Momentum is conserved for all collisions as long as external forces don

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• Momentum is conserved for all collisions as long
  as external forces dont interfere.

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LAW OF CONSERVATION OF MOMENTUM

• In the absence of outside influences, the total
  amount of momentum in a system is conserved.
• The momentum of the cue ball is transferred to
  other pool balls.
• The momentum of the pool ball (or balls) after
  the collision must be equal to the momentum of
  the cue ball before the collision

• p before p after

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8.5 Law of Conservation and Collisions
Motion of the other balls
Motion of the cue ball

• Whenever objects collide in the absence of
  external forces, the net momentum of the objects
  before the collision equals the net momentum of
  the objects after the collision.

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Figure 8.10Momentum of cannon and cannonball
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8.4 Conservation of Momentum
The momentum before firing is zero. After firing,
the net momentum is still zero because the
momentum of the cannon is equal and opposite to
the momentum of the cannonball.
Velocity cannon to left is negative Velocity of
cannonball to right is positive (momentums cancel
each other out!)
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8.5 Two Types of Collisions

• Elastic Collision When objects collide without
  sticking together
• --Kinetic energy is conserved
• --No heat generated
• Inelastic Collision When objects collide and
  deform or stick together.
• --Heat is generated
• --Kinetic energy is not conserved

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Changes in Velocity Conserve Momentum

• A. Elastic collisions with equal massed objects
  show no change in speed to conserve momentum
• http//www.walter-fendt.de/ph14e/ncradle.htm
• http//www.walter-fendt.de/ph14e/collision.htm
• B. Elastic collisions with inequally massed
  objects show changes in speed to conserve
  momentum
• Larger mass collides with smaller masssmaller
  mass objects speed is greater than the larger
  mass object
• Smaller mass object collides with larger mass
  objectlarger mass objects speed is much less
  than the smaller mass object
• http//www.walter-fendt.de/ph14e/collision.htm
• C. Addition of mass in inelastic collisions
  causes the speed of the combined masses to
  decrease in order for momentum to be conserved

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8.5 Examples of Elastic Collisions when the
objects have identical masses

1. A moving ball strikes a ball at rest.

Note purple vector arrow represents velocity
speed and direction
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8.5 Examples of Elastic Collisions when the
objects have identical masses

1. A moving ball strikes a ball at rest.

Momentum of the first ball was transferred to the
second velocity is identical
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8.5 Examples of Elastic Collisions when the
objects have identical masses
b. Two moving balls collide head-on.
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8.5 Examples of Elastic Collisions when the
objects have identical masses
b. Two moving balls collide head-on.
The momentum of each ball was transferred to the
other each kept same speed in opposite direction
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8.5 Examples of Elastic Collisions when the
objects have identical masses
c. Two balls moving in the same direction at
different speeds collide.
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8.5 Examples of Elastic Collisions when the
objects have identical masses
c. Two balls moving in the same direction at
different speeds collide.
The momentum of the first was transferred to the
second and the momentum of the second was
transferred to the first. Speeds to conserve
momentum.
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Example of an elastic collision with objects same
speed but different masses
What happens to the speed of the smaller car
after the elastic collision with the more massive
truck? Notice that the car has a positive
velocity and the truck a negative velocity. What
is the total momentum in this system?
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Example of an elastic collision with objects same
speed but different masses
What happens to the speed of the smaller car
after the elastic collision with the more massive
truck? (the cars speed increases to
conserve momentum) Notice that the car has a
positive velocity and the truck a negative
velocity. What is the total momentum in this
system? (40,000 kg x m/s)
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Start with less mass, end up with more
mass Notice how speed changes to conserve
momentum (more mass, less speedinverse
relationship!)
8.5 Inelastic Collisions
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Calculating conservation of momentum

• Equation for elastic collisions
• m1v1 m2v2 m1v1 m2v2
• Equation for inelastic collision
• m1v1 m2v2 (m1 m2)v2

Before collision
After collision
Before collision
After collision
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Conservation of Momentum in an elastic collision
A
B
Before elastic collision
After elastic collision
Cart A mass 1 kg Cart B mass 1 kg Cart A
speed 5 m/s Cart B speed 0 m/s
Cart A mass 1 kg Cart B mass 1 kg Cart A
speed 0 m/s Cart B speed
5 m/s
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Conservation of Momentum in an elastic collision
A
B
Before elastic collision
After elastic collision
Cart A mass 1 kg Cart B mass 1 kg Cart A
speed 5 m/s Cart B speed -5 m/s
Cart A mass 1 kg Cart B mass 1 kg Cart A
speed -5 m/s Cart B speed 5 m/s
5 m/s
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Conservation of Momentum in an elastic collision
A
B
Before elastic collision
After elastic collision
Cart A mass 1 kg Cart B mass 5 kg Cart A
speed 5 m/s Cart B speed 0 m/s
Cart A mass 1 kg Cart B mass 5 kg Cart A
speed 0 m/s Cart B speed
1 m/s
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Conservation of Momentum in an elastic collision
A
B
Before elastic collision
After elastic collision
Cart A mass 6 kg Cart B mass 1 kg Cart A
speed 10 m/s Cart B speed 0 m/s
Cart A mass 6 kg Cart B mass 1 kg Cart A
speed 2 m/s Cart B speed 48 m/s
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Conservation of Momentum in an inelastic collision
Before inelastic collision
After inelastic collision
Big fish mass 4 kg Small fish mass 1 kg Small
fish speed 5 m/s Large fish speed 0 m/s
Big fish mass Small fish mass Small fish
Large fish speed
5 kg
1 m/s
m1v1 v2 m1 m2
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8.5 Collisions

• think!
• One glider is loaded so it has three times the
  mass of another glider. The loaded glider is
  initially at rest. The unloaded glider collides
  with the loaded glider and the two gliders stick
  together. Describe the motion of the gliders
  after the collision.

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8.5 Collisions

• think!
• One glider is loaded so it has three times the
  mass of another glider. The loaded glider is
  initially at rest. The unloaded glider collides
  with the loaded glider and the two gliders stick
  together. Describe the motion of the gliders
  after the collision.
• Answer The mass of the stuck-together gliders is
  four times that of the unloaded glider. The
  velocity of the stuck-together gliders is one
  fourth of the unloaded gliders velocity before
  collision. This velocity is in the same direction
  as before, since the direction as well as the
  amount of momentum is conserved.

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1. Conservation of Momentum in an elastic
collision
m1v1 v2 m2
A
B
After elastic collision
Before elastic collision
Cart A mass 1 kg Cart B mass 5 kg Cart A
speed 5 m/s Cart B speed 0 m/s
Cart A mass 1 kg Cart B mass 5 kg Cart A
speed 0 m/s Find Cart B speed
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2. Conservation of Momentum in an elastic
collision
m1v1 v2 m2
A
B
Before elastic collision
After elastic collision
Cart A mass 5 kg Cart B mass 2 kg Cart A
speed 0 m/s Find Cart B speed
Cart A mass 5 kg Cart B mass 2 kg Cart A
speed 10 m/s Cart B speed 0 m/s
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8.5 Conservation of momentum for inelastice
collisions

• Consider a 6-kg fish that swims toward and
  swallows a 2-kg fish that is at rest. If the
  larger fish swims at 1 m/s, what is its velocity
  immediately after lunch?

m1v1 v2 m1 m2
Find the speed of the two fish after the
inelastic collision