Speed

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Impulse and momentum
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Momentum

• Momentum is the quantity of motion, measured as
  the product of a bodys mass and its velocity.
• Momentum M V
• Increase mass or velocity and you increase
  momentum.
• Units of momentum are units of mass multiplied by
  units of velocity. Kg. m/s
• Momentum is a vector quantity.

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Momentum

• By adding mass to the puck with its velocity
  gives us momentum

Mmv
6 m/sec
m 170g
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Conservation of Momentum

• Newtons first law of motion may be re-stated
• In the absence of external forces, the total
  momentum of a given system remains constant.
• This is expressed as
• (mv)1 (mv)2

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Impulse

• When external forces act on a body they change
  the momentum present in a body or system
  predictably, through magnitude and time of the
  acting force.
• Impulse is the product of a force and the time
  interval over which the force is applied.
• F t impulse
• More force, or longer time, or both results in an
  increase in acceleration.

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The Impulse-Momentum Relationship

• When an impulse acts on a system, the result is a
  change in the systems total momentum.
• The relationship between impulse and momentum is
  derived from Newtons second law of motion
• F ma

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Impulse

• To show how the momentum of the puck and the
  force acting on the puck are related we are
  looking _at_ impulse
• In hockey there are 3 main types of impulse or
  forces acting on the puck causing acceleration
  and deceleration
• The pass
• The wrist shot
• The slap shot

F(t)mv2-mv1
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Impulse

• The Pass
• Velocity Time on puck

F(t)mv2-mv1
F(2sec) (.17kgx6m/sec)-(.17kgx0m/sec)
mass.17 kg V26 m/sec V10 m/sec T2 sec
F 1.02kg/m/sec
2 sec
F.51kg/m/ or .51N
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Impulse

• The Wrist shot
• Velocity Time on puck

F(t)mv2-mv1
F(1sec) (.17kgx10m/sec)-(1.7kgx0m/sec)
mass.17 kg V210 m/sec V10 m/sec T1 sec
F 1.7kg/m/sec
1 sec
F1.7kg/m/ or 1.7N
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Impulse

• The Slap Shot
• Velocity Time on puck

F(t)mv2-mv1
F(.5sec)(.17kgx12m/sec)-(.17kgx0m/sec)
mass.17 kg V212 m/sec V10 m/sec T.5 sec
F 2.04kg/m/sec
.5 sec
F 4.08kg/m or 4.08N
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Impact

• Impact is a collision characterized by the
  exchange of a large force during a small time
  interval.
• The behavior of the two bodies following impact
  depends largely on their collective momentum but
  also upon the nature of the impact.

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Impact

• Perfectly elastic impact is when the relative
  velocities of the two bodies are the same before
  and after impact.

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Impact

• Perfectly plastic impact occurs when at least one
  of the bodies in contact deforms and does not
  regain its original shape, and the bodies do not
  separate.

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Impact

• Most impacts are neither perfectly plastic or
  elastic but somewhere between the two. The
  coefficient of restitution describes the relative
  elasticity of an impact.
• It is a unit less number between 0 and 1. The
  nearer to 1 the more elastic and the nearer to 0
  the more plastic the impact is.

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Impact Equations

• The conservation of momentum law states that the
  momentum of the two objects before an interaction
  will equal the momentum after the interaction
• ma . va mb . vb ma . va1 mb . vb1
• The coefficient of restitution (e) for dropped
  objects is a term that quantifies how the energy
  stored in a deformed material is returned.
• e vHeight of rebound/ Height of drop
• e v rebound/ v drop
• For a more general form
• e va1 vb1 / vb - va

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Questions

• Lineman A has a mass of 100 kg and is traveling
  with a velocity of 4 m/s when he collides head
  on with lineman B, who has a mass of 90 kg and is
  traveling at 4.5 m/s.If both players remain on
  their feet, what will happen?
• Two skaters gliding on ice run into each other
  head- on. If the two skaters hold onto each other
  and continue to move as a unit after the
  collision, what will be their resultant velocity?
  Skater A has a velocity of 5 m/s and a mass of 65
  kg. Skater B has a velocity of 6 m/s and a mass
  of 60 kg.