Chapter 6: Momentum and Collisions!

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Chapter 6 Momentum and Collisions!
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The Solar System(not to scale!)
A Question for you to ponder Why do the Sun and
all of the planets (except Venus) rotate In the
same direction?
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The Answer lies in the Formation of the Solar
System
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4 billion miles awaydo you see what I see?
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So What?

• What does this have to do with Chapter 6?
• Planet formation is directly tied to the law of
  conservation of momentum!
• Yay for more laws ?

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Linear Momentum

• Momentum describes how the motions of objects are
  changed
• Newtons Laws explain why
• The Linear Momentum equation
• pmv
• Momentum mass x velocity
• MOMENTUM IS A VECTOR!!

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Sample Problem

• A 3000kg elephant is chasing a 1 kg squirrel
  across the road at a velocity of 5 m/s to the
  west. What is the momentum of the elephant? If
  the squirrel is running at 7 m/s west what is its
  momentum?

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Solve the Problem

• Momentum of the elephant
• p mv (3000 kg)(5m/s) 15000 kgm/s West
• Momentum of the squirrel
• pmv (1kg)(7m/s) 7 kgm/s West

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Change in Momentum

• A change in momentum takes force and time
• It takes a lot of force to stop an object that
  has a lot of momentum

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Impulse Momentum Theorem

• A net external force, F, applied to an object for
  a time interval, ?t, will cause a change in the
  objects momentum equal to the product of the
  Force and the time interval.
• In other words

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What does that mean?

• A small force acting for a long time can produce
  the same change in momentum as a large force
  acting for a short time.
• In sports like baseball, this is why follow
  through is important. The longer the bat is in
  contact with the ball, the greater the change in
  momentum will be.

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Sample Problem p. 211 3

• A 0.40 kg soccer ball approaches a player
  horizontally with a velocity of 18 m/s north. The
  player strikes the ball and causes it to move in
  the opposite direction with a velocity of 22 m/s.
  What impulse was delivered to the ball by the
  player?

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What do we know?

• M 0.40 kg
• Vi 18 m/s
• Vf -22 m/s
• What does impulse mean?
• Impulse is equal to F?t
• Impulse is also equal to the objects change in
  momentum

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Solve the problem
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Stopping Distance

• The stopping distance is the distance it requires
  an object to come to rest
• The greater the momentum, the more distance it
  takes to stop

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Sample Problem p.213 2

• A 2500 kg car traveling to the north is slowed
  down uniformly from an initial velocity of 20.0
  m/s by a 6250 N braking force acting opposite the
  cars motion. Use the impulse momentum theorem to
  answer the following questions
• A. What is the cars velocity after 2.50 s?
• B. How far does the car move during 2.50 s?
• C. How long does it take the car to come to a
  complete stop.

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Answer part a.

• Why is F negative?
• Because it is acting opposite the cars motion!

• m 2500 kg
• Vi 20 m/s North
• F -6250 N
• t 2.50 s
• Vf ?

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Use the impulse-momentum theorem!!
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Solve Part B

• How far does the car move in 2.5 s?
• Which kinematic equation should we use?

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Solve Part c

• How long does it take for the car to come to a
  complete stop?
• Use impulse momentum theorem!

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Summary of 6.1

• Momentum is a vector quantity that is equal to
  the product of an objects mass and its velocity
  (pmv)
• Impulse F?t ?p
• A small force applied over a long period of time
  produces the same change in momentum as a large
  force applied over a short period of time

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Section 6.2 Conservation of Momentum

• Remember...we talked about the formation of the
  solar system and conservation of momentum.

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Lets Talk about the Moon
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We are the only inner planet with a large
moonwhy?

• Our moon didnt form with us in the nebula
• We acquired it later through a collision with
  another planetoid
• http//vimeo.com/2015273

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The Moon is trying to leave us

• Every year, the moon moves about 4 cm away from
  the Earth and thus its velocity increases
• Conservation of Momentum says that velocity has
  to come from somewhere. Sothe moon steals it
  from us
• So every year, our rotation slows down adding
  about 0.0002 seconds to our day.

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Momentum is Conserved

• The Law of Conservation of Momentum says
• The total momentum of all objects interacting
  with one another remains constant regardless of
  the nature of the forces between the objects.

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In mathematical form

• Be very careful with your signs when using this
  equation!!

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Collisions

• There are many different ways to describe
  collisions between objects
• In any collision, the total amount of momentum is
  conserved but generally the total kinetic energy
  is not conserved

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Perfectly Inelastic Collisions

• When two objects collide and move together as one
  mass, the collision is perfectly inelastic
• Since the two objects stick together and move as
  one, they have the same final velocity.
• Kinetic Energy IS NOT CONSERVED in PERFECTLY
  INELASTIC COLLISIONS

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Sample Problem p. 219 2

• An 85.0 kg fisherman jumps from a dock into a 135
  kg rowboat at rest on the west side of the dock.
  If the velocity of the fisherman is 4.30 m/s to
  the west as he leaves the dock, what is the final
  velocity of the fisherman and the boat?

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What do we know

• M1 85 kg
• M2 135 kg
• V2,i0
• V1,i -4.30 m/s
• What type of collision is this?
• PERFECTLY INELASTIC because they stick together
  and move as one mass

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• Rearrange the equation and solve for Vf
• Vf 1.66 m/s West

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What is the change in Kinetic Energy for this
problem?

• Initial Kinetic Energy of the boat 0 J
• Initial Kinetic Energy of the fisherman
• KE 0.5mv2 0.5(85kg)(4.3m/s)2785.3 J
• Total Initial KE 0 785.3 J 785.3 J
• Final KE 0.5(85135)(-1.66)2303.1 J
• ?KEKEf Kei 482.2 J

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Elastic Collisions

• In an elastic collision, two objects collide and
  return to their original shapes with no change in
  total energy.
• After the collision, the two objects move
  separately.
• Momentum is conserved
• Kinetic Energy is Conserved

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Sample Problem p.229 2

• A 16.0 kg canoe moving to the left at 12 m/s
  makes an elastic head-on collision with a 4.0 kg
  raft moving to the right at 6.0 m/s. After the
  collision, the raft moves to the left at 22.7
  m/s. Disregard any effects of the water.
• a. Find the velocity of the canoe after the
  collision.

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What do we know?

• V1,i -12 m/s
• V2,i 6 m/s
• V1,f ?
• V 2,f -22.7 m/s
• M1 16 kg
• M2 4 kg

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Conservation of Momentum says

• This is an elastic collision, so we should use
  the following equation

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Rearrange and solve

• We need to solve for V1,f so we should rearrange
  the conservation of momentum equation
• So The final velocity of the canoe is 4.8 m/s
  Left.

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Impulse In Collisions
Think about Newtons 3rd Law Every action force
has an equal and opposite reaction force Since
Impulse F?t then in a collision between
objects, the impulse imparted to each mass is the
same!!!!
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Comparison of Collisions
Perfectly Inelastic Collisions Inelastic Collisions Elastic Collisions
Objects stick together and move as one mass after the collision Momentum is conserved Kinetic Energy is not conserved because it is converted to other types of energy Objects are deformed and move separately after the collision Momentum is conserved KE is not conserved Objects return to their original shapes and move separately after the collision Momentum is conserved Kinetic Energy is conserved
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Summary of Section 6.2 and 6.3

• In all interactions between isolated objects,
  momentum is conserved
• Few collisions are elastic or perfectly inelastic
• Impulse imparted is the same for all objects in a
  collision