Download Collisions: Momentum and Impulse

SC.CE.05.01
Collisions:
Momentum and
Impulse
Momentum:
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The product of the mass of an object and its velocity
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Momentum = “p”
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p=mv
If mass is constant, then a change of momentum
equals mass times change in velocity: Δp=mΔv
A vector quantity
Vector means…
Impulse:

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The average force multiplied by its time interval
of action
Impulse = FΔt
A vector quantity
Vector means…
Simply stated:

Impulse = change in momentum
=Δp
Impulse/momentum principle:
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The impulse acting on an object produces a
change in momentum of the object that is
equal
both in magnitude and
direction to the impulse
For example:
m=7kg
v=2m/s
p=14kg ×m/s
m=0.07kg
v=200m/s
p=14 kg × m/s
Conservation of Momentum:
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When the net external force acting on a system
is zero, the total momentum of the system is
conserved
In other words: the momentum before a collision
will equal the momentum after a collision
When internal forces are equal (but opposite),
momentum is conserved
Example:
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A 100 kg fullback moving straight downfield with a
velocity of 5 m/s collides head on with a 75 kg
defensive back moving in the opposite direction with a
velocity of -4m/s. The defensive back hangs on to the
fullback, and the two players move together after the
collision.
a. What is the initial momentum of each player?
b. What is the total momentum of the system?
c. What is the velocity of the two players
immediately after the collision?
Example (cont’d)
a: What is the initial momentum of
each player?
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Fullback:
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m = 100 kg
v = 5 m/s
p=?
p = mv
p=
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Defensive back:

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m = 75 kg
v = -4 m/s
p=?
p = mv
p=
b. What is the total momentum of the
system?
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p total = p fullback + p defensive back
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p total = 500 kg x m/s + -300 kg x m/s
p total = 200 kg x m/s
c. What is the velocity of the two
players immediately after the collision?
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v=?
m= 100 kg + 75 kg
=175 kg
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p=mv
So: v=p/m
v= 200 kg x m/s
175 kg
Types of Collisions: Perfectly
Inelastic to Perfectly Elastic
Extend your knowledge of momentum
and energy conservation!
Perfectly Inelastic Collisions
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A collision in which the objects stick together
after colliding
No bounce
If p is known before collision for both objects,
we simply add them together to get final p
A lot of the original kinetic energy is
transformed
Example: railroad car coupling, two balls of
clay, a football tackle
Partially Inelastic
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Some kinetic energy is transformed
Elastic
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No kinetic energy is transformed
Atoms collide without “spending” energy
When pool balls collide:
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Most collisions are elastic: both momentum
and kinetic energy are conserved
Momentum is transferred from the cue ball to
the target ball
We can determine the velocity of both balls
after collision
It gets tricky when multiple pool balls are
involved, but I know you can do it!
Collisions at an Angle
Oh geez, here we go…
An Inelastic Two-Dimensional Collision:

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Remember that momentum is a vector
quantity?
Now our football players from Monday are
running perpendicular to one another
p2=300kg x m/s
31°
p1=500kg x m/s
Elastic Two-Dimensional Collisions

Initial kinetic energy = 1/2mv2 must also
equal the sum of the kinetic energies
Collision Type
Characteristics
Examples
Totally elastic
KE
Atomic
Less elastic
Less
More inelastic
Totally inelastic
is conserved
Usually involves
collisions where objects
can’t touch
No damage to either
object
particles with
similar charges
Magnets with similar
poles facing each
other
damage or heat Ball bearings
created
Well inflated
Less sound created
basketball
More damage or
 A ball with very little
heat
bounce
More sound created
Objects`
stick together
and become one system
Involves greatest loss
of KE
A
ball of soft clay
A bad car accident
where cars stick
together