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PROBLEM 17.127 (Continued)
Coefficient of restitution. 4
DAD
D
A
L
vvv
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.
PROBLEM 17.128 (Continued)
(a) Angular velocity.
1
2
(3)(1 ) sin
(3)
emv
MmL
2
(3)(1.5)(0.8)(3)sin 60
(2.4 2.4)(0.75)
(b) Velocity of D.
From Eq. (1),
( ) (0.75)(2.5981) (3sin 60 )(0.5)
0.64976 m/s
Dn
v
()1.5m/s
Dt
v
30
22
(0.64976) (1.5)
1.63468 m/s
D
v
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.
PROBLEM 17.129 (Continued)
Solving Eqs. (1), (2), and (3) simultaneously,
1.599 m/s 1.606 m/s 19.27 rad/s
AB B
vv
19.27 rad/s
B
ω
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.
PROBLEM 17.130 (Continued)
(a) Moments about A:
LL
0.002329 (0.09317)(0.87) 0.003594 (0.06211)
Normal accelerations at C and G.
222
5
L
Gn
Tangential accelerations at C and G.
α
5
L
() ()
22
AB S AB AB C t G S G t
LL
WWLI maImaR
22
1
12 12 4 12
3.3333 0.087226
2
38.214 rad/s
2
5
12
2
PROBLEM 17.130 (Continued)
eff
():
xx
FF
( ) ( ) cos16.7 ( ) sin16.70
Ama ma ma
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.
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.
