978-0077687342 Chapter 14 Part 1

subject Type Homework Help
subject Pages 14
subject Words 1557
subject Authors Brian Self, E. Johnston, Ferdinand Beer, Phillip Cornwell

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CHAPTER 14
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PROBLEM 14.1
A 30-g bullet is fired with a horizontal velocity of 450 m/s and
becomes embedded in block B which has a mass of 3 kg. After
the impact, block B slides on 30-kg carrier C until it impacts
the end of the carrier. Knowing the impact between B and C is
perfectly plastic and the coefficient of kinetic friction between
B and C is 0.2, determine (a) the velocity of the bullet and B
after the first impact, (b) the final velocity of the carrier.
SOLUTION
For convenience, label the bullet as particle A of the system of three particles A, B, and C.
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PROBLEM 14.2
Two identical 1350-kg automobiles A and B are at
rest with their brakes released when B is struck by a
5400-kg truck C which is moving to the left at 8
km/h. A second collision then occurs when B strikes
A. Assuming the first collision is perfectly plastic
and the second collision is perfectly elastic,
determine the velocities of the three vehicles just
after the second collision.
SOLUTION
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PROBLEM 14.3
An airline employee tosses two suitcases, of weight 30 lb and
40 lb, respectively, onto a 50-lb baggage carrier in rapid
succession. Knowing that the carrier is initially at rest and that
the employee imparts a 9-ft/s horizontal velocity to the 30-lb
suitcase and a 6-ft/s horizontal velocity to the 40-lb suitcase,
determine the final velocity of the baggage carrier if the first
suitcase tossed onto the carrier is (a) the 30-lb suitcase,
(b) the 40-lb suitcase.
SOLUTION
BC
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PROBLEM 14.3 (Continued)
ABC
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PROBLEM 14.4
A bullet is fired with a horizontal velocity of 1500 ft/s through
a 6-lb block A and becomes embedded in a 4.95-lb block B.
Knowing that blocks A and B start moving with velocities of
5 ft/s and 9 ft/s, respectively, determine (a) the weight of the
bullet, (b) its velocity as it travels from block A to block B.
SOLUTION
The masses are m for the bullet and A
m and B
m for the blocks.
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PROBLEM 14.5
Two swimmers A and B, of weight 190 lb and 125 lb,
respectively, are at diagonally opposite corners of a floating raft
when they realize that the raft has broken away from its anchor.
Swimmer A immediately starts walking toward B at a speed of 2
ft/s relative to the raft. Knowing that the raft weighs 300 lb,
determine (a) the speed of the raft if B does not move, (b) the
speed with which B must walk toward A if the raft is not to
move.
SOLUTION
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PROBLEM 14.6
A 180-lb man and a 120-lb woman stand side by side at the
same end of a 300-lb boat, ready to dive, each with a 16-ft/s
velocity relative to the boat. Determine the velocity of the
boat after they have both dived, if (a) the woman dives first,
(b) the man dives first.
SOLUTION
2
480
(b) Man dives first.
2
420
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PROBLEM 14.7
A 40-Mg boxcar A is moving in a railroad switchyard with a velocity of 9 km/h toward cars B and C, which
are both at rest with their brakes off at a short distance from each other. Car B is a 25-Mg flatcar supporting a
30-Mg container, and car C is a 35-Mg boxcar. As the cars hit each other they get automatically and tightly
coupled. Determine the velocity of car A immediately after each of the two couplings, assuming that the
container (a) does not slide on the flatcar, (b) slides after the first coupling but hits a stop before the second
coupling occurs, (c) slides and hits the stop only after the second coupling has occurred.
SOLUTION
Each term of the conservation of momentum equation is mass times velocity. As long as the same units are
used in all terms, any unit may be used for mass and for velocity. We use Mg for mass and km/h for velocity
(b) Container slides after 1st coupling, stops before 2nd
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PROBLEM 14.7 (Continued)
(c) Container slides and stops only after 2nd coupling
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PROBLEM 14.8
Two identical cars A and B are at rest on a loading dock with brakes released. Car C, of a slightly different
style but of the same weight, has been pushed by dockworkers and hits car B with a velocity of 1.5 m/s.
Knowing that the coefficient of restitution is 0.8 between B and C and 0.5 between A and B, determine the
velocity of each car after all collisions have taken place.
SOLUTION
AB
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PROBLEM 14.8 (Continued)
Relative velocities:
()()
(0 1.35)(0.5)
A
BAB B A
BA
vve vv
vv
 



CBA
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PROBLEM 14.9
A 20-kg base satellite deploys three sub-satellites, each which
has its own thrust capabilities, to perform research on tether
propulsion. The weights of sub-satellite A, B, and C are 4 kg,
6 kg, and 8 kg, respectively, and their velocities expressed in
m/s are given by vA = 4i - 2j + 2k, vB = i + 4j, vC = 2i + 2j +
4k. At the instant shown, what is the angular momentum HO
of the system about the base satellite?
SOLUTION
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PROBLEM 14.10
For the satellite system of Prob. 14.9, assuming that the
velocity of the base satellite is zero, determine (a) the position
vector r of the mass center G of the system, (b) the linear
momentum mv of the system, (c) the angular momentum HG
of the system about G. Also, verify that the answers to this
problem and to Prob. 14.9 satisfy the equation given in Prob.
14.27.
PROBLEM 14.9 A 20-kg base satellite deploys three sub-
satellites, each which has its own thrust capabilities, to
perform research on tether propulsion. The weights of sub-
satellite A, B, and C are 4 kg, 6 kg, and 8 kg, respectively, and
their velocities expressed in m/s are given by vA = 4i - 2j +
2k, vB = i + 4j, vC = 2i + 2j + 4k. At the instant shown, what
is the angular momentum HO of the system about the base
satellite?
SOLUTION
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PROBLEM 14.10 (Continued)
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PROBLEM 14.11
A system consists of three identical 19.32-lb particles A, B, and C. The
velocities of the particles are, respectively, ,
A
A
vvj
,
BB
vvi
and
.
CC
vvk
Knowing that the angular momentum of the system about
O, expressed in ft lb s
is 1.2 ,
OHk
determine (a) the velocities of
the particles, (b) the angular momentum of the system about its mass
center G.
SOLUTION
1.8
22
 
ijk
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PROBLEM 14.11 (Continued)
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PROBLEM 14.12
A system consists of three identical 19.32-lb particles A, B, and C. The
velocities of the particles are, respectively, ,
A
A
vvj
,
BB
vvi
and
,
CC
vvk
and the magnitude of the linear momentum L of the system
is 9 lb s.
Knowing that ,
GO
HH
where G
H is the angular
momentum of the system about its mass center G and O
H is the
angular momentum of the system about O, determine (a) the velocities
of the particles, (b) the angular momentum of the system about O.
SOLUTION

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PROBLEM 14.12 (Continued)
AA BB CC
mmm

vvvr

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