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Change in momentum
P  MV
Impulse
Impulse  FT
• In order to change the momentum of an
object, an impulse must be applied to it.
Any moving object has
momentum
m
v
• The magnitude of the impulse applied to
the object, will equal the object’s change
in momentum
What is the difference between
impulse and change in
momentum?
Impulse  P
• The equation above does not mean that
impulse and change in momentum are the
same thing.
• It says that their amounts are the same.
Change in momentum by
definition is:
P  MV
The impulse applied to an
object will equal the object’s
change in momentum
FT  MV
When jumping, why will it be less
painful if you flex your body when
you land?
FT  MV
Therefore,
MV
F
T
• The force applied to your body is inversely
proportional to the stopping time.
Conservation of momentum
P  MV
M=100 kg
V=10 m/s
 m 
P  MV  100kg10 
 s 
kg m
 1000
s
kg m
P  900
s
The total momentum before
collision must equal the total
momentum after collision
kg m
kg m
kg m
1000
 900
100
s
s
s
100
kg m
s
to the right
• Notice that to the right is positive and to
the left is negative


In order to conserver
momentum, after collision, the
total momentum must be:
kg m
100
s
to the right
Conservation of momentum
• Since the force on the bullet and gun
must be equal in magnitude and are
applied for the same length of time, the
impulse must have the same magnitude
for both.
Impulse = change in momentum
• Because the gun and bullet have the
same impulse applied to them, they must
have the same change in momentum
Conservation of momentum
• The change in momentum for the
Terminator must be the same as the
change in momentum of the shooter.
Why does landing on the air
bag help to prevent death
Impulse = change in momentum
FT  P
Therefore:
P
F
T
• The air bag provides a longer stopping time
and therefore a smaller force is applied to the
jumper.

How does a padded dash help
to prevent injuries?
Impulse = change in momentum
FT  P
Therefore:
P
F
T
• The padded dash provides a longer stopping
time and therefore a smaller force is applied to
the jumper.

Long barrel results in a larger
time which will produce a larger
change in momentum
Impulse = change in momentum
FT  P
P  MV
• When you change the momentum of
an object, you change its velocity
Why didn’t the professor move
backward as fast as the
marble moved forwad?
P  MV
P
V 
M
• The change in velocity is inversely
proportional to the object’s mass.
• The professor’s mass was much larger
than the marble’s, so he had a tiny
change in velocity.
Is momentum conserved when
a bullet is fired from a gun?
Vgun
Vbullet
Mgun
mbullet
Magnitude of
Pgun
=
Pbullet=
kg m
40
s
kg m
kg m
kg m
40
 40
0
s
s
s
• Yes
• Their masses and velocities are different, but
 will be equal in
their change in momentum
magnitude and opposite in direction
Why can a karate punch apply
a large force?
FT  P
Therefore:
P
F
T
• Because of the small stopping time

As the stopping time
approaches zero, the force
approaches infinity
P
F
T
• Notice the inverse relationship
between the time and the force
