Linear Momentum

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Linear Momentum

• is the product of mass times velocity
• m v

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IMPULSE

• Impulse is the product of the net Force and
  the time of contact.
• IMPULSE FNET ?t

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IMPULSE-MOMENTUM

• The net Force produces acceleration.
• we wish to show that
• Impulse produces momentum.

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Derivation of Impulse -Momentum from Newtons
Second Law

• FNET m a

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Derivation of Impulse -Momentum from Newtons
Second Law

• FNET m a Substitute for a in FNET

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Derivation of Impulse -Momentum from Newtons
Second Law

• FNET m a Substitute for a in FNET
• where a D v
• D t

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Derivation of Impulse -Momentum from Newtons
Second Law

• FNET m a Substitute for a in FNET
• where a D v so FNET m D v
• D t
  D t

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Derivation of Impulse -Momentum from Newtons
Second Law

• FNET m a Substitute for a in FNET
• where a D v so FNET m D v
• D t
  D t
• Then FNET D t m D v D(m v)
• So Impulse FNET D t

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Derivation of Impulse -Momentum from Newtons
Second Law

• FNET m a Substitute for a in FNET
• where a D v so FNET m D v
• D t
  D t
• Then FNET D t m D v D(m v)
• So Impulse FNET D t D(m v) Change in
• Momentum

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Derivation of Impulse -Momentum from Newtons
Second Law

• FNET m a Substitute for a in FNET
• where a D v so FNET m D v
• D t
  D t
• Then FNET D t m D v D(m v)
• So Impulse FNET D t D(m v) Change in
• Momentum

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CONSERVATION

• Conservation in Physics means that a
  
  
  quantitys value does not change after certain
  physical processes.

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CONSERVATION

• Conservation in Physics means that a
  quantitys value does not change after
  certain physical processes.
• That is the value of the quantity is the same
  before and after the process.
• Which quantitys are conserved?

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CONSERVED QUANTITIES

• Linear Momentum Angular Momentum

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CONSERVED QUANTITIES

• Linear Momentum Angular Momentum
• Total Energy Charge

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CONSERVED QUANTITIES

• Linear Momentum Angular Momentum
• Total Energy Charge
• And in special cases mechanical energy
• mass volume

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CONSERVED QUANTITIES

• Linear Momentum Angular Momentum
• Total Energy Charge
• And in special cases mechanical energy
• mass volume
• For elementary particles one finds that
  quantitites such as parity, spin, charge,
  baryon number, charm, color, upness, downness
  and strangeness are conserved.

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Conserving Processes

• For Momentum the conserving process is a
  collision between two or more objects.

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Conserving Processes

• For Momentum the conserving process is a
  collision between two or more objects.
• For energy the conserving process is
  measuring the energy at one time and comparing it
  with the value at a later time.

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SOLVING QUANTATITIVE PROBLEMS

• GURU CA METHOD
• G Write Down the GIVENS ( Assign a symbol and
  unit for each value.)

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SOLVING QUANTATITIVE PROBLEMS

• GURU CA METHOD
• G Write Down the GIVENS ( Assign a symbol and
  unit for each value.)
• U Write down the UNKNOWN (Assign a symbol and
  unit)

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SOLVING QUANTATITIVE PROBLEMS

• GURU CA METHOD
• G Write Down the GIVENS ( Assign a symbol and
  unit for each value.)
• U Write down the UNKNOWN (Assign a symbol and
  unit)
• R Select a RELATIONSHIP (equation)

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SOLVING QUANTATITIVE PROBLEMS

• U Determine if the UNITS desired can be directly
  determined from the givens. If not convert to the
  proper unit.

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Example of Momentum Conservation

• A 50 kg boy on roller skates moving with a speed
  of 5 m/s runs into a 40 kg girl also on skates.
  After the collision they cling together. What is
  their speed?
• G
• U

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Example of Momentum Conservation

• A 50 kg boy on roller skates moving with a speed
  of 5 m/s runs into a 40 kg girl also on skates.
  After the collision they cling together. What is
  their speed?
• G mb 50 kg vb 5 m/s
• U

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Example of Momentum Conservation

• A 50 kg boy on roller skates moving with a speed
  of 5 m/s runs into a 40 kg girl also on skates.
  After the collision they cling together. What is
  their speed?
• G mb 50 kg vb 5 m/s
• mg 40 kg vg 0 m/s
• U

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Example of Momentum Conservation

• A 50 kg boy on roller skates moving with a speed
  of 5 m/s runs into a 40 kg girl also on skates.
  After the collision they cling together. What is
  their speed?
• G mb 50 kg vb 5 m/s
• mg 40 kg vg 0 m/s
• U vf ? m/s

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Example of Conservation of Momentum

• R Sum of Mom before Sum of Mom after

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Example of Conservation of Momentum

• R Sum of Mom before Sum of Mom after
• mb vb mg vg mb vf mg vf

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Example of Conservation of Momentum

• R Sum of Mom before Sum of Mom after
• mb vb mg vg mb vf mg vf
• vf (mb mg) mb vb mg vg

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Example of Conservation of Momentum

• R Sum of Mom before Sum of Mom after
• mb vb mg vg mb vf mg vf
• vf (mb mg) mb vb mg vg
  vf mb vb mgvg (m/s)
• (mb mg)

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Example of Conservation of Momentum

• R Sum of Mom before Sum of Mom after
• mb vb mg vg mb vf mg vf
• vf (mb mg) mb vb mg vg
• vf mb vb mgvg (m/s)
• (mb mg)
• C vf 50 x 5 40 x 0
• 50 40

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Example of Conservation of Momentum

• R Sum of Mom before Sum of Mom after
• mb vb mg vg mb vf mg vf
• vf (mb mg) mb vb mg vb vf
  mb vb mgvg (m/s)
• (mb mg)
• C , A vf 50 x 5 40 x 0 2.78
  (m/s)
• 50 40

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Work

• Work is the product of the net Force times
  the distance moved in the direction of the net
  force.
• (Work) W F d
• Work has units of Joules

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Work - Vertical Direction

• When an object is moved vertically, then
• Work Weight height
• Work m g h
• If work has a negative sign (-) it is being
  lost, if () it is being added to the system.
• In General ...
• Energy is the capacity to do work