Momentum

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Momentum

1. How do we measure the momentum of an object?
2. How is momentum conserved in collisions?
3. Describe an example of angular momentum?

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Linear Momentum
Chapter 6

• Momentum is defined as mass times velocity.
• Momentum is represented by the symbol p, and is a
  vector quantity.
• p mv
• momentum mass ? velocity
• As mass increase momentum increases
• As velocity increase momentum increases.

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Day 1 Practice Problem

• When comparing the momentum of two moving
  objects, which of the following is correct?
• a)The object with the higher velocity will have
  less momentum if the masses are equal.
• b)The more massive object will have less momentum
  if its velocity is greater.
• c)The less massive object will have less momentum
  if the velocities are the same.
• d)The more massive object will have less momentum
  if the velocities are the same.
• What is the momentum of a 60 kg child running at
  3 m/s?

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Day 2 Practice

• Answers
• 1. C
• 2. p mv
• (60.0 kg) (3.0 m/s)
• 180 kg m/s

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Day 2 Momentum is Conserved,
Chapter 6

• 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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Day 2 Momentum is Conserved
Chapter 6

• 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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Day 2 Conservation of Momentum

• BOING! SPLAT! Holy Vectors Batman, its
  Momentum.
• The conservation of momentum is very important in
  the study of collisions (atoms, highway
  accidents, sports science etc..)
• Go to this website and observe how the different
  masses react in a collision. Dont worry about
  the math just yet. Just predict which mass will
  slow down and which will speed up.
• http//www.ux1.eiu.edu/cfadd/1150/07Mom/Spcl.html
  1
• http//www.ux1.eiu.edu/cfadd/1150/07Mom/Exmpl.htm
  l5

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Sample Problem
Chapter 6

• Conservation of Momentum
• A 76 kg boater, initially at rest in a
  stationary 45 kg boat, steps out of the boat and
  onto the dock. If the boater moves out of the
  boat with a velocity of 2.5 m/s to the right,what
  is the final velocity of the boat?

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Sample Problem, continued
Chapter 6

• Conservation of Momentum
• 1. Define
• Given
• m1 76 kg m2 45 kg
• v1,i 0 v2,i 0
• v1,f 2.5 m/s to the right
• Unknown
• v2,f ?

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Sample Problem, continued
Chapter 6

• Conservation of Momentum
• 2. Plan
• Choose an equation or situation Because the
  total momentum of an isolated system remains
  constant, the total initial momentum of the
  boater and the boat will be equal to the total
  final momentum of the boater and the boat.
• m1v1,i m2v2,i m1v1,f m2v2,f

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Sample Problem, continued
Chapter 6

• Conservation of Momentum
• 2. Plan, continued
• Because the boater and the boat are initially at
  rest, the total initial momentum of the system is
  equal to zero. Therefore, the final momentum of
  the system must also be equal to zero.
• m1v1,f m2v2,f 0
• Rearrange the equation to solve for the final
  velocity of the boat.

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Sample Problem, continued
Section 2 Conservation of Momentum
Chapter 6

• Conservation of Momentum
• 3. Calculate
• Substitute the values into the equation and
  solve

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Sample Problem, continued
Chapter 6

• Conservation of Momentum
• 4. Evaluate
• The negative sign for v2,f indicates that the
  boat is moving to the left, in the direction
  opposite the motion of the boater. Therefore,

v2,f 4.2 m/s to the left
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Day 3 Practice Problems

• 1) A roller coaster climbs up a hill at 4 m/s and
  then zips down the hill at 30 m/s. The momentum
  of the roller coaster
• A) is greater up the hill than down the hill.
• B) is greater down the hill than up the hill.
• C) remains the same throughout the ride.
• D) is zero throughout the ride.
• 2) In a two-body collision,
• A) momentum is always conserved.
• B) kinetic energy is always conserved.
• C) neither momentum nor kinetic energy is
  conserved.
• D) both momentum and kinetic energy are always
  conserved.

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Day 3 Practice continued

• 1. The law of conservation of momentum states
  that
• A) the total initial momentum of all objects
  interacting with one another usually equals the
  total final momentum.
• B) the total initial momentum of all objects
  interacting with one another does not equal the
  total final momentum.
• C) the total momentum of all objects interacting
  with one another is zero.
• D) the total momentum of all objects interacting
  with one another remains constant regardless of
  the nature of the forces between the objects.
• 2. Which of the following statements about the
  conservation of momentum is not correct?
• A) Momentum is conserved for a system of objects
  pushing away from each other.
• B) Momentum is not conserved for a system of
  objects in a head-on collision.
• C) Momentum is conserved when two or more
  interacting objects push away from each other.
• D) The total momentum of a system of interacting
  objects remains constant regardless of forces
  between the objects.

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Day 4 Quiz (Lets Go!!!)