2D Collisions

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2D Collisions

• Physics 12

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Clip of the day

• Minutephysics What is fire?
• http//www.youtube.com/watch?v1pfqIcSydgE

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Review Momentum

• Momentum

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Review Conservation of momentum

• Momentum is conserved
• This is an expression of Newtons first law
• An object at rest or in uniform motion will
  remain at rest or in uniform motion unless acted
  on by an external force.

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Conservation of momentum

• In interactions between two bodies/objects,
  momentum of one object can change, but the total
  momentum of the system remains constant.

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Law of Conservation of Momentum (continued)

• The total momentum of objects before a collision
  is the same as the total momentum of the same
  objects after they collide.
• The change in momentum in an isolated system is
  zero. The objects within the system may interact
  and exchange momentum, but the total momentum
  does not change!

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Review Example Collisions in 1D

• A 1.75x104 kg boxcar is rolling down a track
  toward a stationary boxcar that has a mass of
  2.50x104 kg. Just before the collision the first
  car is moving east at 5.45m/s. When the boxcars
  collide, they lock together and continue down the
  track. What is the velocity of the 2 box cars
  after the collision?
• Step 1 draw a diagram!

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• What we know before the collision m11750 kg,
  m22500 kg, v1 5.45 m/s, v2 0
• What we know after the collision m11750 kg,
  m22500 kg, the 2 cars are now stuck together so
  they have the same velocity! Velocity is what we
  are solving for.
• m1v1 m2v2 m1v1' m2v2
• (1750)(5.45) (2500)(0) 1750v
  2500v
• 9537.5 4250v
• 2.24 m/s v

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2D Collisions

• In all collisions, momentum is conserved
• In elastic collisions, energy is also conserved
• As momentum is a vector, we can break momentum
  into components (x and y) and employ the
  conservation of momentum

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Example 2D Collision

• Two cars approach an intersection the first car
  is travelling east at a velocity of 15m/s and the
  car has a mass of 1000.kg. The second car is
  travelling north at a velocity of 10.m/s and has
  a mass of 1200.kg. If the cars collide and stick
  together, determine the following
• The velocity immediately after the collision
• The direction of motion immediately after the
  collision

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Diagram
v15m/s
v?
A
A
B
v10.m/s
B
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Try it ?

• Page 509
• Questions 35-37

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EXPLOSIONS! (and energy)

• Day 2

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Review Question

• Two cars collide at an intersection if they have
  the same mass (1200kg) and after the collision
  they move off at 7.5m/s at 31, determine the
  initial velocity of each car assuming one was
  travelling due north and one was travelling due
  east.

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Answer

• 7.7m/s north and 13m/s east

Physics is such fun!
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Explosion

• During an explosion, momentum must be conserved
  as in a collision
• We will consider simple problems with a limited
  number of pieces following the explosion, however
  this can be applied to any number of particles
• As with collisions, we need to consider before
  and after the explosion

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Example 1

• A small firecracker is sitting on a table and
  explodes into four parts. The initial
  firecracker has a mass of 50.g and three of the
  pieces have masses of 12g, 13g, 18g and move off
  at the following respective velocities 42m/s,
  0., 31m/s, 72 and 28m/s, 183. What is the
  velocity of the fourth piece?

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Explosion Problem
Before
After
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Elastic vs Inelastic Collisons

• Elastic momentum (p) and kinetic energy
  conserved (EK)
• Inelastic momentum (p) conserved but kinetic
  energy NOT conserved (EK)

Review Ek ½ mv2
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Example 2

• A 0.0520 kg golf ball is moving east with a
  velocity of 2.10 m/s when it collides, head on,
  with a 0.155 kg billiard ball. If the golf ball
  rolls directly backward with a velocity of 1.04
  m/s, was the collision elastic?
• Reminders
• Momentum is always conserved in a collision.
• If the collision is elastic, kinetic energy must
  also be conserved.
• Ek ½ mv2

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Try it ?

• The small firecracker from the previous problem
  is thrown when it explodes it is travelling at
  25m/s at a 0. angle. It breaks into the same
  four pieces but the velocities are now 61m/s,
  0., 33m/s, 72 and 15m/s, 183. What is the
  velocity of the fourth piece?
• Page 513
• Question 38
• Page 515
• Questions 39-40

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Explosion Problem
Before
After
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