Momentum and Impulse

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Momentum and Impulse
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Momentum

• Momentum the product of mass and velocity
• Momentum is matter in motion.
• Ex a dog running down the street
• Equation mv p
• p momentum (kgm/s)
• m mass (kg)
• v velocity (m/s)

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• A more massive object has more p than an object
  with less mass.
• An object at rest has no p (v 0)
• If the p of an object changes, the m, v, or both
  MUST change.
• If the v changes, then the object is accelerating
• a produces F
• The greater the F, the greater ?v
• Which means a greater ?p

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Check Your Understanding

• Which has more momentum, a dog running down the
  street or a large semi truck parked on the side
  of the road?
• The running dog has momentum. The truck has no
  momentum because it is not even moving.

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Check Your Understanding

• A 10 kg cart is rolling down the street at 10
  m/s. What is the carts momentum?
• p ?
• m 10 kg
• v 10 m/s
• mv p
• (10)(10) p 100 kgm/s

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Impulse

• The F sustained for a longer period of time
  produces more ?p.
• This relationship of F to t is called impulse.
• Impulse product of force and time interval
  during which the force acts.
• Ex a car colliding with another car
• Equation J F?t
• J impulse (Ns)
• F force (N)
• ?t time (s)

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• Impulse is equal to the change in momentum.
• J ?p pfinal - pinitial
• In collisions, the amount of damage depends on
  several things.
• One is the hardness of surfaces that connect.
• Two softer, more malleable objects will do less
  damage than two harder, more rigid objects.

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• J does not change if an egg is stopped by a more
  or less malleable surface b/c the objects change
  in momentum would be the same either way.
• J is the same for both
• the only thing that changes is the time interval
  of impact.
• As the t increases, the F decreases.
• Ex car crash with and without airbags, landing
  on the ground with bent knees vs. straight legged

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Check Your Understanding

• Why is falling on a floor with more give (like a
  big fluffy pillow) less dangerous than falling on
  a floor with less give (like concrete or brick)?
• Because the floor with more give allows a greater
  time for an object to come to rest. A greater
  time for a change in momentum results in less
  force.

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Check Your Understanding

• When a dish falls, will the impulse be less if it
  lands on carpet than if it lands on hard floor?
• No. The impulse would be the same for either
  surface because the same momentum change occurs
  for each. It is the force that is less for the
  dish on the carpet because of the greater time of
  momentum change.

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Conservation of Momentum

• Law of Conservation of Momentum In the absence
  of an external force, the momentum of a system
  remains unchanged.
• Ex a gun will recoil when fired b/c the
  momentum of the gun and bullet together before
  the shot should equal the total momentum of the
  bullet and the gun after they have been shot.

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• When a cannon is fired, according to Newtons
  3rd, the ball has an equal but opposite force to
  the cannon.
• Same thing with p (within the system of the
  cannon and the ball)the overall p before and
  after do not changeignoring friction.
• Remember p is vector quantity (magnitude AND
  direction)
• If no net force or net J act on a system, the
  momentum of that system cannot be changed.

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Check Your Understanding

• When fighting fires, a firefighter must use great
  caution to hold a hose which emits large amounts
  of water at high speeds. Why would such a task be
  difficult?
• The hose is pushing lots of water (large mass)
  forward at a high speed. This means the water has
  a large forward momentum. In turn, the hose must
  have an equally large backwards momentum, making
  it difficult for the firefighters to manage.

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Check Your Understanding

• A bomb is sitting at rest on the ground. It
  explodes into 3 pieces with a mass of 5 kg, one
  moving at a speed of 3 m/s east, the other moving
  at a speed of 5 m/s northwest, and the last
  moving at a speed of 4 m/s south. What is the
  total momentum of all 3 pieces after the
  explosion?
• Zero! The momentum before equals the momentum
  after.

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Collisions

• The collision of objects clearly shows the
  conservation of p.
• Net momentum before collision Net momentum
  after collision
• Two main types of collisions
• Elastic and inelastic

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Elastic Collisions

• Elastic collision When objects collide without
  being permanently deformed or without generating
  heat
• The momentum from the first object is transferred
  to the second object (or vice versa).
• Elastic bouncing
• Ex billiard balls (pool) Newtons Cradle

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Inelastic Collisions

• Inelastic collisions When colliding objects
  become entangled or coupled together, thereby
  generating heat or disfigurement
• The net p before the collision equals the net p
  after the collision
• Ex car crashes, sports, bumper cars

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