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980 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 981
Problem 5.85
A steel ball is released from rest at the top of the incline as shown, rolls down the
incline, and eventually rebounds off a steel strike plate. The length
LD0:25
m,
✓D25ı
, and
hD0:15
m. Determine the rebound velocity of the ball if the
COR between the ball and the strike plate is
eD0:85
. Neglect friction between
the ball and the incline.
Solution
We divide the problem into three parts. First, determine the velocity of the steel ball as it comes off the
982 Solutions Manual
Computation.
We denote by
Oui
a unit vector parallel to the incline and pointing toward the bottom of the
incline:
OuiDcos ✓O{sin ✓O|
. Hence, using the result in the last of the Eq. (5), we have that the initial
Dynamics 2e 983
Problem 5.86
Newton’s cradle is a common desk toy consisting of a number of
identical pendulums with steel balls as bobs. These pendulums are
arranged in a row in such a way that, when at rest, each ball is tangent
to the next and the cords are all vertical. Assume that the COR for the
impact of a ball with the next is
eD1
.Hint: Although no gaps are
shown between the bobs, assume small gaps are present in all cases
so that the interactions can be examined as two-body impacts.
Explain why if you release the ball to the far left from a certain
angle, the ball in question comes to a stop after impact while all the
other balls do not seem to move except for the ball to the far right,
which swings upward and achieves a maximum swing angle equal to
the initial release angle of the ball to the far left.
Solution
984 Solutions Manual
Problem 5.87
Newton’s cradle is a common desk toy consisting of a number of
identical pendulums with steel balls as bobs. These pendulums are
arranged in a row in such a way that, when at rest, each ball is
tangent to the next and the cords are all vertical. Assume that the
COR for the impact of a ball with the next is
eD1
.Hint: Although
no gaps are shown between the bobs, assume small gaps are present
in all cases so that the interactions can be examined as two-body
impacts.
Explain why if you release the two balls to the far left from a
certain angle, the balls in question come to a stop right after impact
while all the other balls do not seem to move except for the two
balls to the far right, which swing upward and achieve a maximum
swing angle equal to the initial release angle of the two balls to the
far left.
Solution
Treat each impact as only involving two balls. The first impact will occur between
balls
2
and
3
. Because the COR
eD1
and the masses are identical we see from the
Dynamics 2e 985
Problem 5.88
Newton’s cradle is a common desk toy consisting of a number of
identical pendulums with steel balls as bobs. These pendulums are
arranged in a row in such a way that, when at rest, each ball is tangent
to the next and the cords are all vertical. Assume that the COR for the
impact of a ball with the next is
eD1
.Hint: Although no gaps are
shown between the bobs, assume small gaps are present in all cases
so that the interactions can be examined as two-body impacts.
Predict the swing pattern of the system in the figure if you release
from rest, and from a given angle, three of the five balls.
Solution
Treat each impact as only involving two balls. The first impact will occur between
balls
3
and
4
. Because the COR
eD1
and the masses are identical we see from the
986 Solutions Manual
Problem 5.89
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
A
and
B
become entangled. 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.
Solution
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 987
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.
988 Solutions Manual
Problem 5.90
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
.
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.
Dynamics 2e 989
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.
