falls through a distance h before the cord becomes
taut. Derive expressions for the velocity of the block and the angular velocity of the disk
immediately after the impact. Assume that the impact is (a) perfectly plastic, (b) perfectly
elastic.
2
21
2
(2)
22
(3)
Substituting (3) into (2) and using (1) for v
1
,
1
mMvmv
22
m
vgh
2
2
gh
m
212
(4)
PROBLEM 17.125 (Continued)
Substituting (4) into (2) and using (1) for v1
1
2
mM
22
mM
mM
2
mM R
PROBLEM 17.126
A 2-kg solid sphere of radius r 40 mm is
dropped from a height h 200 mm and lands on
a uniform slender plank AB of mass 4 kg and
length L 500 mm which is held by two
inextensible cords. Knowing that the impact is
perfectly plastic and that the sphere remains
attached to the plank at a distance a 40 mm
from the left end, determine the velocity of the
sphere immediately after impact. Neglect the
thickness of the plank.
0.25 m 0.04 m 0.21 m.
La
PROBLEM 17.126 (Continued)
Kinematics.
To locate the instantaneous center C
0.47301 m
0.21 m
tan 0.44397 23.94
( ) 0.51753
( cos30 ) 0.43301
S
G
L
HS a
HS
CH
vCS
vL
Principle of impulse and momentum.
2
2
[() ]
2
SS S AB S AB C
L
mv a m CS m CG I I I
PROBLEM 17.126 (Continued)
2
L
6.05 N s 2.80 N sAdt Bdt
S
PROBLEM 17.127
Member ABC has a mass of 2.4 kg and is attached to a pin support
at B. An 800-g sphere D strikes the end of member ABC with a
vertical velocity
1
v
of 3 m/s. Knowing that
750L
mm and that
the coefficient of restitution between the sphere and member ABC
is 0.5, determine immediately after the impact (a) the angular
velocity of member ABC, (b) the velocity of the sphere.
SOLUTION
(0.800)(3)(0.1875) (0.800)(0.1875) [0.1125 (2.4)(0.1875) ]
D
D
v
PROBLEM 17.127 (Continued)
()
D
A
L
ev v
0.1875 (0.5)(3 0)
D
v
(2)
D
D
PROBLEM 17.128
Member ABC has a mass of 2.4 kg and is attached to a pin
support at B. An 800-g sphere D strikes the end of member
ABC with a vertical velocity
1
v
of 3 m/s. Knowing that
750L
mm and that the coefficient of restitution between the
sphere and member ABC is 0.5, determine immediately after
the impact (a) the angular velocity of member ABC, (b) the
velocity of the sphere.
1
2
1
(1 ) sin 3
v
me Mm
L
PROBLEM 17.128 (Continued)
1
(3)(1 ) sin
emv
PROBLEM 17.129
Sphere A of mass m
A
2 kg and radius r 40 mm rolls without
slipping with a velocity
1
v
2 m/s on a horizontal surface when
it hits squarely a uniform slender bar B of mass m
B
0.5 kg and
length L 100 mm that is standing on end and at rest. Denoting
by
k
the coefficient of kinetic friction between the sphere and
the horizontal surface, neglecting friction between the sphere
and the bar, and knowing the coefficient of restitution between A
and B is 0.1, determine the angular velocities of the sphere and
the bar immediately after the impact.
SOLUTION
Before impact sphere A rolls without slipping so that its instantaneous center of rotation is its contact point
with the floor.
1
1
0.040 m
r
Analysis of impact. Use the principle of impulse and momentum. Let point A be the center of sphere A, point
PROBLEM 17.129 (Continued)
Sphere A alone.
Bar B alone:
PROBLEM 17.130
A large 3-lb sphere with a radius r 3 in. is thrown into a light
basket at the end of a thin, uniform rod weighing 2 lb and length
L 10 in. as shown. Immediately before the impact the angular
velocity of the rod is 3 rad/s counterclockwise and the velocity of the
sphere is 2 ft/s down. Assume the sphere sticks in the basket.
Determine after the impact (a) the angular velocity of the bar and
sphere, (b) the components of the reactions at A.
SOLUTION
Let Point G be the mass center of the sphere and Point C be that of the rod AB.
2
2
PROBLEM 17.130 (Continued)
(a) Moments about A:
LL
Normal accelerations at C and G.
222
5
( ) ( ) (1.2858) 0.6889 ft/s
L
a
222
4
AB AB G S
(2) (3) 0.003594 (0.06211) 0.002329 (0.09317)(0.87)
12 12 4 12
2
12
PROBLEM 17.130 (Continued)
eff
():
xx
FF
( ) ( ) cos16.7 ( ) sin16.70
Ama ma ma
y
y
PROBLEM 17.131
A small rubber ball of radius r is thrown against a rough floor with a
velocity
A
v
of magnitude
0
v
and a backspin
A
of magnitude
0
.
It is observed that the ball bounces from A to B, then from B to A,
then from A to B, etc. Assuming perfectly elastic impact, determine
the required magnitude
0
of the backspin in terms of
0
v
and r.
00
5
0
4
r
PROBLEM 17.132
Sphere A of mass m and radius r rolls without slipping with a
velocity
1
v
on a horizontal surface when it hits squarely an
identical sphere B that is at rest. Denoting by
k
the coefficient
of kinetic friction between the spheres and the surface, neglecting
friction between the spheres, and assuming perfectly elastic
impact, determine (a) the linear and angular velocities of each
sphere immediately after the impact, (b) the velocity of each
sphere after it has started rolling uniformly.