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890 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 891
Problem 5.33
Three space-junk fragments with masses
m1D7:45 kg
,
m2D3:22 kg
,
and
m3D8:45 kg
were the only masses generated from an explosion
that split a single body apart. The fragments are traveling as shown
with
v1D7701 m=s
,
v2D6996 m=s
, and
v3D6450 m=s
. Assume
the velocity vectors of the fragments are coplanar,
✓D25ı
, and
D55ı
. The angles
✓
and
are measured with respect to lines that
are perpendicular to the velocity
Ev2
. If the system is isolated, determine
the mass and velocity of the single body before it exploded.
Solution
The mass
m
of the body before it exploded is equal to the sum of the masses of the
fragments:
892 Solutions Manual
Problem 5.34
A
175 lb
man, initially at rest at
A
on a floating platform, starts
walking to the right with a constant speed
v0D3ft=s
relative to
the platform until he reaches the right end of the platform at
B
.
The platform is attached to the pier by a rope that is initially slack
but that becomes taut before the man reaches
B
. Neglecting any
resistance to the motion of the platform due to the water, determine
the impulse provided to the person/platform system by the rope
when the rope becomes taut.
Solution
Referring to the figure at the right, we model the person and the platform as a
system of two particles subject to their own respective weights, namely,
mpg
Dynamics 2e 893
Problem 5.35
Collar
B
is at rest on a smooth horizontal guide when it is impacted by an
identical collar
A
traveling at a speed
v0D12 ft=s
. The collars are designed
to lock onto each other on impact, so
A
and
B
travel together after impact.
Neglecting friction, determine the common velocity of Aand Bafter impact.
Solution
We model the two collars as a system of particles constrained to move in the horizontal
direction. We assume that the collars
A
and
B
, as a system, are subject only to their
894 Solutions Manual
Problem 5.36
A
260 gr
(
1lb D7000 gr
) bullet
B
is fired into an
8600 lb
SUV
A
,
which is initially moving to the left with a speed
vAD15 mph
. If the
bullet becomes embedded into the SUV, how fast would the impact
speed of the bullet vBneed to be if the SUV is to be stopped cold?
Solution
We model both
A
and
B
as a system of particles. We assume that
A
and
B
, as a system, are subject only to their own weights
mAg
and
mBg
,
Dynamics 2e 895
Problem 5.37
These problems are an introduction to perfectly plastic impact (which we will cover in Section 5.2). In
each problem, model the vehicles
A
and
C
as particles and treat the swarm of bugs
B
hitting the vehicles
as a single particle. Also assume that the swarm of bugs sticks perfectly to each vehicle (this is what is
meant by a perfectly plastic impact).
An
80;000 lb
semitruck
A
(the maximum weight allowed in many states) is traveling at
70 mph
when
it encounters a swarm of mosquitoes
B
. The swarm is traveling at
1mph
in the opposite direction of the
truck. Assuming that the entire swarm sticks to the truck, the mass of each mosquito is
2mg
, and that all
of these mosquitoes do not significantly damage the truck, how many mosquitoes must have hit the truck
if it slows down by
2mph
on impact? If the same number of mosquitoes hit a small SUV
C
weighing
3000 lb and traveling at 70 mph, by how much would the SUV slow down?
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.
896 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 897
Problem 5.38
These problems are an introduction to perfectly plastic impact (which we will cover in Section 5.2). In
each problem, model the vehicles
A
and
C
as particles and treat the swarm of bugs
B
hitting the vehicles
as a single particle. Also assume that the swarm of bugs sticks perfectly to each vehicle (this is what is
meant by a perfectly plastic impact).
An
80;000 lb
semitruck
A
(the maximum weight allowed in many states) is traveling at
70 mph
when
it encounters a swarm of worker bees
B
. The swarm is traveling at
12 mph
in the opposite direction of
the truck. Assuming that the entire swarm sticks to the truck, the mass of each bee is
0:1
g, and that all of
these bees do not significantly damage the truck, how many bees must have hit the truck if it slows down
by
2mph
on impact? If the same number of bees hit a small SUV
C
weighing
3000 lb
and traveling at
70 mph, by how much would the SUV slow down?
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.
898 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 899
Problem 5.39
These problems are an introduction to perfectly plastic impact (which we will cover in Section 5.2). In
each problem, model the vehicles
A
and
C
as particles and treat the swarm of bugs
B
hitting the vehicles
as a single particle. Also assume that the swarm of bugs sticks perfectly to each vehicle (this is what is
meant by a perfectly plastic impact).
An
80;000 lb
semitruck
A
(the maximum weight allowed in many states) is traveling at
70 mph
when
it encounters a swarm of dragonflies
B
. The swarm is traveling at
33 mph
in the opposite direction of the
truck. Assuming that the entire swarm sticks to the truck, the mass of each dragonfly is
0:25
g, and that all
of these dragonflies do not significantly damage the truck, how many dragonflies must have hit the truck if
it slows down by
2mph
on impact? If the same number of dragonflies hit a small SUV
C
weighing
3000 lb
and traveling at 70 mph, by how much would the SUV slow down?
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.
