Goal: To understand momentum

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Goal To understand momentum

• Objectives
• To Learn about What momentum is
• To learn about how to calculate Momentum in 2
  dimensions
• To understand How is momentum changed?
• To understand the Conservation of momentum
• To learn about Why momentum is useful to
  understand.
• Tomorrow To learn about applications to the
  conservation of momentum

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What is momentum

• In reality momentum is quite simply a measure of
  your ability to create change.
• Momentum p mv
• Lets do a quick sample
• 1) A car with mass of 500 kg moves at a velocity
  of 20 m/s. What is the cars momentum?

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Another example

• Two cars are headed towards one another.
• The first car has 700 kg of mass and moves at a
  velocity of 20 m/s North
• The 2nd car has 1400 kg of mass and moves at a
  velocity of 10 m/s South.
• What is the combined momentum of the cars (yes
  momentum has direction)?

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Momentum in 2 dimensions

• Each dimension has momentum.
• So, you have to find the total momentum for each
  dimension separately.
• Then at the end you can get a magnitude if you
  want, but usually it is more useful to keep them
  separate much like you keep a checking account
  separate from a savings account.

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Straight Foreward 2 D question

• A car is heading North with a mass of 1000 kg and
  a velocity of 12 m/s.
• A 2nd car is heading East with a mass of 750 kg
  and a velocity of 20 m/s.
• Which car has a greater magnitude of momentum?
• What is the combined magnitude of momentum for
  both cars combined

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Changing momentum

• How do you change momentum?
• You use what is called an impulse.
• Impulse change in momentum
• Impulse mass change in velocity
• Impulse F t
• Note that F ma
• So, Impulse m (a t)
• What does acceleration time equal?

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Example

• A car runs into a mailbox.
• The mass of the mailbox is 10 kg and the mass of
  the car is 800 kg.
• If the car imparts a 2000 N force to the mailbox
  for 0.4 seconds find
• A) The impulse on the mailbox
• B) The new velocity of the mailbox (set impulse
  to mass change in velocity)?
• C) What is the impulse the mailbox imparts on the
  car? (What, you have forgotten about Newtons
  3rd law already?)
• D) How much does the cars momentum change?
• E) What is the net change in momentum (i.e. if
  you add the changes in momentum of the car and
  mailbox what do you get)?

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Conservation of momentum!

• Momentum is almost always conserved in a
  collision.
• In fact it is conserved for each dimension.
• Total p before Total p after
• Quick question will kinetic energy be
  conserved?

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Energy?

• Sometimes kinetic energy is also conserved.
• Collisions that conserve kinetic energy are
  called elastic collisions.
• Collisions where energy is not conserved are
  called inelastic collisions.

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Oooh, oooh, fender benderThe pips from that
car commercial

• In many collisions energy is transferred.
• Energy is transferred to sound energy, heat
  energy, and used to crumple a car.
• These collisions are always inelastic collisions.
• So, if you get hit by a car, you want it to be an
  elastic collision!
• You will fly faster and further, but the initial
  impact wont use energy to bend and break things.

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Rear end crash

• A speeding car of mass 800 kg attempting to elude
  the police crashes into a 600 kg car sitting
  parked at the intersection.
• Ignoring brakes and friction, if the initial
  velocity of the speeding car is 50 m/s forward
  and the final velocity of the speeding car is 10
  m/s forward then what will the final velocity of
  the other car be?
• There are 2 ways to do this problem

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Head on collision

• Car 1 25 m/s East and a mass of 800 kg.
• Car 2 30 m/s West and a mass of 900 kg.
• A) What is the net momentum of the two cars
  combined before the collision.
• C) After the crash Car 1 moves West at a velocity
  of 5 m/s. What will the final velocity of car 1
  be? Hint, total momentum

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T Bone!

• Car 1 mass of 650 kg and headed North at 10 m/s
• Car 2 mass of 750 kg and headed west at 5 m/s.
• Car 1 T Bones Car 2 and car 1 comes to a complete
  stop.
• A) Before the crash what are the momentums in the
  north and west directions?
• B) After the crash how much momentum will car 1
  have?
• C) After the crash what is the north and west
  velocity of Car 2 (hint will the west velocity
  change?)
• D) What is the magnitude of the final velocity
  for car 2?

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If time Ball off a wall

• You bounce a 0.15 kg ball off of the wall.
• The ball hits the wall at 20 m/s forward and when
  it bounces it returns (backward) at 80 of the
  SPEED of when it hit the wall.
• A) What is the change in velocity for the ball
  (remember direction)?
• B) What is the change in momentum?
• C) If the ball is in contact with the wall for
  0.6 seconds then what is the average force that
  the wall imparts to the ball?
• D) What is the acceleration the wall gives the
  ball?

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Conclusion

• Momentum mass velocity
• Momentum is conserved!
• Momentum is conserved in every direction!
• If you run into something or it runs into you
  at high velocity dont bounce!