PROBLEM 14.44
In a game of pool, ball A is moving with the velocity
00
vvi
when it strikes balls B and C, which are at rest side by side.
Assuming frictionless surfaces and perfectly elastic impact (i.e.,
conservation of energy), determine the final velocity of each
ball, assuming that the path of A is (a) perfectly centered and
that A strikes B and C simultaneously, (b) not perfectly centered
and that A strikes B slightly before it strikes C.
PROBLEM 14.44 (Continued)
PROBLEM 14.44 (Continued)
PROBLEM 14.45
The 2-kg sub-satellite B has an initial velocity
vB
= 3 m/s
j
. It is connected to the
20-kg base-satellite A by a 500-m space tether. Determine the velocity of the base
satellite and sub-satellite immediately after the tether becomes taut (assuming no
rebound).
PROBLEM 14.46
A 900-lb space vehicle traveling with a velocity 0(1500 ft/s)vk
passes through the origin O. Explosive
charges then separate the vehicle into three parts A, B, and C, with masses of 150 lb, 300 lb, and 450 lb,
respectively. Knowing that shortly thereafter the positions of the three parts are, respectively, A(250, 250, 2250),
B (600, 1300, 3200), and C (–475, –950, 1900), where the coordinates are expressed in ft, that the velocity of B
is (500 ft/s) (1100 ft/s) (2100 ft/s) ,
B vijk
and that the x component of the velocity of C is 400 ft/s,
determine the velocity of part A.
PROBLEM 14.46 (Continued)
PROBLEM 14.47
Four small disks A, B, C, and D can slide freely on a frictionless horizontal
surface. Disks B, C, and D are connected by light rods and are at rest in the
position shown when disk B is struck squarely by disk A, which is moving to
the right with a velocity 0
v (38.5 ft/s)i. The weights of the disks are
A
W B
W C
W 15 lb, and D
W 30 lb. Knowing that the velocities of the
disks immediately after the impact are
A
v B
v (8.25 ft/s)i, C
v C
vi, and
D
v D
vi, determine (a) the speeds C
v and ,
D
v (b) the fraction of the
initial kinetic energy of the system which is dissipated during the collision.
A
A
PROBLEM 14.48
In the scattering experiment of Problem 14.26, it is known that
the alpha particle is projected from A0(300, 0, 300) and that it
collides with the oxygen nucleus C at (240, 200,100),Q where
all coordinates are expressed in millimeters. Determine the
coordinates of Point 0
B
where the original path of nucleus B
intersects the zx plane. (Hint: Express that the angular
momentum of the three particles about Q is conserved.)
PROBLEM 14.26 In a scattering experiment, an alpha particle A
is projected with the velocity 0(600 m/s)
ui
(750 m/s)
j
(800 m/s)k into a stream of oxygen nuclei moving with a
common velocity v0(600 m/s) .
j After colliding successively
with nuclei B and C, particle A is observed to move along the
path defined by the Points 1(280, 240,120)A and A2 (360, 320,
160), while nuclei B and C are observed to move along paths
defined, respectively, by 1(147, 220,130),B 2(114, 290,120),B
and by C1(240, 232, 90) and 2(240, 280, 75).C All paths are
along straight lines and all coordinates are expressed in
millimeters. Knowing that the mass of an oxygen nucleus is
four times that of an alpha particle, determine the speed of each
of the three particles after the collisions.
PROBLEM 14.48 (Continued)
PROBLEM 14.49
Three identical small spheres, each of weight 2 lb, can slide
freely on a horizontal frictionless surface. Spheres B and C
are connected by a light rod and are at rest in the position
shown when sphere B is struck squarely by sphere A which is
moving to the right with a velocity v0 (8 ft/s)i. Knowing
that θ = 45° and that the velocities of spheres A and B
immediately after the impact are A
v 0 and
B
v (6 ft/s)i
()
By
v j, determine ()
B
y
v and the velocity of C immediately
after impact.