Recoil and Collisions 8.01 W07D1

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Recoil and Collisions8.01W07D1
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Todays Reading Assignment W07D1

• Young and Freedman 8.3-8.4

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Conservation of Momentum System and Surroundings

• For a fixed choice of system, we can consider
  the rest of the universe as the surroundings.
  Then, by considering the system and surroundings
  as a new larger system, all the forces are
  internal and so change in momentum of the
  original system and its surroundings is zero,

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Concept Question Choice of System

• Drop a stone from the top of a high cliff.
  Consider the earth and the stone as a system. As
  the stone falls, the momentum of the system
• 1. increases in the downward direction.
• 2. decreases in the downward direction.
• 3. stays the same.
• 4. not enough information to decide.

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Concept Question Jumping on Earth

• Consider yourself and the Earth as one system.
  Now jump up. Does the momentum of the system
• Increase in the downward direction as you rise?
• Increase in the downward direction as you fall?
• Stay the same?
• Dissipate because of friction?

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Recoil
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Concept Question Recoil

• Suppose you are on a cart, initially at rest on a
  track with very little friction. You throw balls
  at a partition that is rigidly mounted on the
  cart. If the balls bounce straight back as shown
  in the figure, is the cart put in motion?
• 1. Yes, it moves to the right.
• Yes, it moves to the left.
• No, it remains in place.

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Strategy Momentum of a System

• 1. Choose system
• 2. Identify initial and final states
• 3. Identify any external forces in order to
  determine whether any component of the momentum
  of the system is constant or not

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Problem Solving Strategies Momentum Flow Diagram

• Identify the objects that comprise the system
• Identify your choice if reference frame with an
  appropriate choice of positive directions and
  unit vectors
• Identify your initial and final states of the
  system
• Construct a momentum flow diagram as follow
• Draw two pictures one for the initial state and
  the other for the final state. In each picture
  choose symbols for the mass and velocity of each
  object in your system, for both the initial and
  final states. Draw an arrow representing the
  momentum. (Decide whether you are using
  components or magnitudes for your velocity
  symbols.)

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Table Problem Recoil

• A person of mass m1 is standing on a cart of
  mass m2 that is on ice. Assume that the contact
  between the carts wheels and the ice is
  frictionless. The person throws a ball of mass m3
  in the horizontal direction (as determined by the
  person in the cart). The ball is thrown with a
  speed u with respect to the cart.
• What is the final velocity of the ball as seen by
  an observer fixed to the ground?
• What is the final velocity of the cart as seen by
  an observer fixed to the ground?

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Momentum Flow Diagram Recoil
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Table Problem Sliding on Slipping Block

• A small cube of mass m1 slides down a circular
  track of radius R cut into a large block of mass
  m2 as shown in the figure below. The large block
  rests on a , and both blocks move without
  friction. The blocks are initially at rest, and
  the cube starts from the top of the path. Find
  the velocity of the cube as it leaves the block.

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Collisions
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Collisions

• Any interaction between (usually two) objects
  which occurs for short time intervals Dt when
  forces of interaction dominate over external
  forces.
• Of classical objects like collisions of motor
  vehicles.
• Of subatomic particles collisions allow study
  force law.
• Sports, medical injuries, projectiles, etc.

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Collision Theory Energy

• Types of Collisions
• Elastic
• Inelastic
• Completely Inelastic Only one body emerges.
• Superelastic

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Demo Ball Bearing and Glass B60

• http//tsgphysics.mit.edu/front/index.php?pagedem
  o.php?letnumB2060show0
• Drop a variety of balls and let students guess
  order of elasticity.

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Concept Question Inelastic Collision

• Cart A is at rest. An identical cart B, moving
  to the right, collides with cart A. They stick
  together. After the collision, which of the
  following is true?
• Carts A and B are both at rest.
• Carts A and B move to the right with a speed
  greater than cart B's original speed.
• Carts A and B move to the right with a speed less
  than cart B's original speed.
• Cart B stops and cart A moves to the right with
  speed equal to the original speed of cart B.

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Concept Question Inelastic Collision

• A cart moving at speed v collides with an
  identical stationary cart on an airtrack, and the
  two stick together after the collision. What is
  their speed after colliding?
• v
• 1/2 v
• zero
• 2/3 v
• 1/3 v
• None of the above.

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Table Problem Totally Inelastic Collision
A car of mass m1 moving with speed v1,i
collides with another car that has mass m2 and
is initially at rest. After the collision the
cars stick together and move with speed vf. What
is the speed vf of the cars immediately after the
collision?
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Concept Question Elastic Collision

• Cart A is at rest. An identical cart B, moving
  to the right, collides elastically with cart A.
  After the collision, which of the following is
  true?
• Carts A and B are both at rest.
• Cart B stops and cart A moves to the right with
  speed equal to the original speed of cart B.
• Cart A remains at rest and cart B bounces back
  with speed equal to its original speed.
• 4. Cart A moves to the right with a speed
  slightly less than the original speed of cart B
  and cart B moves to the right with a very small
  speed.

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Demo and Worked Example Two Ball Bounce

• Two superballs are dropped from a height h
  above the ground. The ball on top has a mass M1.
  The ball on the bottom has a mass M2. Assume that
  the lower ball collides elastically with the
  ground. Then as the lower ball starts to move
  upward, it collides elastically with the upper
  ball that is still moving downwards. How high
  will the upper ball rebound in the air? Assume
  that M2 gtgt M1.

M2gtgtM1
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Table Problem Three Ball Bounce

• Three balls having the masses shown are dropped
  from a height h above the ground. Assume all the
  subsequent collisions are elastic. What is the
  final height attained by the lightest ball?

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Mini-ExperimentAstro-Blaster
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Two Dimensional Collisions
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Two Dimensional Collisions Momentum Flow Diagram

• Consider a collision between two particles. In
  the laboratory reference frame, the incident
  particle with mass m1, is moving with an initial
  given velocity v1,0. The second target particle
  is of mass m2 and at rest. After the collision,
  the first particle moves off at an angle q1,f
  with respect to the initial direction of motion
  of the incident particle with a final velocity
  v1,f. Particle two moves off at an angle q2,f
  with a final velocity v2,fThe momentum diagram
  representing this collision is sown below.

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Table Problem Elastic Collision in 2-d

• In the laboratory reference frame, an incident
  particle with mass m1, is moving with given
  initial speed v1,i. The second target particle
  is of mass m2 and at rest. After an elastic
  collision, the first particle moves off at a
  given angle ?1,f with respect to the initial
  direction of motion of the incident particle with
  final speed v1,f. Particle two moves off at an
  angle ?2,f with final speed v2,f. Find the
  equations that represent conservation of momentum
  and energy. Assume no external forces.

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Momentum and Energy Conservation

• No external forces are acting on the system
• Collision is elastic

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Strategy

• Three unknowns v1,f , v2,f, and ?2,f
• First squaring then adding the momentum equations
  and equations and solve for v2,f in terms of
  v1,f.
• Substitute expression for v2,f kinetic energy
  equation and solve quadratic equation for v1,f
• Use result for v1,f to solve expression for v2,f
• Divide momentum equations to obtain expression
  for ?2,f

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Next Reading Assignment W07D2

• Young and Freedman 8.3-8.4
• Experiment 4 Momentum and Collisions