Conservation of Momentum

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Conservation of Momentum
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Law of Conservation of Momentum

• If no net force acts on a system, then the total
  momentum of the system does not change.

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Conservation of Momentum

• When objects interact the total momentum is
  conserved- it doesnt change
• Lets use the example of colliding billiard
  balls
• The total momentum of the billiard balls before
  the collision is equal to the total momentum
  after the collision

Total momentum before Total
momentum after
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Conservation of Momentum

• The Collision of two billiard balls

p1 4 kgm/s
p2 0 kgm/s
p2 4 kgm/s
p1 0 kgm/s
Total momentum before 4 kgm/s 0 kgm/s 4
kgm/s
Total momentum after 0 kgm/s 4 kgm/s 4
kgm/s
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Conservation of Momentum (Collisions)

• Momentum is conserved when objects interact in an
  event
• An example of an event is a collision
• We will distinguish between two types of
  collisions elastic collisions and inelastic
  collisions

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Elastic Collisions

• A collision is elastic when two objects bounce
  off of each other (billiard balls)
• For two objects
• m1v1i m2v2i m1v1f m2v2f

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Elastic Collisions

• Two 0.5 kg billiard balls collide elastically.
  The 1st ball has an initial velocity of 2 m/s and
  the 2nd ball is initially at rest. If the 1st
  ball comes to a stop after the collision what is
  the velocity of the 2nd ball after the collision?
• m1v1i m2v2i m1v1f m2v2f
• (0.5)(2) (0.5)(0) (0.5)(0) (0.5) v2f
• 1 (0.5) v2f
• v2f 2 m/s

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Inelastic Collisions

• A collision is inelastic when two objects collide
  and stick together
• For two objects
• m1v1i m2v2i (m1 m2)vf

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Inelastic Collision

• Vince Wilfork (130 kg) runs towards Peyton
  Manning (100 kg) with a velocity of 7 m/s and
  sacks Peyton in an inelastic collision, who
  before the sack is just standing there. What is
  the velocity of Peyton and Vince after the sack?
• m1v1i m2v2i (m1 m2)vf
• (130)(7) (100)(0) (130 100)vf
• 910 230vf
• vf 3.96 m/s

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Other Events

• Firing a gun
• A 12 kg gun fires a .01 kg bullet and the bullet
  flied off with a velocity of 150 m/s. What is the
  recoil velocity of the gun?
• Total momentum before 0
• 0 Total momentum after
• 0 (12)vf (.01)(150)
• -1.5 12vf
• vf -.125 m/s