Momentum!!!

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Conservation of Momentum
A corner stone of physics is the conservation of
momentum. This can be seen in all types of
collisions.
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Momentum Review Question

• Imagine a rubber and steel bullet each with the
  same mass and velocity. They each hit a wood
  block. The rubber bullet bounces off, while the
  steel bullet burrows into the block. Which one
  moves the wood block more?

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• The steel bullet burrows into the block
  transferring all of its momentum to the block.
  ?P mv It moves the block.

The rubber bullet bounces off transferring more
momentum. If it bounces at the same speed, but
opposite direction, ?P 2mv. Thus, the block
moves twice as much.
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Conservation of Momentum

• In all collisions or interactions, momentum of a
  system is always conserved.
• You may have previously learned about
  conservation of mass or energy from chemistry
  class...

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• Since momentum is a vector quantity, direction
  must be taken into account to see that momentum
  truly is conserved.

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Rifle and Bullet Example

• The rifle and bullet can be considered a system.
  Before firing, they are both motionless and have
  a total momentum of 0.

After firing, the total momentum still equals 0.
The rifle has momentum to the left, the bullet to
the right. The rifle has a much larger mass so
its velocity is less, but their momentum is still
conserved.
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Types of Collisions

• Elastic collision momentum is conserved. The
  objects colliding arent deformed or smashed,
  thus no kinetic energy is lost. Ex billiard
  ball collisions

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Inelastic collision momentum is still
conserved. Kinetic energy is lost. This often
happens when object interlock or stick together.
The objects are also often deformed or crunched.
Ex car crash
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Conservation of Momentum Problems

• When solving problems involving the conservation
  of momentum, the most important thing to consider
  is

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• This cannon recoils quite a bit! The momentum of
  the projectile flying forwards must be equaled by
  the cannon itself recoiling backwards.

The movable parts of the cannon help reduce some
of this effects by increasing the time of the
recoil. Thus, the force is lessened.
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Explosion Sample Problem

• A 300 kg cannon fires a 10 kg projectile at 200
  m/s. How fast does the cannon recoil backwards?

BOOM!
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Solution Set up

• The momentum of the projectile must be equal in
  size to the momentum of the cannon.
• They must be equal since they must cancel each
  other out, initial momentum is 0!

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Calculation
Before firing, velocity 0m/s.

• P after P before
• mcannonvcannon mprojvproj 0
• (300 kg) (vcannon) (10kg) (200m/s) 0

Negative sign indicates the cannon moves in the
opposite direction to the projectile
vcannon -6.67 m/s
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• Q Why does the cannon move so much slower
  compared to the projectile?
• A It is much more massive, more inertia.

Q What does the negative sign indicate? AThe
cannon moves in the opposite direction compared
to the projectile.
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Hit and Stick Sample Problem
Joe has a mass of 70kg and is running at 7 m/s
with a football. He slams into 110kg Biff who
was initially motionless. During this collision,
Biff holds onto and tackles Joe. This type of
event may be called a hit and stick collision.
What is their resulting velocity after the
collision?
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Hit and Stick Solution
Biffs initial velocity is zero, so this term
drops out.
Since they stick together, add their masses.
Do math carefully
Since all velocities were in the same direction,
no signs are needed here.
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• Collisions do not always take place in a nice
  neat line

Often, collisions take place in 2 or 3 dimensions
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Another Example

• One ball collides into another. By using
  momentum vector components, you can predict the
  result

Y components cancel out X components add up to
previous P
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• Its easiest to break the momentum into X and y
  components. Since momentum is always conserved

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Sample Problem

• Two pool balls, each 0.50kg collide. Initally,
  the first moves at 7 m/s, and the second is
  motionless. After the collision, the first moves
  40o to the left of its original direction, the
  second moves 50o to the right of its original
  direction. Find both velocities after the
  collision.

After Collision
Before Collision
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• The X and Y components of momentum are both
  conserved. You can visualize this several ways

After the collision, the sum of the X components
equals the original momentum. The y components
cancel out since there was no momentum in that
direction originally.
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• Without using components, it can also be noticed
  that both momentum vectors after the collision
  add up to the original momentum vector

Remember that vectors can be moved anywhere as
long as their magnitude and relative direction
are unchanged.
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Problem Solution
Diagram NOT to scale!
Use trig to find the momentum of ball B. Then
find its velocity
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• Now find the velocity of ball A

5.36 m/s
Notice how the velocities of the balls dont add
up to the original velocity. Also, when added as
scalars the momentums dont add up either. Only
as vectors do the momentum vectors seem to be
conserved.
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• Questions???