Momentum

1
Momentum

• Physics 1010
• Dr. Don Franceschetti
• February 10, 2006

2
Guide questions

• Isnt there an easier way to solve physics
  problems than by using Newtons laws?
• Why do football players wear so much padding?
• How do real CSIs determine what happened in a
  crash when there are no survivors?
• How do you measure the speed of a speeding
  bullet?
• How do particle physicists study collisions of
  particles that they cant see?

3
Feynmanns Chess Game Analogy

• Studying nature is like watching a complex game
  being played at high speed and trying to figure
  out the rules from what we see.

4
Chess analogy, contd

• You look for simple plays where only a few
  pieces are involved
• You notice some constanciessome things are
  conserved
• You eventually get an idea of an overall strategy
• You are allowed to rearrange the game board a
  little bit

5
Dynamical View

• Newtons three laws and the various force laws
  come from observing and experimenting with simple
  situations.

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Conservation View

• Certain quantities are conserved
• Momentum
• Energy
• Angular momentum.
• Knowing these conservation laws lets us solve a
  lot of problems, especially when we dont know
  the detailed nature of the forces

7
Strategy View in Mechanics(Geniuses Only)

• For any process that begins with particles at
  given position at time t1 and ends with them at
  given positions at time t2,nature selects paths
  for the particles such that a certain quantity
  called the action is minimum for the path
  actually taken. (Principle of Least Action)
• This is weird but nonetheless true. It can be
  shown equivalent to Newtons laws.

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Momentum

• The momentum of an object is the product of its
  mass and velocity.
• Pmv
• Because velocity is a vector, momentum is a
  vector.
• Newtons first law tells us that if the net force
  on an object is zero, the momentum does not
  change
• Momentum has units of kg m / s

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Net force produces momentum change

• If a constant force acts for time interval t.
• Ft mat m Dv D (mv)
• Ft is called the impulse delivered by the net
  force.
• The units of impulse are Ns which are the same
  as kg m / s
• For a force which varies in time we can
  calculate the impulse it delivers using calculus,
  or from D (mv).

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Objects with lots of momentum

• Planets and moons
• Asteroids (usually)
• Supertankers
• Railroad trains
• Jumbo jets

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Events with lots of impulse

• Baseball hitting bat
• Golf club hitting ball
• Boxer hitting boxer
• Ball bouncing from
• floor/wall
• Bullet hitting target
• Billiard ball collision
• Car collisions
• Elementary particle collisions

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For the same momentum change

• You can reduce the force experienced by
  lengthening the time of contact. So,
• Baseball catchers wear front padding
• Football players wear shoulder pads
• Manic patients get padded cells
• Boxers wear padded gloves
• You should roll with the punches
• But if you want to maximize force, keep the time
  short--karate

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Law of Momentum Conservation

• The momentum of a system is the sum of the
  momenta of the objects that make it up.
• In the absence of external forces, the momentum
  of any system is conserved.
• For a system of one object, this is Newtons
  first law
• For a system of more than one object, this
  follows from Newtons third law

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Collisions

• Are interactions in which very strong forces act
  for very short times.
• Generally, we can ignore external forces for the
  duration of the collision.
• Momentum is conserved in collisions.
• Explosions and sticking are examples of
  collisions in which the number of objects
  changes.

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Collisions can be

• Elastic no lasting deformation of any object or
  heat produced
• Inelastic some lasting deformation or heat
  produced
• Completely inelastic objects stick together

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Review

• Q6.1 Which has the greater momentum, a heavy
  truck at rest or a moving skateboard?
• Q6.4 Is the impulse momentum relationship
  related to Newtons third law?

17
Review

• Q 6.22 Railroad car A rolls at a certain speed
  and makes a perfectly elastic collision with car
  B of the same mass. After the collision, car A
  is observed to be at rest. How does the speed of
  car A compare with the speed of car B?

18
Review

• E 6.3. In terms of impulse and momentum, why do
  air bags in cars reduce the chances of injury in
  accidents.
• E 6.14 If a ball is projected upward with 10 kg
  m/s of momentum, what is the momentum of recoil
  of the world? Why do we not feel this?

19
Review

• P 6.1 What is the impulse needed to stop a 10-kg
  bowling ball moving at 6 m/s?
• Q 5.8 To produce a net force on a system, must
  there be an externally applied force?

20
Review

• E 5.6 When you drop a rubber ball on the floor it
  bounces almost to the original height. What
  causes the ball to bounce?
• E 5.13 Why does a rope climber pull downward on
  the rope to move upward?