Momentum

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Momentum
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Linear Momentum

• Momentum is the measure of inertia in motion.
• Momentum equals mass times velocity
• Momentum is symbolized by p
• Specifically, momentum mass velocity
• Like velocity, momentum is a vector.
• Momentum is parallel to velocity

p
m
v
3
Linear Momentum
Just as a truck and a roller skate have different
inertia, they (generally) have different momenta.
Question (i) Does the truck always have more
inertia than the roller skate? (ii) What about
momentum?

• Yes (mass larger)
• (ii) No e.g. a roller skate rolling has more
  momentum than stationary truck. Momentum depends
  on speed as well as mass .

4
Linear Momentum

• How can the momentum of an object be changed?
• By changing its mass, or, more usually, its
  velocity i.e. by causing an acceleration.
• What causes acceleration?
• A force

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Do this

• An object with a mass of 2500Kg is traveling at 5
  meters per second. Calculate the momentum of the
  object.

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Law of Action Redefined

• Newton originally framed the second law (action)
  in terms of momentum, not velocity.
• The rate of change in momentum is proportional to
  the net force and the change is in the same
  direction as the force

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Conservation of Momentum

• The total momentum of any group of objects
  remains the same unless acted upon by an outside
  force.

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Conservation of Momentum

• Momentum is conserved when objects collide.
• Momentum after a collision must be the same as
  momentum before the collision.
• Momentum is conserved during a collision, because
  all forces acting in collision are internal
• Net momentum before collision net momentum
  after collision

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Two types of collisions

• Elastic
• Occurs when both momentum and kinetic energy are
  conserved
• Inelastic
• Occurs when momentum is conserved but kinetic
  energy is not.

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Elastic Collisions
b) Head-on collision each ball reverses its
momentum
a) The moving ball comes to rest, the other moves
off with the speed of the colliding ball.
pi pp 0
pi p1
pf p2 pi
pi -pp 0
These are both elastic collisions no lasting
deformation or heat or sound
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Inelastic Collisions

• Many collisions are inelastic - where heat
  and/or sound is generated, and/or objects deform.
  Even so, momentum is still conserved .

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• Note that net momentum before net momentum
  after (always in collision, whether elastic or
  inelastic)

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Bounce

• A falling ball has a momentum.

• After hitting the floor there has been a change
  in momentum.
• The change is due to a force from the floor.

pf
pi
FN
next
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Two Bodies

• When two bodies strike each other they exert a
  force on each other.
• The forces are equal and opposite.

F12
F21
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Two Balls

• Two balls fall at the same rate due to gravity,
  but with different momenta.

• Ball 1 bounces from the ground.
• Ball 2 bounces from ball 1.

pf2
pi2
pf1
pi1
16
Momentum Change

• If two forces are equal in magnitude, then the
  changes in momentum are equal in magnitude.

F12
pf1
pi2
pi1
pf2
F21
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Internal Forces

• Two objects can be considered together.
• This is called a system.
• The internal forces cancel out from the law of
  reaction.
• The external forces remain.

F12
Fg2
F21
Fg1
18
Double Bounce

• Initially both balls go down together with the
  same velocity.

• The lower ball hits the upper ball and momentum
  is conserved between the balls.

• The lower ball gets a force from the floor and
  changes momentum.

pi2
pf2
pi2
pi1
pf1
pm1
next
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Law of Reaction Redefined

• The law of reaction can be defined in terms of
  momentum.
• In an isolated system the total momentum is
  conserved.

20
Storm Damage

• A house takes damage from the force of a 60 mph
  gale-force wind. If the house is subject to a
  hurricane at 120 mph the force on the house is
• A) Equal.
• B) Two times stronger.
• C) Four times stronger.
• D) Eight times stronger.

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Storm Force

• At 60 mph the momentum of the air is due to the
  mass (m) and velocity (v).

• At 120 mph the speed is double.
• Half as much time to get the same amount of mass

p mv
p m(2v)