Impulse

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Impulse Momentum
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From Newton 2

• Previously Work-Energy
• S F m a multiply both sides by d
• S F d m a d (note a d ½ Dv2)
• S F d ½ m Dv2
• S W DKE
• Define Work and Kinetic Energy

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From Newton 2Two New ConceptsImpulse Momentum
Impulse Change in Momentum
Momentum
Momentum is vector in direction of
velocity. Impulse is vector in direction of
force.
Impulse
Change In Momentum
N-s
Kg m/s
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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. Can you briefly explain why the dishes
  were not given much impulse by the tablecloth.

Impulse is defined as force time the change in
time. If the change in time is very small, the
impulse is going to be small.
The dishes just didnt feel like moving
The cloth may have been made out of a slick
material (i.e. silk) so the friction is
negligible
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Preflight 2 3

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

yes, when two objects have the same mass and
velocities and they push off each other..momentum
is zero and kinetic energy is nonezero.
2 balls traveling at the same speed hit each
other head-on.
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Change in Momentum ACT
If the bear and the ball have equal masses, which
toy experiences the greater change in momentum?
Change in momentum Dp pafter - pbefore Teddy
Bear Dp 0-(-mv) mv Bouncing Ball Dp
mv-(-mv) 2mv
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Change in Momentum ACT2
A 10 kg cart collides with a wall and changes
its direction. What is its change in x-momentum
Dpx?

1. -30 kg m/s
2. -10 kg m/s
3. 10 kg m/s
4. 20 kg m/s
5. 30 kg m/s

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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 ? same impulse
In which case is the average force greater A)
Floor B) Foam C) the same
Dp F Dt F Dp/Dt Smaller Dt larger F
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Pushing Off

• Fred (75 kg) and Jane (50 kg) are at rest on
  skates facing each other. Jane then pushes Fred
  w/ a constant force F 45 N for a time Dt3
  seconds. Who will be moving fastest at the end
  of the push?
• A) Fred B) Same C) Jane

Fred F 45 N (positive direct.) I 45 (3)
N-s 135 N-s I Dp mvf mvi I/m vf -
vi vf 135 N-s / 75 kg 1.8 m/s
Jane F -45 N Newtons 3rd law I -45 (3)
N-s -135 N-s I Dp mvf mvi I/m vf -
vi vf -135 N-s / 50 kg -2.7 m/s
Note Pfred Pjane (1.8) 75 (-2.7) 50 0!
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Momentum Change ACT

• A car w/ mass 1200 kg is driving north at 40
  m/s, and turns east driving 30 m/s. What is the
  magnitude of the cars change in momentum?
• A) 0 B) 12,000 C) 36,000 D) 48,000 E) 60,000

Pinitial m vinitial (1200 Kg) x 40 m/s
48,000 kg m/s North Pfinal m vfinal (1200
Kg) x 30 m/s 36,000 kg m/s East
North-South Pfinal Pinitial (0 48000)
-48,000 kg m/s
30 m/s
East-West Pfinal Pinitial (36000 - 0)
36,000 kg m/s
40 m/s
Magnitude Sqrt(P2North P2East ) 60,000 kg
m/s
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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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• 4. IP Two air track carts move toward one
  another on an air track. Cart 1 has a mass of
  0.45 kg and a speed of 1.1 m/s. Cart 2 has a mass
  of 0.65 kg. (a) What speed must cart 2 have if
  the total momentum of the system is to be zero?
  (b) Since the momentum of the system is zero,
  does it follow that the kinetic energy of the
  system is also zero? (c) Verify your answer to
  part (b) by calculating the systems kinetic
  energy.

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• 9. In a typical golf swing, the club is in
  contact with the ball for about 0.0010 s. If the
  45-g ball acquires a speed of 67 m/s, estimate
  the magnitude of the force exerted by the club on
  the ball.
•  
•  

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• 5. A 0.150-kg baseball is dropped from rest.
  If the magnitude of the baseballs momentum is
  just before it lands on the ground, from what
  height was it dropped?