Reading Quiz - Momentum

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Reading Quiz - Momentum

• 1. Which is true? Conservation of the total
  momentum of a system
• ___ 1. holds only when mechanical energy is
  conserved.
• ___ 2. holds for any system.
• ___ 3. follows from Newtons second law.
• ___ 4. is equivalent to Newtons third law.

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• 2. A rocket is propelled forward by ejecting gas
  at high speed. The forward motion is a
  consequence of
• ___ 1. conservation of energy.
• ___ 2. conservation of momentum.
• ___ 3. both of the above.
• ___ 4. neither of the above.

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• 3. The impulse delivered to a body by a force is
• ___ 1. defined only for interactions of short
  duration.
• ___ 2. equal to the change in momentum of the
  body.
• ___ 3. equal to the area under an F vs. x graph.
• ___ 4. defined only for elastic collisions.

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• 4. In an elastic collision
• ___ 1. energy is conserved.
• ___ 2. momentum is conserved.
• ___ 3. the magnitude of the relative velocity is
  conserved.
• ___ 4. all of the above

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Linear Momentum

• The linear momentum p of an object of mass m
  moving with velocity v is defined as
• Note vector nature!
• Newtons 2nd law can be re-expressed as

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Impulse

• Many forces are variable and act for a short
  period of time (as in collisions). A useful
  quantity is the impulse I of such a force
• Equivalent average force of the impulsive force

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Conceptual Questions

• 1) Momentum is most closely related to
• ____ a) kinetic energy
• ____ b) potential energy
• ____ c) impulse
• ____ d) power
• ____ e) none of the above

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• 2) An object that has momentum must also have
• ____ a) acceleration
• ____ b) impulse
• ____ c) kinetic energy
• ____ d) potential energy

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• 3) Two equal-mass bullets traveling with the same
  speed strike a target. One of the bullets is
  rubber and bounces off, the other is metal and
  penetrates, coming to rest in the target. Which
  exerts the greater impulse on the target?
• ____ a) the rubber bullet
• ____ b) the metal bullet
• ____ c) both exert the same
• ____ d) not enough information
• ____ e) none of these

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Quantitative Questions

• 1) What effect on its momentum does doubling the
  kinetic energy of a moving object have?
• 2) The head of a golf club is in contact with a
  46 gram golf ball for 0.50 milliseconds, and as a
  result, the ball flies off at 70 m/s. Find the
  average force that was acting on the ball during
  the impact.

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Conservation of Linear Momentum

• The total momentum of a system composed of many
  particles is simply the vector sum of the
  individual momentum of each particle.
• An isolated system is one in which the only
  forces present are those between the objects of
  the system.
• It follows from Newtons 3rd law that the total
  momentum of an isolated system of bodies remains
  constant.

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Quantitative Problems

• 1) A 13 gram bullet traveling 230 m/s penetrates
  a 2.0 kg block of wood and emerges going 170 m/s.
  If the block is stationary on a frictionless
  surface when hit, how fast does it move after the
  bullet emerges?
• 2) A spacecraft moving at 10 km/s breaks apart
  into 2 pieces of equal mass, one of which moves
  off at 4 km/s in a direction opposite to the
  original direction. Find the speed and direction
  of the other piece.

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• 3) An astronaut outside an orbiting space craft
  uses a pistol that ejects a gas in order to
  maneuver in space. Suppose the astronaut in her
  space suit have a total mass of 100 kg and the
  pistol ejects 12 gm of gas per second at a speed
  of 650 m/s. How long should the astronaut operate
  the pistol in order to have a speed of 1 m/s?

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Collisions

• Important Momentum is always conserved in all
  collisions! Not energy or kinetic energy!!
• Elastic collision - one where total kinetic
  energy is conserved.
• Inelastic collision - one where total kinetic
  energy is not conserved.
• Completely inelastic collision - one in which the
  colliding bodies stick together after the
  collision.

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Conceptual Question

• 1) In an elastic collision
• ____ a) momentum is conserved but not KE
• ____ b) KE is conserved but not momentum
• ____ c) momentum and KE are both conserved
• ____ d) neither momentum nor KE is conserved

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Quantitative Problems

• 1) A pair of bumper cars collide elastically as
  one approaches the other directly from the rear.
  One has a mass of 450 kg and the other 550 kg. If
  the lighter one approaches at 4.5 m/s and other
  is moving at 3.7 m/s, calculate (a) their
  velocities after the collision, and (b) the
  change in momentum of each.

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• 2) A 30 kg girl who is running at 3 m/s jumps on
  a stationary 10 kg sled on a frozen lake. How
  fast does the sled then move?
• 3) Two people, one of mass 75 kg and the other of
  mass 60 kg, sit in a rowboat of mass 80 kg. With
  the boat initially at rest, the two people, who
  have been sitting at opposite ends of the boat
  2.0 m apart from each other, now exchange seats.
  How far and in what direction will the boat move?
• (Hint it can be shown that the net force acting
  on a system of particles equals the total mass
  times the acceleration of the center of mass
  )

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Collisions in Higher Dimensions

• When a collision between 2 objects is not head on
  (called a glancing collision), the collision
  becomes 2- or 3-dimensional.
• Since momentum is a vector quantity, for these
  glancing collisions, each component of momentum
  must be individually conserved

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• If collisions are also elastic, then the total
  kinetic energy is also conserved

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Conceptual Problem

• Two identical balls moving with the same speed
  towards each other along the x-axis suffer a
  glancing collision. After the collision,
• ____ a) they bounce back and move along the x-
  axis.
• ____ b) they must necessarily stick together and
  stop moving.
• ____ c) they can move off in any direction but
  must have equal and opposite velocities.
• ____ d) not enough information is given.

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Quantitative Problems

• 1) Two shuffleboard disks of equal mass, one
  orange and the other yellow, are involved in a
  perfectly elastic glancing collision. The yellow
  disk is initially at rest and is struck by the
  orange disk moving with a speed of 5 m/s. After
  the collision, the orange disk moves along a
  direction that makes an angle of 37? with its
  initial direction of motion and the velocity of
  the yellow disk is perpendicular to that of the
  orange disk (after the collision. Determine the
  final speed of each disk.

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• 2) After a completely inelastic collision, two
  objects of the same mass and same initial speed
  are found to move away together at half their
  initial speed. Find the angle between the initial
  velocities of the objects.