Law of Conservation of Momentum and Collisions

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Law of Conservation of Momentum and Collisions

• Chapter 8.4-8.5

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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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Read Page 131

• Read 1st paragraph
• What does Newtons 3rd law have to say about the
  net force of the cannon-cannonball system?
• Why is the momentum of the cannon-cannonball
  system equal to zero before and after the firing?

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Read Page 131

• Read 1st paragraph
• What does Newtons 3rd law have to say about the
  net force of the cannon-cannonball system?
• The net force of this system equals zero because
  the action and reaction forces cancel each other
  out
• Why is the momentum of the cannon-cannonball
  system equal to zero before and after the firing?
• The momentum in the system must be conserved so
  if the system starts with zero momentum, it must
  end with zero momentum.

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Read Page 131

• Read 2nd paragraph
• Why is momentum a vector quantity?
• Explain the difference between the momentum of
  the cannon and the momentum of the cannonball,
  and the momentum of the cannon-cannonball system.

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Read Page 131

• Read 2nd paragraph
• Why is momentum a vector quantity?
• Momentum is a quantity that expresses both
  magnitude and direction.
• Explain the difference between the momentum of
  the cannon and the momentum of the cannonball,
  and the momentum of the cannon-cannonball system.
• After the firing occurs, both the cannon and
  cannonball have the same momentum (big mass,
  small velocity vs. small mass, big velocity).
  But since the momentum for each is moving in the
  opposite direction, the momentums cancel out,
  causing the cannon-cannonball systems momentum
  to equal zero.

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Read Page 131

• Read 3rd paragraph
• Why do physicists use the word conserved for
  momentum?
• State the law of conservation of momentum.

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Read Page 131

• Read 3rd paragraph
• Why do physicists use the word conserved for
  momentum?
• The word conserved refers to quantities that do
  not change.
• State the law of conservation of momentum.
• In the absence of an external force, the momentum
  of a system remains the same.

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Read Page 131

• What does system mean?
• In terms of momentum conservation, why does a
  cannon recoil when fired?

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Final Thoughts about Page 131

• What does system mean?
• The word system refers to a group of interacting
  elements that comprises a complex whole.
• In terms of momentum conservation, why does a
  cannon recoil when fired?
• The cannon must recoil in order for momentum to
  be conserved. (The momentum of the
  cannon-cannonball system was zero before the
  firing, and must remain zero after the firing.)

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Read Page 131

• What does conservation of momentum mean?
• Conservation of momentum means that the amount of
  momentum in a system does not change.
• Why is the momentum cannon-cannonball system
  equal to zero?
• The momentum of the cannonball cancels out the
  recoil of the cannon (both move in opposite
  directions with an equal amount of momentum.

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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
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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