PROBLEM 14.50
Three small spheres A, B, and C, each of mass m, are connected to a
small ring D of negligible mass by means of three inextensible,
inelastic cords of length l. The spheres can slide freely on a frictionless
horizontal surface and are rotating initially at a speed 0
v about ring D
which is at rest. Suddenly the cord CD breaks. After the other two
cords have again become taut, determine (a) the speed of ring D,
(b) the relative speed at which spheres A and B rotate about D, (c) the
fraction of the original energy of spheres A and B that is dissipated
when cords AD and BD again became taut.
PROBLEM 14.50 (Continued)
PROBLEM 14.51
In a game of billiards, ball A is given an initial velocity 0
v along
the longitudinal axis of the table. It hits ball B and then ball C,
which are both at rest. Balls A and C are observed to hit the sides
of the table squarely at
A
and C, respectively, and ball B is
observed to hit the side obliquely at .
B
Knowing that
04 m/s,v 1.92 m/s,
A
v and 1.65 m,a determine (a) the
velocities B
v and C
v of balls B and C, (b) the Point C
where
ball C hits the side of the table. Assume frictionless surfaces and
perfectly elastic impacts (that is, conservation of energy).
PROBLEM 14.51 (Continued)
PROBLEM 14.52
For the game of billiards of Problem 14.51, it is now assumed
that 05v
m/s, 3.2
C
v m/s, and 1.22c m. Determine
(a) the velocities
A
v and B
v of balls A and B, (b) the Point
A
where ball A hits the side of the table.
PROBLEM 14.51 In a game of billiards, ball A is given an initial
velocity 0
v along the longitudinal axis of the table. It hits ball B
and then ball C, which are both at rest. Balls A and C are
observed to hit the sides of the table squarely at
A
and C
,
respectively, and ball B is observed to hit the side obliquely at .
B
Knowing that 04 m/s,v 1.92 m/s,
A
v and 1.65 m,a
determine (a) the velocities B
v and C
v of balls B and C, (b) the
Point C
where ball C hits the side of the table. Assume
frictionless surfaces and perfectly elastic impacts (that is,
conservation of energy).
A
PROBLEM 14.53
Two small disks A and B, of mass 3 kg and
1.5 kg, respectively, may slide on a
horizontal, frictionless surface. They are
connected by a cord, 600 mm, long, and
spin counterclockwise about their mass
center G at the rate of 10 rad/s. At
0,
t
the
coordinates of G are 00
0, 2 m,xy
and
its velocity is 0
(1.2 m/s) (0.96 m/s) .vi j
Shortly thereafter, the cord breaks; disk A is
then observed to move along a path parallel
to the y axis and disk B along a path which
intersects the x axis at a distance b
7.5 m
from O. Determine (a) the velocities of A
and B after the cord breaks, (b) the distance
a from the y-axis to the path of A.
PROBLEM 14.53 (Continued)
PROBLEM 14.54
Two small disks A and B, of mass 2 kg and 1 kg,
respectively, may slide on a horizontal and
frictionless surface. They are connected by a cord
of negligible mass and spin about their mass center
G. At
0,
t
G is moving with the velocity 0
v
and
its coordinates are 0
x
0, 0
1.89 m.y
Shortly
thereafter, the cord breaks and disk A is observed to
move with a velocity
(5 m/s)
A
vj
in a straight
line and at a distance
2.56 ma
from the y-axis,
while B moves with a velocity
(7.2 m/s) (4.6 m/s)
B
vij
along a path
intersecting the x-axis at a distance
7.48 mb
from the origin O. Determine (a) the initial velocity
0
v
of the mass center G of the two disks, (b) the
length of the cord initially connecting the two disks,
(c) the rate in rad/s at which the disks were spinning
about G.
PROBLEM 14.54 (Continued)
PROBLEM 14.55
Three small identical spheres A, B, and C, which can slide on a horizontal, frictionless surface, are attached to
three 9-in-long strings, which are tied to a ring G. Initially, the spheres rotate clockwise about the ring with
a relative velocity of 2.6 ft/s and the ring moves along the x-axis with a velocity
0
v
(1.3 ft/s)
i
.
Suddenly,
the ring breaks and the three spheres move freely in the xy plane with A and B, following paths parallel to the
y-axis at a distance 1.0 ft
a
from each other and C following a path parallel to the x-axis. Determine
(a) the velocity of each sphere, (b) the distance d.