PROBLEM 13.156
Collars A and B, of the same mass m, are moving toward each other
with identical speeds as shown. Knowing that the coefficient of
restitution between the collars is e, determine the energy lost in the
impact as a function of m, e and v.
12
PROBLEM 13.157
One of the requirements for tennis balls to be used in official competition is that, when dropped onto a rigid
surface from a height of 100 in., the height of the first bounce of the ball must be in the range 53 in.
58 in.h≤≤
Determine the range of the coefficient of restitution of the tennis balls satisfying this requirement.
PROBLEM 13.158
Two disks sliding on a frictionless horizontal plane with opposite velocities of the
same magnitude
0
v
hit each other squarely. Disk A is known to have a weight of
6-lb and is observed to have zero velocity after impact. Determine (a) the weight of
disk B, knowing that the coefficient of restitution between the two disks is 0.5,
(b) the range of possible values of the weight of disk B if the coefficient of
restitution between the two disks is unknown.
SOLUTION
PROBLEM 13.159
To apply shock loading to an artillery shell, a 20-kg pendulum A is
released from a known height and strikes impactor B at a known
velocity v0. Impactor B then strikes the 1–kg artillery shell C.
Knowing the coefficient of restitution between all objects is e,
determine the mass of B to maximize the impulse applied to the
artillery shell C.
SOLUTION
PROBLEM 13.159 (Continued)
B
PROBLEM 13.160
Packages in an automobile parts supply house are transported to
the loading dock by pushing them along on a roller track with
very little friction. At the instant shown, packages B and C are
at rest and package A has a velocity of 2 m/s. Knowing that the
coefficient of restitution between the packages is 0.3, determine
(a) the velocity of package C after A hits B and B hits C, (b) the
velocity of A after it hits B for the second time.
SOLUTION
BC
PROBLEM 13.160 (Continued)
PROBLEM 13.161
Three steel spheres of equal mass are suspended from the ceiling by cords of
equal length which are spaced at a distance slightly greater than the diameter of
the spheres. After being pulled back and released, sphere A hits sphere B, which
then hits sphere C. Denoting by e the coefficient of restitution between the
spheres and by
0
v
the velocity of A just before it hits B, determine (a) the
velocities of A and B immediately after the first collision, (b) the velocities of B
and C immediately after the second collision. (c) Assuming now that n spheres are
suspended from the ceiling and that the first sphere is pulled back and released as
described above, determine the velocity of the last sphere after it is hit for the first
time. (d) Use the result of part c to obtain the velocity of the last sphere when
8n=
and
0.9.e=
SOLUTION
(
a) First collision (between A and B)
0
2
CB
PROBLEM 13.161
(Continued)
Solving equations (3) and (4) simultaneously
( ) ( ) ( )
0
1
11
ve e
v ve
+
′= ++
80
PROBLEM 13.162
At an amusement park there are 200–kg bumper cars A, B, and C that have riders with masses of 40 kg, 60 kg,
and 35 kg respectively. Car A is moving to the right with a velocity
2 m/s
A=v
and car C has a velocity vB
1.5 m/s=
to the left, but car B is initially at rest. The coefficient of restitution between each car is 0.8.
Determine the final velocity of each car, after all impacts, assuming (a) cars A and C hit car B at the same
time, (b) car A hits car B before car C does.
SOLUTION
C
PROBLEM 13.162 (Continued)
B
PROBLEM 13.162 (Continued)
127.50 kg m/s.
= ⋅
PROBLEM 13.163
At an amusement park there are 200–kg bumper cars A, B, and C that have riders with masses of 40 kg, 60 kg,
and 35 kg respectively. Car A is moving to the right with a velocity
2 m/s
A
=v
when it hits stationary car B.
The coefficient of restitution between each car is 0.8. Determine the velocity of car C so that after car B
collides with car C the velocity of car B is zero.
PROBLEM 13.163 (Continued)
PROBLEM 13.164
Two identical billiard balls can move freely on a horizontal
table. Ball A has a velocity v0 as shown and hits ball B, which is
at rest, at a Point C defined by
θ
= 45°. Knowing that the
coefficient of restitution between the two balls is e = 0.8 and
assuming no friction, determine the velocity of each ball after
impact.
00
2
Bn
PROBLEM 13.164 (Continued)
(A)
PROBLEM 13.165
Two identical pool balls of 2.37-in. diameter may move freely on a pool
table. Ball B is at rest and ball A has an initial velocity
0
.v=vi
(a) Knowing that
2 in.b=
and
0.7,e=
determine the velocity of each ball
after impact. (b) Show that if
1,e=
the final velocities of the balls form a
right angle for all values of b.
SOLUTION
Geometry at instant of impact.
2
b
PROBLEM 13.165 (Continued)
PROBLEM 13.166
A 600–g ball A is moving with a velocity of magnitude 6 m/s when it is
hit as shown by a 1-kg ball B which has a velocity of magnitude 4 m/s.
Knowing that the coefficient of restitution is 0.8 and assuming no
friction, determine the velocity of each ball after impact.
2.314 2.314 ( )
() 0
Bt
Bt
Bt
v
v
′
−=−+
′=
PROBLEM 13.166 (Continued)
n–direction: