Momentum and Impulse

1
Momentum and Impulse
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What is Momentum?

• Momentum The product of the mass and velocity
  of an object. Has magnitude and direction.
• Momentum p mv
• P momentum
• M mass
• V velocity
• Units kgm/s

3
Inertia?

• Remember Newtons 1st Law?
• An object at rest will stay at rest
• and
• An object in motion will stay in motion in the
  same speed and direction unless acted on by an
  outside force.

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Whats Inertia Got to Do with It?

• Momentum is directly related to the second part
  of Newtons 1st Law
• An object in motion stays in motion (same speed
  and direction) unless acted on by a force

5
Lets practice

• A 1200 kg car drives west at 25 m/s for 3 hours.
  What is the cars momentum?
• Identify the variables
• 1200 kg mass
• 25m/s, west velocity
• 3 hours time
• P mv 1200 x 25 30000 kg m/s, west

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How hard is it to stop a moving object?

• Impulse Product of force and time interval
  during which the force acts. Impulse equals
  momentum change.
• Impulse F?t
• F force (N)
• ?t time elapsed (s)
• Units Ns

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How hard is it to stop a moving object?

• Using Newtons 2nd Law we get
• Impulse change in momentum
• F?t m?v

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Why does an egg break or not break?

• An egg dropped on a tile floor breaks, but an egg
  dropped on a pillow does not. Why?
• F?t m?v
• In both cases, m and ?v are the same.
• If ?t goes up, what happens to F, the force?
• Right! Force goes down. When dropped on a
  pillow, the egg starts to slow down as soon as it
  touches it. A pillow increases the time the egg
  takes to stops.

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Practice Problem

• A 57 gram tennis ball falls on a tile floor. The
  ball changes velocity from -1.2 m/s to 1.2 m/s
  in 0.02 s. What is the average force on the
  ball?
• Identify the variables
• Mass 57 g 0.057 kg
• ?velocity 1.2 (-1.2) 2.4 m/s
• Time 0.02 s
• using F?t m?v
• F x (0.02 s) (0.057
  kg)(2.4 m/s)
• F 6.8 N

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Car Crash

• Would you rather be in a head on collision
  with an identical car, traveling at the same
  speed as you, or a brick wall?
• Assume in both situations you come to a
  complete stop.
• Take a guess

http//techdigestuk.typepad.com/photos/uncategoriz
ed/car_crash.JPG
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Car Crash (cont.)

• The answer is
• It Does Not Matter!
• Look at F?t m?v
• In both situations, ?t, m, and ?v are the same!
  The time it takes you to stop depends on your
  car, m is the mass of your car, and ?v depends
  on how fast you were initially traveling.

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Conservation of Momentum
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Conservation of Momentum

• Just like energy, momentum is conserved.
• The total momentum at the start will equal the
  total momentum at the end

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Vectors!

• Remember that momentum is a vector value, so if
  two momentums are in opposite directions, they
  are opposite signs and end up cancelling (at
  least in part)

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Two Flavors!!

• Collisions may be
• Elastic the objects completely bounce off each
  other
• Billiards (pool) ball have elastic
  collisions
• Inelastic the objects stick together at the
  collision and travel together thereafter
• Car Crashes have become inelastic with
  better engineering

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Momentum Formulas

• The standard formula for momentum is
• Pmv
• What happens if we have two objects that collide
  and bounce off each other..elastic??
• We can make a formula for this due to the
  conservation of momentum!
• M1V1i M2V2i M1V1f M2V2f

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Practice Elastic

• A 50 kg skater traveling at 10 m/s hits a 40 kg
  skater sitting still, imparting all his momentum
  into the 2nd skater. What is the velocity of the
  2nd skater?
• M1V1i M2V2i M1V1f M2V2f
• (50 kg)(10 m/s) (40 kg)(0 m/s) (50 kg)(0 m/s)
  (40 kg)V2f
• (500 kgm/s) (0 kgm/s) (0 kgm/s) (40
  kg)V2f
• 12.5 m/s V2f

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Practice Problem

• A 50 kg skater traveling at 10 m/s hits a 40 kg
  skater sitting still. The 1st skater ends up at 2
  m/s. What is the velocity of the 2nd skater?
• M1V1i M2V2i M1V1f M2V2f
• (50 kg)(10 m/s) (40 kg)(0 m/s) (50 kg)(2 m/s)
  (40 kg)V2f
• (500 kgm/s) (0 kgm/s) (100 kgm/s) (40
  kg)V2f
• 10 m/s V2f

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Practice Problem

• A 50 kg skater traveling at 20 m/s hits a 40 kg
  skater moving in the same direction at 3 m/s. The
  1st skater ends up at 5 m/s. What is the velocity
  of the 2nd skater?
• M1V1i M2V2i M1V1f M2V2f
• (50 kg)(20 m/s) (40 kg)(3 m/s) (50 kg)(5 m/s)
  (40 kg)V2f
• (1000 kgm/s) (120 kgm/s) (125 kgm/s) (40
  kg)V2f
• 24.875 m/s V2f

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Inelastic Collision Formula

• Since the objects travel together after the
  collision, we have a slightly different formula
  for inelastic collisions
• M1V1i M2V2i (M1 M2)Vf
• This shows the final momentum is created by the
  total mass of the two objects together

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Practice Inelastic

• A 50 kg skater traveling at 20 m/s picks up a 40
  kg passenger skating sitting still, what is the
  velocity of the two skaters?
• M1V1i M2V2i (M1 M2)Vf
• (50 kg)(20 m/s) (40 kg)(0 m/s) (90 kg)Vf
• (1000 kgm/s) (0 kgm/s) (90 kg)Vf
• 11.1 m/s Vf

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Practice Problem

• A 50 kg skater traveling at 20 m/s picks up a 40
  kg passenger skating in the same direction at 5
  m/s, what is the velocity of the two skaters?
• M1V1i M2V2i (M1 M2)Vf
• (50 kg)(20 m/s) (40 kg)(5 m/s) (90 kg)Vf
• (1000 kgm/s) (200 kgm/s) (90 kg)Vf
• 13.3 m/s Vf

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Practice Problem

• A 50 kg skater traveling at 20 m/s picks up a 40
  kg passenger skating in the opposite direction at
  5 m/s, what is the velocity of the two skaters?
• M1V1i M2V2i (M1 M2)Vf
• (50 kg)(20 m/s) (40 kg)(-5 m/s) (90 kg)Vf
• (1000 kgm/s) - (200 kgm/s) (90 kg)Vf
• 8.89 m/s Vf