960 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 961
Problem 5.72
Two bumper cars
A
and
B
collide head-on as shown. The weights of
A
and
B
(including the drivers) are
WAD635 lb
and
WBD650 lb
, respectively. In addition,
the preimpact speeds of Aand Bare v
AD6ft=s and v
BD4ft=s, respectively.
Determine the postimpact speeds of
A
and
B
if the COR for the impact is
eD0:65.
Solution
We model the impact of
A
and
B
as a direct central impact of two particles. The impact-
relevant FBD of
A
and
B
as a system is shown below in the figure at the right. We will
962 Solutions Manual
Problem 5.73
Two bumper cars
A
and
B
collide head-on as shown. The weights of
A
and
B
(including the drivers) are
WAD635 lb
and
WBD650 lb
, respectively. In addition,
the preimpact speeds of Aand Bare v
AD6ft=s and v
BD4ft=s, respectively.
Determine the COR of the impact and the postimpact speed of
B
if the postimpact
speed of Ais equal to zero.
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 963
Problem 5.74
Consider a direct central impact for two spheres. Let
mA
,
mB
, and
e
denote
the mass of sphere
A
, the mass of sphere
B
, and the COR, respectively. If
sphere
B
is at rest before the collision, determine the relation that
mA
,
mB
,
and
e
need to satisfy in order for
A
to come to a complete stop right after
impact.
Solution
964 Solutions Manual
Problem 5.75
A bullet
B
of mass
mB
traveling with a speed
v0D1200 m=s
ricochets off a fixed steel plate
A
of mass
mA
. Let
mAmB
so that it can be assumed that
mB=m
A!0
. If the incidence angle of the bullet is
✓D15ı
and the COR of the impact is
eD0:5
, determine the rebound angle
, as well as the bullet’s
rebound speed.
Solution
Dynamics 2e 965
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.
Problem 5.76
The official rules of tennis specify that
The ball shall have a [re]bound of more than
53 in:
(
134:62 cm
) and less than
58 in:
(
147:32 cm
) when dropped
100 in:(254:00 cm) upon a concrete base.
Understanding the expression “when dropped” as “when dropped from
rest,” determine the range of acceptable CORs for the collision of a tennis
ball with concrete.
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 967
Problem 5.77
The official rules of basketball specify that a basketball is properly inflated
such that when it is dropped onto the playing surface from
a height of about
1800 mm
measured from the bottom of the
ball, it will rebound to a height, measured to the top of the
ball, of not less than about
1200 mm
nor more than about
1400 mm.
Based on this rule, ignoring the diameter of the ball, and understanding
the expression “when it is dropped” as “when it is dropped from rest,”
determine the range of acceptable CORs for the collision between the ball
and the court’s surface.
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.
968 Solutions Manual
A Ford Excursion
A
, with a mass
mAD3900 kg
and traveling with a speed
vAD25 km=h
, collides head-on with a Mini Cooper
B
, with a mass
mBD
1200 kg
, traveling in the opposite direction with a speed
vBD15 km=h
. Model
the impact of
A
and
B
as an unconstrained direct central impact of particles
and determine the time needed for each car to stop if the cars slide after impact
with kD0:8 and if the impact’s COR is eD0:1.
Solution
We divide the problem into two parts. First, we analyze the impact between
A
and
B
. Second we analyze the
motion of Aand Bafter the collision.
Dynamics 2e 969
Sliding motion Aand Bafter impact.