A rolling stone

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A rolling stone

• Gathers momentum!
• December 14/15, 2009

2
Miscellaneous

• Tests back today!
• Make ups by Thursday.

3
Today

• Momentum carries us through Winter Break
• Momentum
• p???
• Impulse
• Stopping distance

4
p as in progress

• Momentum is related to inertia
• An object in motion
• p m v
• Try it without your TI 83, 89 or 92.7!
• A 2,250 kg truck has a velocity of 10 m/s east
• p ?
• 22,500 kg m/s east

5
Momentum changes when

• If you kick a soccer ball
• You apply a force
• For some amount of time
• The velocity changes
• It accelerates
• We learned this from Newtons 2nd law
• F ma

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Newton thought about momentum

• F ma
• a ?v/?t
• F m ?v/?t
• Force is equal to a change in momentum over time
• If you multiply both sides by ?t
• F ?t m ?v
• ?p m?v
• ?p mvf mvi
• F ?t is called IMPULSE

7
Impulse force x time

• Think of follow through
• Whether you are golfing, playing soccer or boxing
• Follow through is essential
• Why? What does it do?

8
A car runs into a median barrel

• It has a mass of 700 kg and is traveling at 15
  m/s
• Comes to a rest in 0.30 seconds
• How much force is applied to the car?
• How about if the collision takes 3xs as long?

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Dont forget the earlier units

• A 2.0 kg rock falls off of a cliff and free falls
  for 10 meters.
• At the bottom of the cliff it lands in a marsh
  and after 0.4 seconds comes to a rest.
• What force is applied to the rock by the mud in
  the swamp?

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Stopping distance

• You can determine the amount of time it takes to
  stop an object
• Provided you know
• Force applied
• Mass
• Starting velocity
• How can you use that information to determine the
  stopping distance?
• ?x ½ (vf vi) ?t

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Hit the brakes!

• A 1500 kg car is moving along at 40 m/s
• Brakes are applied with a force of 6,250 N.
• What is the time it takes to 10 m/s?
• How far does it go?

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The rock bounces

• Lets start with the same initial scenario.
• But the rock hits dirt and bounces
• With an upward velocity of 1.0 m/s
• After contact with the ground for the same period
  of time (0.4 seconds)
• Now, what is the force?
• How can you use this idea?

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Think about this one

• Same as before, but I tell you it bounces to a
  height of 4 meters

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Collisions Momentum

• Dec 16/17, 2009
• And a quick Stopping Distance review

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Today

• Homework review
• Collisions
• Lab

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Homework 6A, 6B

• 6A
• 1) 2,500 kgm/s RIGHT
• 2) 120 kgm/s NW 94 kgm/s NW 27 kgm/s NW
• 3) 46 m/s east

• 6B
• 1) 380 N LEFT
• 2) 1,100 N up
• 3) 16.0 kgm/s south
• 4) 9.0 m/s right 15 m/s left

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Revisit Stopping Distance

• A 2250 kg car traveling at 20 m/s west
• Slows to 5 m/s
• If the braking force is 8450 N east
• How much time does it take?
• How far do you go?
• Lets look at what how far wed go if the mass
  were bigger
• Say twice as massive

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Collisions
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Imagine

• That you are floating in outer space
• A small asteroid comes along traveling at some
  velocity
• And hits you in the chest
• What happens to the asteroid and what happens to
  you?
• Well, it depends

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It depends?

• You might stop the asteroid and you go flying
  away
• You might hang onto the asteroid and you both
  meander away
• You bounce off the asteroid and both of you keep
  moving

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So, what can we say?

• The total momentum of the system will be
  conserved!
• Total momentum before sum of the momentum after
• m1v1i m2v2i m1v1f m2v2f

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Conservation of momentum

• The total momentum of the system will be
  conserved!
• Total momentum before sum of the momentum after
• m1v1i m2v2i m1v1f m2v2f

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Why?

• Newtons 3rd Law
• If 2 objects collide what can we say about the
  force felt by each object?
• What about the time
• (F?t)object 1 (-F?t)object 2
• m1v1f - m1v1i -(m2v2f - m2v2i )
• Lets combine i and f terms
• m1v1i m2v2i m1v1f m2v2f

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A conventional collision

• m1v1i m2v2i m1v1f m2v2f
• Object A (3 kg) moving at 6 m/s right
• Object B (2 kg) moving at 5 m/s left
• They collide and afterwards
• Object A is moving left at 4 m/s
• What is the velocity of Object B?

25
Never stand up in a canoe

• m1v1i m2v2i m1v1f m2v2f
• You (76 kg) are in a boat (45 kg) next to a dock
• You step out of the boat with a velocity of 2.5
  m/s
• The boat moves away from the dock
• HOW FAST IS IT GOING?

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How would this change if

• The boat and the person were approaching the dock
  at 1 m/s?
• How fast would the person have to leave the boat
  (above) in order to have it stop when she jumped
  out?

27
Look at this from another angle
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Lunch!
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Lunch to go!
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Todays lab

• Make your own collision (no vectors)
• Some suggestions

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Collisions elastic and inelastic

• Dec 18, 2009
• Jan 4, 2010

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Homework

• 6C
• 1) 5.33 s 53.3 m
• 2 a) 14 m/s north
• 2 b) 42 m north
• 2 c) 8.0 s
• 3) 12,200 N east
• 53.3 m

• 6D
• 1) 1.90 m/s
• 2) 1.66 m/s
• 3 a) 12.0 m/s
• 3 a) 9.6 m/s
• 3 a) 11.7 m/s
• 4) 38 kg

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Collisions!
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Inelastic vs elastic?

• What is the difference between a ball bouncing on
  the concrete floor
• And an egg breaking on the sidewalk?
• Or billiard balls hit by a cue ball
• And a car crash where the 2 cars are smooshed
  together?

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(Perfectly?) inelastic

• When 2 objects stick together after a collision
• They often deform and/or heat up
• the momentum equation becomes
• m1v1i m2v2i (m1 m2)vf
• Momentum is conserved!
• But kinetic energy is NOT!

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Example

• Two clay balls collide head on in a perfectly
  inelastic collision.
• Ball A mass 4 kg velocity 4 m/s
• Ball B mass 2 kg velocity - 4 m/s
• Find the final velocity
• Calculate the KE before and after

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Perfectly elastic

• When 2 objects bounce off of each other we go
  back to the original equation
• AND kinetic energy is conserved

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Example

• Two balls collide head on in a perfectly elastic
  collision.
• Ball A mass 0.40 kg velocity 3.0 m/s
• Ball B mass 0.60 kg velocity 0.0 m/s
• Ball A has a final velocity of -0.6 m/s
• Find the final velocity of Ball B
• Calculate the KE before and after

41
What do you think?

• You observe a collision where the objects bounce
  apart
• You determine that momentum is conserved.
• But kinetic energy is not conserved.
• What type of collision is this?
• We call this inelastic
• Not perfectly inelastic, just inelastic.

42
Collisions arent always head on

• What happens when a cue ball hits a billiard ball
  off center?
• Is momentum conserved?
• Sure, we just have to look at both x, and y
  components separately.

43
Vectors!
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Lets consider a simple situation

• Ball of 2.0 kg heads along the x axis at 4 m/s
• Strikes a ball of equal mass
• The first ball goes 37 degrees up from the x
  axis at 2 m/s.
• What is the velocity of the other ball?
• Speed and direction

45
Momentum Lab

• The point?
• IS MOMENTUM CONSERVED?
• Transfer to your lab sheet and graphically or
  mathematically determine if momentum was
  conserved.
• Be precise I expect you to use a straight edge
  and measuring devices.

46
Collisions elastic and inelastic

• Dec 11/12, 2008

47
Homework

• 6C
• 1) 5.33 s 53.3 m
• 2 a) 14 m/s north
• 2 b) 42 m north
• 2 c) 8.0 s
• 3) 12,200 N east
• 53.3 m

• 6D
• 1) 1.90 m/s
• 2) 1.66 m/s
• 3 a) 12.0 m/s
• 3 a) 9.6 m/s
• 3 a) 11.7 m/s
• 4) 38 kg

48
Collisions!
49
(No Transcript)
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(No Transcript)
51
Inelastic vs elastic?

• What is the difference between a ball bouncing on
  the concrete floor
• And an egg breaking on the sidewalk?
• Or billiard balls hit by a cue ball
• And a car crash where the 2 cars are smooshed
  together?

52
Perfectly inelastic

• When 2 objects stick together after a collision
• They often deform and/or heat up
• the momentum equation becomes
• m1v1i m2v2i (m1 m2)vf
• Momentum is conserved!
• But kinetic energy is NOT!

53
Example

• Two clay balls collide head on in a perfectly
  inelastic collision.
• Ball A mass 4 kg velocity 4 m/s
• Ball B mass 2 kg velocity - 4 m/s
• Find the final velocity
• Calculate the KE before and after

54
Perfectly elastic

• When 2 objects bounce off of each other we go
  back to the original equation
• AND kinetic energy is conserved

55
Example

• Two balls collide head on in a perfectly elastic
  collision.
• Ball A mass 0.40 kg velocity 3.0 m/s
• Ball B mass 0.60 kg velocity 0.0 m/s
• Ball A has a final velocity of -0.6 m/s
• Find the final velocity of Ball B
• Calculate the KE before and after

56
What do you think?

• You observe a collision where the objects bounce
  apart
• You determine that momentum is conserved.
• But kinetic energy is not conserved.
• What type of collision is this?
• We call this inelastic
• Not perfectly inelastic, just inelastic.

57
Collisions arent always head on

• What happens when a cue ball hits a billiard ball
  off center?
• Is momentum conserved?
• Sure, we just have to look at both x, and y
  components separately.

58
Vectors!
59
Lets consider a simple situation

• Ball of 2.0 kg heads along the x axis at 4 m/s
• Strikes a ball of equal mass
• The first ball goes 37 degrees up from the x
  axis at 2 m/s.
• What is the velocity of the other ball?
• Speed and direction

60
Momentum Lab

• The point?
• IS MOMENTUM CONSERVED?
• Transfer to your lab sheet and graphically or
  mathematically determine if momentum was
  conserved.
• Be precise I expect you to use a straight edge
  and measuring devices.

61
Snow

• January 5/6, 2009

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Today, Thursday and Monday

• Today
• Review
• Ballistic Pendulum
• Thursday
• Egg drop lab
• Review

• Monday
• Unit test

63
Top Ten Scientific Discoveries

• 2008

64
Large Hadron Collider

• Bad news
• Start up still pending
• Good news
• no black holes!

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This unit

• Momentum
• p mv
• Impulse Momentum Theory
• Ft m?v
• stopping distance
• Conservation of momentum
• Collision types
• Perfectly Elastic KE conserved
• Inelastic

66
Homework for today

• 6E
• 1) 3.75 m/s
• 2) 1.83 m/s
• 3) 4.25 m/s

• 6F
• 1) 0.43 m/s -16.7 J
• 2) 6.2 m/s south -3.9 J
• 6G
• 1) 0.225 m/s
• 2) 4.8 m/s

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What happens when things bounce?

• Bigger change in momentum
• Means bigger impulse.
• The paintball experience

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Dont forget

• Conservation of ME
• Free fall
• Constant acceleration

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Why

• Why cant we use conservation of energy for
  collisions?
• Why cant we just use conservation of momentum
  for everything?
• Try this on for size

70
Egg-citing!!

• December 15/18, 2008

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Today

• Egg Drop!!
• Determine mass of your device before the drop
• Homework
• Concept review
• Complete and turn in
• Labs momentum, vector and egg-celeration
• Review sheet - start

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When I call your name

• Bring your
• Lab partner
• Device
• Lab Sheet with drawing
• After I give you the egg
• Determine the mass of the device and egg
• Take a seat and be patient
• Dont drop your egg

73
Homework for today

• 6E
• 1) 3.75 m/s
• 2) 1.83 m/s
• 3) 4.25 m/s

• 6F
• 1) 0.43 m/s -16.7 J
• 2) 6.2 m/s south -3.9 J
• 6G
• 1) 0.225 m/s
• 2) 4.8 m/s

74
This unit

• Momentum
• p mv
• Impulse Momentum Theory
• Ft m?v
• stopping distance
• Conservation of momentum
• Collision types
• Perfectly Elastic KE conserved
• Inelastic

75
What happens when things bounce?

• Bigger change in momentum
• Means bigger impulse.
• The paintball experience

76
Dont forget

• Conservation of ME
• Free fall
• Constant acceleration

77
Using your data

• Determine the impulse required from the concrete
  to stop your device.
• If the time of the impulse was 0.05 seconds, what
  was the force?
• If the maximum force the egg could survive was
  1.5 N, how long should the time of the impulse
  be?
• Did the mass make any difference?