Chapter 9: Momentum

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Chapter 9 Momentum

• Brent Royuk
• Phys-111Concordia University

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Linear Momentum

• Definition
• Units
• Multiple Objects
• Take the vector sum to get the total for the
  system
• Newtons Second Law

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Impulse

• Rearrange the previous equation
• Units
• Impulse F ?t only if F is constant.
• Otherwise you have to find the area under the
  curve of a F-t graph.
• See graph, p. 245

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Impulse Examples

• Push a 50 kg box with a force of 200 N for 3.0 s.
  How fast is it going?
• A 0.10 kg golf ball gets teed off at 40 m/s in
  1.0 ms. How hard was it hit?

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The Impulse Bargain
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The Impulse Bargain

• Bend legs when landing.
• Let glove recoil when catching a baseball.
• Follow through when batting to increase contact
  time.
• Airbags

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Conservation of Momentum

• So we have
• What if Fnet 0?
• The Law
• If the net force acting on an object is zero, its
  momentum is conserved.
• Internal vs. External Forces

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Conservation of Momentum

• Before and after pictures
• Professor Goddard does not know the relation
  between action and reaction and the need to have
  something better than a vacuum against which to
  react. He seems to lack the basic knowledge
  ladled out daily in high schools. 1921 New York
  Times editorial about Robert Goddard's
  revolutionary rocket work. "Correction It is
  now definitely established that a rocket can
  function in a vacuum. The Times regrets the
  error." NY times, July 1969.

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Conservation of Momentum

• Examples
• Two skaters stand facing each other and push
  against each others hands. Their masses are 80
  kg and 60 kg. If the 80 kg skater moves away at
  a speed of 1.2 m/s, how fast is the other skater
  moving?
• Springy-dingy go-karts
• A stream of bullets, each with a mass of 3.8 g,
  is fired horizontally with a speed of 1100 m/s
  into a large wooden block of mass 12 kg at rest
  on a frictionless table. How fast will the block
  be moving if it absorbs 8 bullets?

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Conservation of Momentum

• Examples
• A 75 kg man is riding on a 39 kg cart traveling
  at a speed of 2.3 m/s. He jumps off in such a
  way as to land on the ground with zero horizontal
  speed. What is the new speed of the cart?
• A motionless 50 kg boy on ice skates catches a
  2.0 kg medicine ball and subsequently moves with
  a speed of 2.0 m/s. How fast was the ball
  moving? Is this realistic?

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Collisions

• Example
• Consider two 2000 kg boxcars. One moves at 1.0
  m/s and hits the other, coupling. Find speed
  with momentum. Compare kinetic energies.

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Elastic vs. Inelastic

• Momentum is always conserved, energy need not be.
• Elastic bouncy? yes
• Things that stick together are completely
  inelastic clay vs. superballs.
• Happy/unhappy balls
• Derive fractional energy relationship for
  completely inelastic collisions (stationary
  target)
• Little hitting big vs. big hitting little
• Go-Carts

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Elastic vs. Inelastic

• Consider Final velocities in a completely
  elastic collision with a stationary target
• Result

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Elastic Collisions
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Newtons Cradle
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2-D Collisions
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2-D Collisions

• A collision occurs as described below. Both
  balls have the same mass. Find the speeds of
  both balls after the collision.

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The Ballistic Pendulum
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Center of Mass

• Whats it good for?
• The balance point
• A system of particles moves like a single
  particle at its COM
• Forces acting through the COM produce no torque
• Can apply to a system of unconnected particles or
  to a compound object

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Center of Mass

• Definition
• This is doable for discrete particles, difficult
  for continuous mass distributions you need
  calculus

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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples
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Center of Mass Examples