Momentum and Collisions

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Momentum and Collisions

• Dr. Robert MacKay

Clark College, Physics
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Introduction

• Review Newtons laws of motion
• Define Momentum
• Define Impulse
• Conservation of Momentum
• Collisions
• Explosions
• Elastic Collisions

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Introduction

• Newtons 3 laws of motion
• 1. Law of inertia
• 2. Net Force mass x acceleration
• ( F M A )
• 3. Action Reaction

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Law of interia (1st Law)

• Every object continues in its state of rest, or
  of uniform motion in a straight line, unless it
  is compelled to change that state by forces
  impressed upon it.
• acceleration 0.0 unless the objected is acted
  on by an unbalanced force

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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

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Newtons Law of Action Reaction (3rd Law)

• You can not touch without being touched

For every action force there is and equal and
oppositely directed reaction force
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Newtons Law of Action Reaction (3rd Law)
Ball 1
Ball 2
F2,1
F1,2
F1,2 - F2,1
For every action force there is and equal and
oppositely directed reaction force
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Momentum , p

• Momentum mass x velocity
• is a Vector
• has units of kg m/s

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Momentum , p (a vector)

• Momentum mass x velocity
• p m v
• p ?

8.0 kg
6.0 m/s
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Momentum , p

• Momentum mass x velocity
• p m v
• p 160.0 kg m/s

8.0 kg
V ?
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Momentum , p

• Momentum is a Vector
• p m v
• p1 ? p2 ?

V 8.0 m/s
m1 7.5 kg
m2 10.0 kg
V -6.0 m/s
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Momentum , p

• Momentum is a Vector
• p m v
• p1 60 kg m/s p2 - 60 kg m/s

V 8.0 m/s
m1 7.5 kg
m2 10.0 kg
V -6.0 m/s
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Momentum , p

• Momentum is a Vector
• p m v
• p1 60 kg m/s p2 - 60 kg m/s
• the system momentum is zero.,

V 8.0 m/s
m1 7.5 kg
m2 10.0 kg
V -6.0 m/s
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M a
• F M (?V/?t)
• F ?t M ?V
• F ?t M (VF-V0)
• F ?t M VF- M V0
• F ?t ?p Impulse F?t
• The Impulse the change in momentum

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Newtons 2nd Law

• Net Force Mass x Acceleration
• F ?t ?p Impulse F ?t
• The Impulse the change in momentum

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Newtons Law of Action Reaction (3rd Law)
Ball 1
Ball 2
F2,1
F1,2
F1,2 - F2,1
For every action force there is and equal and
oppositely directed reaction force
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Newtons Law of Action Reaction (3rd Law)
Ball 1
Ball 2
F2,1
F1,2
F1,2 - F2,1 F1,2?t - F2,1 ?t ?p2 - ?p1
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Conservation of momentum
Ball 1
Ball 2
F2,1
F1,2
If there are no external forces acting on a
system (i.e. only internal action reaction
pairs), then the systems total momentum is
conserved.
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Explosions2 objects initially at rest

• A 30 kg boy is standing on a stationary 100 kg
  raft in the middle of a lake. He then runs and
  jumps off the raft with a speed of 8.0 m/s. With
  what speed does the raft recoil?

V8.0 m/s
after
V?
M100.0 kg
M100.0 kg
before
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Explosions2 objects initially at rest

• A 30 kg boy is standing on a stationary 100 kg
  raft in the middle of a lake. He then runs and
  jumps off the raft with a speed of 8.0 m/s. With
  what speed does the raft recoil?

V8.0 m/s
after
V?
M100.0 kg
M100.0 kg
before
p before p after 0 30kg(8.0 m/s) -
100 kg V 100 kg V 240 kg m/s V 2.4
m/s
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Explosions
If Vred9.0 m/s Vblue?
9.0 m/s
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Explosions
If Vred9.0 m/s Vblue3.0 m/s
9.0 m/s
3.0 m/s
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Stick together2 objects have same speed after
colliding

• A 30 kg boy runs and jumps onto a stationary 100
  kg raft with a speed of 8.0 m/s. How fast does he
  and the raft move immediately after the collision?

V8.0 m/s
V?
M100.0 kg
M100.0 kg
after
before
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Stick together2 objects have same speed after
colliding

• A 30 kg boy runs and jumps onto a stationary 100
  kg raft with a speed of 8.0 m/s. How fast does he
  and the raft move immediately after the collision?

V8.0 m/s
V?
M100.0 kg
M100.0 kg
after
before
p before p after 30kg(8.0 m/s) 130 kg
V 240 kg m/s 130 kg V V 1.85 m/s
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Stick together2 objects have same speed after
collidingThis is a perfectly inelastic collision
V8.0 m/s
V?
M100.0 kg
M100.0 kg
after
before

• A 30 kg boy runs and jumps onto a stationary 100
  kg raft with a speed of 8.0 m/s. How fast does he
  and the raft move immediately after the collision?