IMPULSE AND MOMENTUM
Chapter 7
7.1 The Impulse-Momentum Theorem
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This section deals with time-varying forces affecting
the motion of objects.
The effects of these forces will be discussed using
the concepts of impulse and linear momentum.
Consider this high-speed camera picture of
a bat and ball collision. Describe it. To
learn more go to
http://www.fsus.fsu.edu/mcquone/scicam/
ActionReaction.htm
Definition of Impulse
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The impulse (J) of a force is the product of the
average force (F) and the time interval (∆t) during
which the force acts:
Impulse is a vector quantity
Direction is the same as average force direction
SI Unit: Newton •second (N•s)
J  Ft
Practically Speaking
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Large impulses produce large changes in motion.
I see… a large average force
over a long time period will
produce one very large
change in a baseball’s motion.
But a more massive ball will
have a smaller velocity after
being hit.
Hint for baseball and softball!
Linear Momentum
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The linear momentum (p) of an object is the product
of the object’s mass (m) and velocity (v).
Momentum is a vector quantity
SI Unit: kilogram•meter/second (kg•m/s)
p  mv
Impulse-Momentum Theorem
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By combining what we know about Newton’s 2nd
Law, impulse, and momentum we can derive the
Impulse-Momentum Theorem
vf  v0
a
t
acceleration
 F  m(
v f  v0
t
Combined with Newton’s
2nd Law
)
mv f  mv0
t
The net average force is
a change in momentum
per unit of time.
Impulse-Momentum Theorem
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When a net force acts on an object, the impulse of
the force is equal to the change in momentum of the
object:
Impulse = Change in Momentum
( F )t  mvf  mv0
**If solving for (F), the force you solve for will be the force that
is causing the change in momentum. Be careful when
interpreting questions!
Example: A Rainstorm (pg. 199)
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During a storm, rain comes down with a velocity of
v0= -15m/s and hits the roof of a car
perpendicularly. The mass of rain per second that
strikes the car roof is 0.600kg/s. Assuming that the
rain comes to rest upon striking the car, find the
average force exerted by the rain on the roof.
Hint: Momentum is a vector! For motion in one
dimension, be sure to indicate the direction by
assigning a plus or a minus sign to it.
Hailstones vs. Raindrops
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Just like the happy ball and sad ball, raindrops and
hailstones will fall in a very similar manner.
The raindrops will come to a stop after hitting the
car roof. Hailstones will bounce.
Given all the same variables for mass, time, and
initial velocity, the hailstones will apply a greater
force to the roof than the raindrops will.
Make sure you can explain this!
7.2 The Principle of Conservation of
Linear Momentum
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The impulse-momentum theorem leads to the
principle of conservation of linear momentum.
Consider collisions like those discussed in class
(baseball, cars, etc).
Collisions will be affected by the mass and velocity
of all objects involved in collision.
Internal and External forces acting on the system
must also be considered.
Internal vs. External
Internal
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Forces that the objects
within the system exert
on each other.
Baseball force on bat,
bat force on ball.
External
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Forces exerted on the
objects by agents
external to the system
Weight of the ball and
the bat (weight is a
force coming from the
Earth)
Friction, air resisitance
Conservation of Linear Momentum
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In an isolated system (no net external forces are
acting), the total momentum before collision is equal
to the total momentum after collision.
It is important to realize that the total linear
momentum may be conserved even when the kinetic
energies of the individual parts of the system
change.
m v  m v  m1v1  m2v2
'
1 1
'
2 2
7.3 Collisions on One Dimension
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There are many different types of collisions and
situations to analyze.
Atoms and subatomic particles completely transfer
kinetic energy to and from one another.
In “our world”, KE is generally converted into heat
or used in creating permanent damage to an
object.
Because of the differences in collision types, we
categorize them into to main groups.
Types of Collisions
Elastic

Inelastic
One in which the total
kinetic energy of the
system after the
collision is equal to the
total kinetic energy
before collision
Give examples of elastic,
inelastic, and completely
inelastic collisions!
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The total KE of the
system is NOT the same
before and after
collision.
If the objects stick
together after colliding,
the collision is called
completely inelastic.
7.4 Collisions in Two Dimensions
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Examples of collisions so far have been one
dimensional. We have used (+) or (-) in order
indicate direction.
We must remember, however, that momentum is a
vector quantity and has to be treated as such.
The law of conservation of momentum holds true
when objects move in two dimensions (x and y)
In these cases, the x- and y- components are
conserved separately. Use vector addition to solve!
Remember: by definition p is in the same direction
as v
7.4 Center of Mass
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The center of mass (cm) is a point that represents
the average location for the total mass of a system.
xcm
If the two masses are
equal, it would make
sense that the center
of mass is ½ way
between the
particles.
m1 x1  m2 x2

m1  m2
If there are more than
two masses and they
are not aligned in a
plane, it would be
necessary to find the
x- and y- components
of the center of mass
of each.
To find the velocity of
the center of mass use
the equation…
vcm
m1v1  m2v2

m1  m2
Helpful websites and hints
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Navigate your text website. VERY helpful.
www.physicsclassroom.com (navigate to
momentum)
Continue to draw pictures and LABEL EVERYTHING!
Practice, practice, practice
Be careful of signs!