PROBLEM 14.13
A system consists of three particles A, B, and C. We know
that 3
A
m
kg, 2
B
m
kg, and 4
C
m kg and that the
velocities of the particles expressed in m/s are, respectively,
422,
Avijk
43,
Bvij
and 242.
C vijk
Determine the angular momentum O
Hof the system about O.
PROBLEM 14.14
For the system of particles of Prob. 14.13, 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 G
H of the system about G. Also verify that he
answers to this problem and to problem 14.13 satisfy the
equation given in Prob. 14.27.
PROBLEM 14.14 (Continued)
PROBLEM 14.15
A 13-kg projectile is passing through the origin O with a velocity v0 (35 m/s)i when it explodes into two
fragments A and B, of mass 5 kg and 8 kg, respectively. Knowing that 3 s later the position of fragment A is
(90 m, 7 m, –14 m), determine the position of fragment B at the same instant. Assume 9.81
y
ag m/s2
and neglect air resistance.
PROBLEM 14.16
A 300-kg space vehicle traveling with a velocity v0 (360 m/s)i passes through the origin O at t 0.
Explosive charges then separate the vehicle into three parts A, B, and C, with mass, respectively, 150 kg, 100 kg,
and 50 kg. Knowing that at t 4 s, the positions of parts A and B are observed to be A (1170 m, –290 m,
–585 m) and B (1975 m, 365 m, 800 m), determine the corresponding position of part C. Neglect the effect
of gravity.
PROBLEM 14.17
A 2-kg model rocket is launched vertically and reaches an
altitude of 70 m with a speed of 30 m/s at the end of powered
flight, time t 0. As the rocket approaches its maximum
altitude it explodes into two parts of masses 0.7 kg
A
m and
1.3 kg.
B
m Part A is observed to strike the ground 80 m west
of the launch point at t 6 s. Determine the position of part B at
that time.
PROBLEM 14.18
An 18-kg cannonball and a 12-kg cannonball are chained
together and fired horizontally with a velocity of 165 m/s from
the top of a 15-m wall. The chain breaks during the flight of the
cannonballs and the 12-kg cannonball strikes the ground
at t 1.5 s, at a distance of 240 m from the foot of the wall, and
7 m to the right of the line of fire. Determine the position of the
other cannonball at that instant. Neglect the resistance of the
air.
PROBLEM 14.19
Car A was traveling east at high speed
when it collided at Point O with car B,
which was traveling north at 45 mi/h. Car
C, which was traveling west at 60 mi/h,
was 32 ft east and 10 ft north of Point O
at the time of the collision. Because the
pavement was wet, the driver of car C
could not prevent his car from sliding into
the other two cars, and the three cars,
stuck together, kept sliding until they hit
the utility pole P. Knowing that the
weights of cars A, B, and C are,
respectively, 3000 lb, 2600 lb, and 2400
lb, and neglecting the forces exerted on
the cars by the wet pavement, solve the
problems indicated.
Knowing that the speed of car A was 75
mi/h and that the time elapsed from the
first collision to the stop at P was 2.4 s,
determine the coordinates of the utility
pole P.
PROBLEM 14.19 (Continued)
PROBLEM 14.20
Car A was traveling east at high speed
when it collided at Point O with car B,
which was traveling north at 45 mi/h. Car
C, which was traveling west at 60 mi/h,
was 32 ft east and 10 ft north of Point O
at the time of the collision. Because the
pavement was wet, the driver of car C
could not prevent his car from sliding into
the other two cars, and the three cars,
stuck together, kept sliding until they hit
the utility pole P. Knowing that the
weights of cars A, B, and C are,
respectively, 3000 lb, 2600 lb, and 2400
lb, and neglecting the forces exerted on
the cars by the wet pavement, solve the
problems indicated. Knowing that the
coordinates of the utility pole are
46 ft
P
x and 59 ft,
P
y determine
(a) the time elapsed from the first
collision to the stop at P, (b) the speed of
car A.