CPI: Lecture 11 Momentum and Impulse

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CPI Lecture 11Momentum and Impulse
Exam I
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Momentum is Conserved

• Momentum is Conserved meaning it can not be
  created nor destroyed
• Can be transferred
• Total Momentum does not change with time.
• This is a BIG deal!

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Pushing Off

• Fred and Jane are on skates facing each other.
  Jane then pushes Fred w/ Force F
• N2L Fred FJF mFred a
• DvFred a Dt
• (FJF/mFred) Dt
• mFred DvFred FJF Dt
• N2L Jane FFJ mJane a
• DvJane a Dt
• (F/mJane) Dt
• mJane DvJane FJF Dt
• N3L For every action, there is an equal and
  opposite reaction. FFJ-FJF
• mFred DvFred -mJane DvJane

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Momentum is Conserved!

• Define Momentum p m v
• m1 Dv1 -m2 Dv2
• Dp1 -Dp2
• Dp1 Dp2 0 !Momentum is Conserved!
• Spinitial Spfinal
• Example Jane pushes Fred so he is going 2.0 m/s.
  If Fred is twice as heavy as Jane, how fast does
  Jane end up moving.
• Spinitial Spfinal
• 0 mFred VFred mJane VJane
• VJane mFred VFred / mJane 4 m/s

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Preflight 2 3

• Two identical balls are dropped from the same
  height onto the floor. In case 1 the ball bounces
  back up, and in case 2 the ball sticks to the
  floor without bouncing. In which case is the
  impulse given to the ball by the floor the
  biggest?
• 1. Case 1
• 2. Case 2
• 3. The same

Bouncing Ball I Dp mvfinal m vinitial
m( vfinal-vinitial) 2 m v
Sticky Ball I Dp mvfinal m vinitial
m( 0-vinitial) m v
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Momentum is Vector

• Example 7.1 A car w/ mass 1200 kg is driving
  north at 30 m/s, and turns east driving 13.6 m/s.
  What is the magnitude of the cars change in
  momentum?

Pinitial m vinitial (1200 Kg) x 30 m/s
36000 kg m/s North Pfinal m vfinal (1200 Kg)
x 13.6 m/s 16320 kg m/s East
North-South Pfinal Pinitial (0 36000)
-36000 kg m/s
13.6 m/s
East-West Pfinal Pinitial (16320 - 0)
16320 kg m/s
30 m/s
Magnitude Sqrt(P2North P2East ) 39526 kg m/s
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Impulse changes Momentum

• Define Impulse I FDt
• Change in momentum requires Force acting over a
  time or Impulse.
• Recall mDv FDt
• Or Dp FDt
• Dp I

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Preflight 1

• A few weeks ago I did a lecture demonstration
  where I yanked a tablecloth out from under some
  dishes. After reading section 7.1, in particular
  equation 7.1, can you briefly explain why the
  dishes were not given much impulse by the
  tablecloth.

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Preflight 4

• In both cases of the above question, the
  direction of the impulse given to the ball by the
  floor is the same. What is this direction?
• 1. Upward
• 2. Downward

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ACTs
You drop an egg onto 1) the floor 2) a thick
piece of foam rubber. In both cases, the egg does
not bounce. In which case is the impulse
greater? A) Floor B) Foam C) the same
I DP Same change in momentum
In which case is the average force greater A)
Floor B) Foam C) the same
Dp F Dt F Dp/Dt Smaller Dt large F
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Impulse and Momentum Summary

• Fave?t ? I pf - pi ?p
• For single object.
• F 0 ? momentum conserved (?p 0)
• For collection of objects
• ?Fext 0 ? total momentum conserved (?Ptot 0)
• Fext mtotal a

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Preflight 5 6

• Is it possible for a system of two objects to
  have zero total momentum while having a non-zero
  total kinetic energy?
• 1. YES
• 2. NO

the example of the ice skaters starting from rest
and pushing off of each other...the total
momentum is zero because they travel in opposite
directions but the kinetic energy is not zero
(they start with none and gain a bunch)
If it has zero momentum, it must not be moving.
So all kinetic energy must be transferred to
potential energy.
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ACT

• Movies often show someone firing a gun loaded
  with blanks. In a blank cartridge the lead bullet
  is removed and the end of the shell casing is
  crimped shut to prevent the gunpowder from
  spilling out. When a gun fires a blank, is the
  recoil greater than, the same as, or less than
  when the gun fires a standard bullet?
• 1. greater than
• 2. same as
• 3. less than

If there is no bullet then pbullet 0 so pgun 0
As if ice skater had no one to push
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Summary

• Momentum p mv
• Momentum is VECTOR
• Momentum is conserved (when SF 0)
• S mvinitial S mvfinal
• Impulse I FDt
• Gives change in momentum I Dp