Chapter 7: Impulse, Momentum, and Collisions

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Chapter 7 Impulse, Momentum, and Collisions

• Up to now we have considered forces which have a
  constant value throughout the motion and no
  explicit time duration
• Now, lets consider a force which has a time
  duration (usually short) and with a magnitude
  that may vary with time examples a bat hitting
  a baseball, a car crash, a asteroid or comet
  striking the Earth, etc.
• It is difficult to deal with a time-varying
  force, so we usually take the mean value

F
t
tf
t0
?t
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• Define a new quantity by multiplying the force
  by the time duration - a vector,
  points in the same direction as the
  force - has units of N s
• Define another quantity, but which gives a
  measure of the motion (similar to
  KE) - a vector, points in same
  direction as the velocity - units of kg
  m/s N s
• Linear momentum and KE are related

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Example A car of mass 760 kg is traveling east at
a speed of 10.0 m/s. The car hits a wall and
rebounds (moving west) with a speed of 0.100 m/s.
Determine its momentum and KE before and after
the impact. Determine the impulse.
Solution Given m 750 kg,
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• Now, from the definition of acceleration and
  Newtons 2nd Law

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Impulse-Momentum Theorem

• The Impulse-Momentum Theorem says that if an
  impulse (forcetime duration) is applied to an
  object, its momentum changes
• In this example, the impact of the car with the
  wall applies an impulse to the car ? cars p
  changes

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Example Problem 7.13
A 0.500-kg ball is dropped from rest at a point
1.20 m above the floor. The ball rebounds
straight upward to a height of 0.700 m. What are
the magnitude and direction of the impulse of the
net force applied to the ball during the
collision with the floor?
y
0
Solution Given m 0.500 kg, h01.20 m, h30.7
m, h1h20
3
1
2
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Method need momentum before and after impact ?
need velocities ? use conservation of
energy Conservation of mechanical energy is
satisfied between 0 and 1 and between 2 and 3,
but not between 1 and 2
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Collisions

• Involves two (or more) objects which may have
  their motion (velocity, momentum) altered by
  collisions
• These concepts are applicable to the collisions
  of atoms, billiard balls, cars, planetary
  objects, galaxies, etc.
• Say, we have a collection of interacting
  particles numbered 1, 2, 3, We can define the
  Total Momentum of the system (all the particles)
  as just the sum of all the individual momenta

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• Imagine that these particles interact in some
  way collide and scatter
• As long as there are no net external forces
  acting on the system (collection of objects), the
  Total Linear Momentum does not change
• Which means the Total Linear Momentum is the
  same before the collision, during the collision,
  and after the collision
• Conservation of Linear Momentum