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160
6
CHAPTER
OUTLINE
6.1
Momentum and Impulse
6.2
Conservation of
Momentum
6.3
Collisions
6.4
Glancing Collisions
6.5
Rocket Propulsion
© Reuters/Corbis
A small buck from the massive
bull transfers a large amount of
momentum to the cowboy, resulting
in an involuntary dismount.
Momentum and Collisions
What happens when two automobiles collide? How does the impact affect the motion of
each vehicle, and what basic physical principles determine the likelihood of serious injury?
How do rockets work, and what mechanisms can be used to overcome the limitations im
posed by exhaust speed? Why do we have to brace ourselves when Fring small projectiles at
high velocity? ±inally, how can we use physics to improve our golf game?
To begin answering such questions, we introduce
momentum
. Intuitively, anyone or any
thing that has a lot of momentum is going to be hard to stop. In politics, the term is
metaphorical. Physically, the more momentum an object has, the more force has to be applied
to stop it in a given time. This concept leads to one of the most powerful principles in physics:
conservation of momentum
. Using this law, complex collision problems can be solved without
knowing much about the forces involved during contact. We’ll also be able to derive informa
tion about the average force delivered in an impact. With conservation of momentum, we’ll
have a better understanding of what choices to make when designing an automobile or a
moon rocket, or when addressing a golf ball on a tee.
6.1 MOMENTUM AND IMPULSE
In physics, momentum has a precise defnition. A slowly moving brontosaurus has
a lot oF momentum, but so does a little hot lead shot From the muzzle oF a gun. We
thereFore expect that momentum will depend on an object’s mass and velocity.
The linear momentum
oF an object oF mass
m
moving with velocity
is the
product oF its mass and velocity :
[6.1]
SI unit: kilogrammeter per second (kg
?
m/s)
p
:
;
v
:
v
:
p
:
Doubling either the mass or the velocity oF an object doubles its momentum; dou
bling both quantities quadruples its momentum. Momentum is a vector quantity
Linear momentum
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Momentum and Impulse
161
with the same direction as the object’s velocity. Its components are given in two di
mensions by
p
x
±
mv
x
p
y
±
mv
y
where
p
x
is the momentum of the object in the
x
direction and
p
y
its momentum
in the
y
direction.
Changing the momentum of an object requires the application of a force. This
is, in fact, how Newton originally stated his second law of motion. Starting from
the more common version of the second law, we have
[6.2]
where the mass
m
and the forces are assumed constant. The quantity in parenthe
ses is just the momentum, so we have the following result:
The change in an object’s momentum
divided by the elapsed time
D
t
equals the constant net force
acting on the object:
[6.3]
This equation is also valid when the forces are not constant, provided the limit is
taken as
D
t
becomes inFnitesimally small. Equation 6.3 says that if the net force on
an object is zero, the object’s momentum doesn’t change. In other words, the linear
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 Spring '08
 Turner
 Mass, Momentum

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