Momentum, Impulse, and Collisions

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Momentum, Impulse, and Collisions
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Momentum (P)

• A quantity that expresses the motion of a body
  and its resistance to slowing down.
• P mv
• P momentum (kg.m/s or N.s)
• m mass (kg)
• v velocity (m/s)

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Try it

• A toy car has a mass of 5kg. If it is moving at a
  velocity of 5m/s, what is its momentum?
• 25kgm/s
• What is the momentum of a 25kg boy moving at a
  speed of 1m/s?
• 25kgm/s

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Worksheet Answers
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Project Time
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Impulse

• measures a change in momentum arrived at by
  multiplying the average force acting on a body by
  the length of time it acts.
• Impulse F(t)
• F force (N or Newtons)
• t time (s)

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Another one

• An 8N force acts upon an object for 5 seconds.
  What impulse is given this object?
• 40Ns

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Impulse-momentum Theorem

• Force is reduced when the time interval of an
  impact is increased.
• Examples
• Nets or giant air mattresses used to catch people

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Putting it all together

• Fma (Newtons 2nd Law)
• a?v/t
• Insert ?v/t for a in Fma
• This gives us Fm?v/t
• Multiply by t to get-
• F(t) m(vf-vi)
• Notice impulse, on the left side, is equal to the
  change in momentum of an object.

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Try it

• A ball changes velocity from 20m/s to 30m/s. If
  it has a mass of 5kg, what impulse was necessary
  to cause this change?
• 50Ns
• How long would it take a 5N force to change the
  velocity of the ball?
• (Hint use ImpulseF(t))
• 10s

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Law of Conservation of Momentum

• The Law of Conservation of Momentum
• The total momentum of all objects interacting
  with one another remains constant regardless of
  the nature of the forces between the objects.
• m1v1,i m2v2,i m1v1,f m2v2,f
• total initial momentum total final momentum

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Conservation of Momentum

• PICTURE THIS

• So far we only have considered the momentum of
  only one object at a time.
• Now we will look at two or more objects
  interacting with each other.

• You are playing pool. You strike the cue ball it
  hits the 8 ball. The 8 ball had no momentum
  before they collided.
• During the collision the cue ball loses momentum
  and the 8 ball gains momentum.
• The momentum the cue ball loses is the same
  amount that the 8 ball gained.

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Momentum is Conserved

• Newtons third law leads to conservation of
  momentum
• During the collision, the force exerted on each
  bumper car causes a change in momentum for each
  car.
• The total momentum is the same before and after
  the collision.

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Elastic Collisions

• A collision in which the total momentum and the
  total kinetic energy are conserved is called an
  elastic collision.
• Elastic means that after a collision the objects
  remain separated.
• Two objects collide and return to their original
  shapes with no loss of total kinetic energy.
  After the collision the two objects move
  separately.
• Both the total momentum and total kinetic energy
  are conserved.

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Inelastic Collisions

• Perfectly inelastic collision
• A collision in which two objects stick together
  after colliding and move together as one mass is
  called a perfectly inelastic collision.
• Example The collision between two football
  players during a tackle.

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Video time

• http//youtu.be/Dz5q0KKSlf4

• http//www.youtube.com/watch?vFSAR86MMJ2wsafety_
  modetruepersist_safety_mode1safeactive

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Kinetic Energy in Inelastic Collisions

• In an inelastic collision the total kinetic
  energy does not remain constant when the objects
  collide and stick together.
• Some energy is converted into sound energy and
  internal energy as the objects deform during the
  collision.
• Elastic in physics refers to a material that when
  work is done to deform the material during a
  collision the same amount of work is done to
  return the material to its original shape.
• Inelastic material does not return to its
  original shape and therefore some energy is
  converted to sound or heat.

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Real Collisions

• Most collisions are not perfectly inelastic (they
  dont stick together and move as one)
• Most collisions are not elastic.
• Even nearly elastic collisions result in some
  decrease of kinetic energy.
• A football deforms when kicked
• A sound is produced (sound signifies a decrease
  in kinetic energy)

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For all intensive purposes

• We will consider all collisions in which objects
  do not stick together to be elastic collisions.
• Therefore, total momentum and total kinetic
  energy will stay the same before and after the
  collision.

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There are 2 types of collisions

• Elastic
• m1iv1i m2iv2i m1fv1f m2fv2f
• Where 1 implies object 1, 2 implies object 2
• Where i implies initial f implies final
• Inelastic
• m1iv1i m2iv2i mTvT
• Where T implies total
• Use and velocities to show direction.

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Try these

• A 2kg ball strikes another ball head on at an
  initial velocity of 2m/s. If the second ball had
  a mass of 3kg and was initially moving at -1m/s,
  what is the final velocity of the 2kg ball if the
  vf of the 3kg ball is now 1.33m/s?
• Set it up-
• m1iv1i m2iv2i m1fv1f m2fv2f
• 2kg(2m/s)3kg(-1m/s) 2kg(v1f)3kg(1.33m/s)
• v1f -1.5m/s

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Last one

• A 500kg car is driving at a velocity of 10m/s.
  Another car (700kg) hits it from behind at a
  velocity of 25m/s and the two cars interlock
  bumpers. What is the resulting velocity of the
  two cars?
• Set it up-
• m1iv1i m2iv2i mTvT
• 500kg(10m/s)700kg(25m/s) 1,200kg(vT)
• vT 18.75 m/s