Impulse and Momentum

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Impulse and Momentum

• 9.1 Momentum and Impulse
• 9.2 Solving impulse and momentum problems
• 9.3 Conservation of momentum
• 9.4 Explosions
• 9.5 Inelastic Collisions
• 9.6 Momentum in two Dimension
• 9.7 Angular Momentum

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Collision
The rapidly changing magnitude Of the force
during collision
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Momentum

• Fx(t) max(t) m(dVx)/dt
• We define
• Momentum
• Momentum is a vector
• Its x-component and y-component are

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Impulse

• From above
• Impulse is equal to momentum change
• We define
• Impulse

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Quick think
What is the carts change of momentum ?
30kgm/s
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Ex.9.1
3000N
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Momentum Bar Charts

• From

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Conservation of Momentum
The sum of the momentum does not change
Ie. The sum of the momentum after the Collision
equals the sum of the momentum Before the
collision.
T
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Law of conservation of momentum

• The total momentum of an isolated system
• is a constant. Interactions within the system
• do not change the system momentum.

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Objects A and C are made of different materials,
with different springiness, but they have the
same mass and initially at rest.When ball B
collides with object A, the ball ends up at rest.
When B is thrown with the same speed and collides
with object C, the ball rebounds to the left.
Compare the velocities of A and C after the
collisions. Is Va Greater than, equal to, or less
than Vc.
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Explosions

• An explosion, where the particles of the system
  move apart from each other after a intense
  interaction.
• Ex. Recoil. A rifle firing a bullet
• Before the total momentum is zero
• After The total momentum is
• From

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Inelastic Collision

• If, after collision, the energy does not
  conserve, this kind of collision is called as
  Inelastic collision.
• Perfectly inelastic collision A collision in
  which the two objects stick together and move
  with a common final velocity. Ex. Bullet
  embedding itself in the wood.
• The law of conservation of momentum for perfectly
  inelastic collision

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Ex. 9.8 Momentum in a car cracsh
(1) Find the deceleration from V1x to stop (2)
Find the velocity V1x, using kinematics equation,
this is the velocity after collision. (3)
Find velocity of Volkswagen before collision
using the law of momentum conservation
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Momentum in Two Dimensions

• Momentum conservation involve motion in a plane
• Each component of momentum is conserved

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Momentum in a 2D car crash
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Angular momentum

• Angular momentum is defined as
• L rmv
• Law of conservation of angular momentu
• The angular momentum of a particle (or system of
  particles) in circular motion does not change
  unless there is a net torque.