990 Solutions Manual
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Dynamics 2e 991
Problem 5.91
A
31;000 lb
truck
A
and a
3970 lb
sports car
B
collide at an intersection.
Right before the collision, the truck and the sports car are traveling at
v
AD60 mph
and
v
BD50 mph
. Assume that the entire intersection
forms a horizontal surface.
Letting the line of impact be parallel to the ground and to the preim-
pact velocity of the truck, determine the postimpact velocities of
A
and
B
if the contact between
A
and
B
is frictionless and the COR
eD0:1
.
Furthermore, assuming that the truck and the car slide after impact and
that the coefficient of kinetic friction is
kD0:7
, determine the position
at which
A
and
B
come to a stop relative to the position they occupied
at the instant of impact.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
992 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 993
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
994 Solutions Manual
Problem 5.92
Competition billiard balls and tables need to adhere to strict standards
(see the Billiard Congress of America for standards in the United States).
Specifically, billiard balls must weigh between 5.5 and
6oz
, and they must
be 2:25 ˙0:005 in:in diameter.
Treating the objects as particles, determine whether or not it is possible
to have a moving ball
A
hit a stationary ball
B
so that
A
stops right after
the impact, if
A
and
B
have the same diameter but not the same weight
(since it is possible to have a weight difference of up to
0:5 oz
while staying
within regulations). Assume that the COR
eD1
.Hint: Since the balls
must be treated as particles and not as finite-size bodies, the fact that one
can impart spin to a real ball is not relevant to the solution of this problem.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 995
Problem 5.93
Competition billiard balls and tables need to adhere to strict standards
(see the Billiard Congress of America for standards in the United States).
Specifically, billiard balls must weigh between 5.5 and
6oz
, and they must
be 2:25 ˙0:005 in:in diameter.
Professional billiard players can easily impart to a ball a speed of
20 mph
. Assume the tolerance on the ball diameter to be
1=100 in:
instead
of
5=1000 in:
and determine the outcome of the collision between (a)
a
2:26 in:
diameter ball traveling at
20 mph
with a stationary
2:24 in:
diameter ball (i.e., each ball is at the extreme limit of tolerance relative to
the nominal diameter) and (b) a
2:24 in:
diameter ball traveling at
20 mph
with a stationary
2:26 in:
diameter ball. Assume that the COR
eD1
and
that the weights of the two balls are identical. Furthermore, assume that
the contact between the balls and the table can be treated as essentially
frictionless. Hint: The difference in size implies that the LOI is not parallel
to the table.
Solution
We divide the overall solution into two parts. We first consider case (a), in which the stationary ball is smaller
996 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 997
Case (b).
998 Solutions Manual
Problem 5.94
Ball
B
is stationary when it is hit by an identical ball
A
as shown, with
ˇD45ı
.
The preimpact speed of ball Ais v0D1m=s.
Determine the postimpact velocity of ball
B
if the COR of the collision
eD1.
Solution
We model the impact of
A
and
B
as an unconstrained oblique central
impact of two particles. The impact-relevant FBD of
A
and
B
as a
Dynamics 2e 999
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