950 Solutions Manual
Problem 5.66
An
8600 lb
Ford Excursion
A
traveling with a speed
vAD55 mph
collides head-on with a
1990 lb
Smart Fortwo
B
traveling in the oppo-
site direction with a speed
vBD35 mph
. Determine the postimpact
velocity of the two cars if the impact is perfectly plastic.
Solution
Dynamics 2e 951
Problem 5.67
A
323 gr
bullet (
1lb D7000 gr
) hits a
2kg
block that is initially at rest.
After the collision, the bullet becomes embedded in the block, and they
slide a distance of
0:31
m. If the coefficient of friction between the
block and the ground is
kD0:7
, determine the preimpact speed of
the bullet. Although the definition of the unit “grain” is given in terms
of pounds, express the answer in SI units.
Solution
952 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 953
Problem 5.68
A
323 gr
bullet
B
(
1lb D7000 gr
) moving at
v0D800 ft=s
hits a
4lb
block
A
that is initially at rest. The block is attached to an uncompressed spring of
stiffness
kD6000 lb=ft
. After the collision, the bullet becomes embedded in
the block. Neglecting friction between the block and the surface on which it
slides, determine the compression of the spring required to bring the system to
a stop.
Solution
We model the bullet
B
and the block
A
as particles of masses
mA
and
mB
,
respectively. Since
B
becomes embedded in
A
, we model the collision of
954 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 955
Problem 5.69
The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as
a measure of the performance of firearms and ammunition (nowadays, the ballistic pendulum has been
replaced by the ballistic chronograph, an electronic device). The ballistic pendulum is a simple pendulum
that allows one to record the maximum swing angle of the pendulum arm caused by the firing of a bullet
into the pendulum bob.
Letting
L
be the length of the pendulum’s arm (whose mass is assumed to be negligible),
mA
be the
bob’s mass, and
mB
be the mass of the bullet, and assuming that the pendulum is at rest when the weapon
is fired, derive the formula that relates the pendulum’s maximum swing angle to the impact velocity of the
bullet.
Solution
We model the bullet
B
and the block
A
as particles of masses
mA
and
mB
, respectively. Since
B
becomes embedded in
A
, we model
956 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 957
Problem 5.70
The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as
a measure of the performance of firearms and ammunition (nowadays, the ballistic pendulum has been
replaced by the ballistic chronograph, an electronic device). The ballistic pendulum is a simple pendulum
that allows one to record the maximum swing angle of the pendulum arm caused by the firing of a bullet
into the pendulum bob.
Let LD1:5 m and mAD6kg. For George Washington’s 0.58 caliber pistol, which fired a roundball
of mass
mBD87
g, it is found that the maximum swing angle of the pendulum is
✓max D46ı
. Determine
the preimpact speed of the bullet B.
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.
958 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 959
Problem 5.71
The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as
a measure of the performance of firearms and ammunition (nowadays, the ballistic pendulum has been
replaced by the ballistic chronograph, an electronic device). The ballistic pendulum is a simple pendulum
that allows one to record the maximum swing angle of the pendulum arm caused by the firing of a bullet
into the pendulum bob.
Suppose we want to build a ballistic pendulum to test rifles using standard NATO
7:62 mm
ammunition,
i.e., ammunition for which a (single) cartridge weighs roughly
147 gr
(
1lb D7000 gr
) and the muzzle
speed is typically
2750 ft=s
. If the pendulum’s length is taken to be
5ft
, and if we are to fire from a short
distance so that there is a negligible decrease in speed before the bullet reaches the pendulum, what is the
minimum weight we need to give to the pendulum bob to avoid having the pendulum swing to an angle
greater than 90ı?
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.