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PROBLEM 13.142
The last segment of the triple jump track-and-field event is the
jump, in which the athlete makes a final leap, landing in a sand-
filled pit. Assuming that the velocity of a 80-kg athlete just
before landing is 9 m/s at an angle of 35° with the horizontal
and that the athlete comes to a complete stop in 0.22 s after
landing, determine the horizontal component of the average
impulsive force exerted on his feet during landing.
SOLUTION
PROBLEM 13.143
The design for a new cementless hip implant is to be studied using an
instrumented implant and a fixed simulated femur. Assuming the punch applies
an average force of 2 kN over a time of 2 ms to the 200 g implant determine
(a) the velocity of the implant immediately after impact, (b) the average
resistance of the implant to penetration if the implant moves 1 mm before
coming to rest.
SOLUTION
200 g 0.200 kg
m
= =
ave
2( ) (2)(0.001)
∆
ave
PROBLEM 13.144
A 28-g steel-jacketed bullet is fired with a velocity of 650 m/s toward
a steel plate and ricochets along path CD with a velocity 500 m/s.
Knowing that the bullet leaves a 50-mm scratch on the surface of the
plate and assuming that it has an average speed of 600 m/s while in
contact with the plate, determine the magnitude and direction of the
impulsive force exerted by the plate on the bullet.
6
8.6558
F 103.87 kN
83.33 10
y
−
= =
×
PROBLEM 13.145
A 25-ton railroad car moving at
2.5 mi/h is to be coupled to a 50
ton car which is at rest with
locked wheels
( 0.30).
k
m
=
Determine (a) the velocity of
both cars after the coupling is
completed, (b) the time it takes
for both cars to come to rest.
SOLUTION
PROBLEM 13.145 (Continued)
(1553)(3.6667) 0.1898
(0.30)(100,000)
t
= =
0.190 st=
PROBLEM 13.146
At an intersection car B was traveling south and car A was
traveling 30° north of east when they slammed into each other.
Upon investigation it was found that after the crash the two cars
got stuck and skidded off at an angle of 10° north of east. Each
driver claimed that he was going at the speed limit of 50 km/h and
that he tried to slow down but couldn’t avoid the crash because the
other driver was going a lot faster. Knowing that the masses of
cars A and B were 1500 kg and 1200 kg, respectively, determine
(a) which car was going faster, (b) the speed of the faster of the
two cars if the slower car was traveling at the speed limit.
SOLUTION
A
A
PROBLEM 13.147
The 650-kg hammer of a drop-hammer pile driver falls from a height of
1.2 m onto the top of a 140-kg pile, driving it 110 mm into the ground.
Assuming perfectly plastic impact
( 0),e=
determine the average
resistance of the ground to penetration.
SOLUTION
PROBLEM 13.147 (Continued)
AV
AV
PROBLEM 13.148
A small rivet connecting two pieces of sheet metal is being clinched
by hammering. Determine the impulse exerted on the rivet and the
energy absorbed by the rivet under each blow, knowing that the head
of the hammer has a weight of 1.5 lbs and that it strikes the rivet with
a velocity of 20 ft/s. Assume that the hammer does not rebound and
that the anvil is supported by springs and (a) has an infinite mass
(rigid support), (b) has a weight of 9 lb.
SOLUTION
21
HA
mm
PROBLEM 13.148 (Continued)
PROBLEM 13.149
Bullet B weighs 0.5 oz and blocks A and C both weigh
3 lb. The coefficient of friction between the blocks and
the plane is
0.25.
k
m
=
Initially the bullet is moving at
v0 and blocks A and C are at rest (Figure 1). After the
bullet passes through A it becomes embedded in block
C and all three objects come to stop in the positions
shown (Figure 2). Determine the initial speed of the
bullet v0.
SOLUTION
Masses:
62
0.5 970.5 10 lb s /ft
1
B
PROBLEM 13.149 (Continued)
06
−
0
PROBLEM 13.150
A 180-lb man and a 120-lb woman stand at opposite ends 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
PROBLEM 13.151
A 75-g ball is projected from a height of 1.6 m with a horizontal
velocity of 2 m/s and bounces from a 400-g smooth plate
supported by springs. Knowing that the height of the rebound is
0.6 m, determine (a) the velocity of the plate immediately after
the impact, (b) the energy lost due to the impact.
SOLUTION
Just before impact
2 (1.6) 5.603 m/s
y
vg= =
Just after impact
2 (0.6) 3.431 m/s
y
vg= =
(a) Conservation of momentum:
(y+
)
ball ball plate plate
0
yy
mv mv m v
′′
+=− +
plate
(0.075)(5.603) 0 0.075(3.431) 0.4v′
+=− +
plate
1.694 m/sv′=
(b) Energy loss
Initial energy
2
1
1
( ) (0.075)(2) 0.075 (1.6)
2
TV g+= +
PROBLEM 13.152
A ballistic pendulum is used to measure the speed of high-speed
projectiles. A 6-g bullet A is fired into a 1-kg wood block B
suspended by a cord of length l= 2.2 m. The block then swings
through a maximum angle of θ= 60o. Determine (a) the initial speed
of the bullet vo, (b) the impulse imparted by the bullet on the block,
(c) the force on the cord immediately after the impact
SOLUTION
( )
2
1
AB AB
AB
v
T mm g
l
=++
PROBLEM 13.153
A 1-oz bullet is traveling with a velocity of 1400 ft/s when it impacts and becomes
embedded in a 5-lb wooden block. The block can move vertically without friction.
Determine (a) the velocity of the bullet and block immediately after the impact, (b) the
horizontal and vertical components of the impulse exerted by the block on the bullet.
SOLUTION
2
1
PROBLEM 13.153 (Continued)
PROBLEM 13.154
In order to test the resistance of a chain to impact, the chain is suspended from
a 240-lb rigid beam supported by two columns. A rod attached to the last link
is then hit by a 60-lb block dropped from a 5-ft height. Determine the initial
impulse exerted on the chain and the energy absorbed by the chain, assuming
that the block does not rebound from the rod and that the columns supporting
the beam are (a) perfectly rigid, (b) equivalent to two perfectly elastic springs.
SOLUTION
PROBLEM 13.154 (Continued)
22
gg
PROBLEM 13.155
The coefficient of restitution between the two collars is known to be
0.70. Determine (a) their velocities after impact, (b) the energy loss
during impact.
