Impulse and Momentum

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Impulse and Momentum
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Linear momentum impulse

• Linear momentum is defined as the product of mass
  and velocity
• pmv, pxmvx , py mvy
• units of momentum are kgm/s
• From Newtons 2nd law
• F ma Fm?v/ ? t F ? p/ ? t
• The rate of momentum change with respect to time
  is equal to the resultant force on an object
• The product of Force and time is known as
  IMPULSE
• J F ? t
• units of impulse are Ns

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Linear momentum impulse
Examples of impulses being applied on everyday
objects
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Impulse Momentum Theorem
F ? tm ? v You apply an impulse on an object and
you get an equal change in momentum
Area under a Force vs time graph
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Impulse Graph
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Conservation of momentum2 particle system
For gravitational or electrostatic force
F12 is force of 1 on 2 F21 is force of 2
on 1
m2
m1
F12
F21
F12 dp1/dt F21 dp2/dt
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Conservation of momentum2 particle system
From Newtons 3rd Law F12 - F21 or F12
F21 0
F12 is force of 1 on 2 F21 is force of 2
on 1
m2
m1
F12
F21
F12 F21 dp1/dt dp2/dt 0 d(p1 p2)/dt 0
Since this derivative is equal to 0
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Conservation of momentum2 particle system
Since this derivative is equal to 0
d(p1 p2)/dt 0 then integration yields p1 p2
a CONSTANT
F12 is force of 1 on 2 F21 is force of 2
on 1
m2
m1
F12
F21
Thus the total momentum of the system of 2
particles is a constant.
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Conservation of linear momentum
Provided the particles are isolated from external
forces, the total momentum of the particles will
remain constant regards of the interaction
between them
F12
m1
F21
m2
Simply stated when two particles collide,their
total momentum remains constant. pi pf p1i
p2i p1f p2f (m1v1)i (m2v2)i (m1v1)f
(m2v2)f
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Collisions
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Collisions
Event when two particles come together for a
short time producing impulsive forces on each
other., No external forces acting. Or for the
enthusiast External forces are very small
compared to the impulsive forces
Types of collisions 1) Elastic- Momentum and
Kinetic energy conserved 2) Inelastic- Momentum
conserved, some KE lost 3) Perfectly(completely)
Inelastic- Objects stick together
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Collisions in 1 d
Perfectly Elastic 1) Cons. of mom. 2) KE lost in
collision 3) KE changes to PE
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Elastic Collision Calculation2 objects
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Collisions - Examples
Computer Simulations example 2, problems 5,24,29
Serway Problems 27,29,33,37
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Collisions in 2 dimensions
After Collision
x momentum before collision equals x momentum
after the collision
mavaf
?1
mavafx
mavax
Before collision
mb vel0 p0
mbvbxf
?2
mbvbf
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Collisions in 2 dimensions
mavax mavafx mbvbxf or mavax mavaf cos?1
mbvbf cos?2
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Collisions in 2 dimensions
After Collision
y momentum before collision equals y momentum
after the collision
mavaf
?1
mavax
mavayf
Before collision
mb vel0 p0
Velocity y axis 0 pyo
?2
Mbvbyf
mbvbf
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Collisions in 2 dimensions
0 mavafy - mbvbfy or 0 mavaf sin?1 -mbvbf sin?2
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Collisions in 2 dimensions
0 mavaf sin?1 -mbvbf sin?2
mavax mavaf cos?1 mbvbf cos?2