Chapter 9: Momentum and Conservation

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Chapter 9 Momentum and Conservation

• Newtons Laws applied

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Dynamics of Physics

• Dynamics are the CAUSES of CHANGE in Physics.
• Recall that position is changed by velocity.
• Velocity is changed by acceleration.
• Acceleration is caused by a net force.
• Properties that remain constant are described as
  CONSERVED.

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Impulse and Momentum

• Momentum is described by Newtons 3 laws of
  motion as the quantity of motion.
• If no net force acts on a body, its velocity is
  constant.
• If a net force acts on a body, velocity is
  changed. (acceleration)
• Forces on objects change over time.
• Identify before, during, and after in an
  interaction.

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Developing Impulse

• F ma can be rewritten to substitute a rate of
  change in velocity for acceleration.
• multiplying both sides by ?t, then
• Impulse is a force over a period of time. (Ns)
• Since a FORCE causes a velocity to CHANGE, then
  an IMPULSE causes MOMENTUM to change. (kgm/s)

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Impulse-Momentum Theorem
Can also be stated as
The symbol for Momentum is ?. Thus, ? mv.
Impulse Change in Momentum The force is not
constant, and the impulse is found using the
AVERAGE FORCE times the time interval, or finding
the area under the curve of a force-time graph.
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Vectors

• Velocity is a vector, so momentum is a vector.
• Force is a vector, so impulse is a vector.
• Vectors have positive and negative directions
  associated with them. Traditionally, positive
  direction is right and left is negative.

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Saving lives with Physics

• A large change in momentum comes from a large
  impulse.
• Since Impulse is F?t, you can have a large force
  OR a large time of contact to produce a large
  impulse.
• In a car crash, an air bag extends the TIME of
  contact to reduce the FORCE of impact. The
  Impulse is the same whether you hit the air bag,
  or the steering wheel. Thus the ?mv is the same.
• Car crash video clip
• Car crash with seatbelts

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Angular Momentum

• Just like linear momentum is mv, a ROTATING
  object has momentum also. The momentum of a
  rotating object is called Angular Momentum and
  depends on the objects mass, distance from the
  center axis of rotation, and tangential velocity.
  If the radius gets smaller, the velocity
  increases to maintain constant angular momentum.
  Like water going down the toilet, or a hurricane,
  or planets around a star (sun).

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Practice Problem

• A 0.144kg baseball is pitched horizontally at
  38.0m/s. After it is hit by the bat, it moves at
  the same speed, but in an opposite direction.
• What was the change in momentum of the ball?
• What was the impulse delivered by the bat?

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Batter Up Solution

• Given mball 0.144kg, v38.0 m/s, direction
  direction after ball leaves bat
• Unknown F?t ??
• Solve
• ?? mv2-mv1 m(v2 v1)
• (0.144kg)(38.0m/s-(-38.0m/s))
• (0.144kg)(76.0m/s) 10.9 kg-m/s
• Impulse change in momentum
• 10.9 N-s

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Your turn to practice

• Do pg. 204-205 Practice Problems 1,2,3,4,5,6
• Do pg.217 s 1,2,4,6,7
• Do pg. 218 s 22-27

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Conservation of Momentum

• Forces are a result of an interaction between
  objects moving in opposite directions.
• During collisions, the force of one object on
  another is in strength but opposite in
  direction to the force of the second object on
  the first.
• The time interval for the force is the same for
  both objects, so the Impulse is and opposite.

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What about Momenta?

• According to the I-M theorem, the final momentum
  the impulse the initial momentum.
• In a collision, the final momenta must be equal
  to the sum of the initial momenta in a system and
  thus Momentum is Conserved.

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Defining Closed Systems

• A system that doesnt gain or lose mass is said
  to be a closed system.
• All forces within a closed system are called
  internal forces.
• All forces outside a closed system are considered
  external forces.
• In a system, objects that collide can either
  stick together (inelastic collision), or come
  apart (elastic collision). Momentum of the
  collision in a closed system with no net external
  force is still conserved.

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Car collision problem

• A 2275kg car going 28m/s rear-ends an 875kg
  compact car going 16m/s on ice in the same
  direction. The cars stick together. How fast
  does the wreckage move after the collision?

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Car crash solution
Because the cars stick together, their velocities
after the collision are equal. So, vA2 vB2
v2 mAvA1 mBvB1 (mAmB)v2 So v2 25 m/s,
as we can see when mass increases, velocity must
decrease to conserve momentum.
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Explosions

• As with the 2 skaters in Fig 9-8, if they both
  start at rest and A gives B a push, both skaters
  will move in opposite directions. The push is an
  internal force. The total momentum of the system
  must be zero after the push as it was zero before
  the push. The momenta of the skaters will be
  equal and opposite after the push.
• The chemicals in a rocket exploding to propel the
  rocket are internal forces as they are expelled
  into space propelling the rocket along.
• mAvA2 -mBvB2

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Ch 9 Homework

• Please complete the following
• Pg. 210 Prac. Probs. 7,8,9, 12
• Pg. 218 Rev s 28,34,35, and 36.