Question:
Two identical pool balls with a 2.37-in. diameter may move freely
on a pool table. Ball
B
is at rest, and ball
A
has an initial velocity of
v
=
v
0
i
. (
a
) Knowing that
b
= 2 in. and
e
= 0.7, determine the
velocity of each ball after impact. (
b
) Show that if
e
= 1, the final
velocities of the balls form a right angle for all values of
b
.
Fig. P13.165
Answer :
Draw the velocity diagram, impact phases of ball A and ball B as
shown in figures.

From figure 1, calculate the angle between the horizontal and the normal direction
of the impact.
Here,
is the diameter of the balls and
is the horizontal distance between the
two balls.
Substitute
for
and
for
.
(a)

From the figure, using the principle of impulse and momentum, calculate the
velocity of the balls
A
and
B
in the tangential direction.
Ball
A
â€“
Here,
is the mass of the ball,
is the velocity of the ball before the impact,
is the force on the ball,
is the velocity of ball
A
in the tangential direction,
is the initial velocity of ball
A
and
is the final velocity of ball
A
.
Substitute
for
.
â€¦â€¦ (1)
Ball
B
â€“
Here,
is the initial velocity of ball
B

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- Summer '16
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- Velocity, initial velocity, Ball B