Impulse

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Impulse

• J FDt
• Unit N-s kg-m/s

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Momentum
p mv Unit kg-m/s
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Impulse-Momentum Thm.
FDt maDt
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CONSERVATION OF MOMENTUM

• Assuming an isolated system where no
• Outside forces are acting on the system,
• Total momentum of the system will be a constant
  that is, total momentum before will equal total
  momentum after.

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Derivation of Cons. of Momentum
F21 mAvA mAvA F12 -F21 mBvB
mBvB mAvA mAvA mBvB mBvB
mAvA mBvB mAvA mBvB
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Example of Conservation of Momentum Newtons
Experiment
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Conservation of Momentum

• mAvA mBvB mAvA mBvB
• mA mass of object A
• mB mass of object B
• vA velocity of object A before collision
• vB velocity of object B before collision

vA velocity of object A after collision vB
velocity of object B after collision
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Inelastic Collisions

• Inelastic Collisions have the following
• properties
• (1) the objects stick together after collision
• (2) kinetic energy is lost and turned into
• heat energy
• (3) momentum is conserved

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Inelastic Collisions 2

• mAvA mBvB mAv mBv

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Special cases of inelastic collisions

• Case 1 mA lt mB
• v
• V 0
• Case 2 mA gt mB
• V VA

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Elastic Collisions

• Elastic collisions have the below properties
• (1) the objects bounce off each other
• (2) no kinetic energy is lost and no heat is
  produced
• (3) momentum is conserved

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Elastic Collisions 2
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Special Cases of Elastic Collisions

• Case 1 mA mB vA 0 , vB vA
• Case 2 mA lt mB
• VA -VA
• Case 3 mA gt mB
• vA vA

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Fraction of K.E. transferred in elastic collisions

• ftransferred 4b/(1b) 2
• mA/mB
• Case 1 mA mB ,b 1, f 4(1)/(11)2 1
• Case 2 mAltmB , b 0 , f 0
• Case 3 mAgtmB , b infinity , f 4/b 0

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Collisions in 2-dimensions
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2-dim. Collisions (2)

• See active figure 9.13 at pse6.com
• mAvA mAvAx mBvBx
• 0 mAvAy mBvBy
• mAvA mAvAcosqA mBvBcosqB
• 0 mAvAsinqA mBvBsinqB

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Ballistic Pendulum
vB mAvA/(mAmB) Mgh (1/2)MvB2
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Recoil momentum