1. Unit 5: Conservation of Momentum
Force and Momentum and Conservation of Momentum (9-1,9-2, 9-3)
Collisions (9-4, 9-5, 9-6)
Collisions, Center of Mass (9-7,9-8)
Catch-up, Rocket Propulsion, and Quiz Three Review (9-9,9-10)
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2. Schedule This Friday, March 30th Wednesday, April 4th
No Class
Wednesday, April 4th
Finish Conservation of Momentum
Review of Conservation of Energy and Momentum
Friday, April 6th
Test Conservation of Energy & Momentum
Crib sheet: single 3”x5” note card.
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3. Conservation of Energy and Momentum in Collisions
In two-body collisions difficult to describe the force Newton’s 2nd Law hard to use.
But if external forces are absent or negligible, conservation of momentum connects the initial and final states of the system.
If the two objects suffer no deformation during the collision then kinetic energy is also conserved and equal before and after the collision. This is called an elastic collision.
Actually some of the kinetic energy may be lost to deformation heat. This is called an inelastic collision.
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4. KE Constant Elastic KE Decreases Inelastic
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5. The Classic Inelastic Collision: A Ballistic Pendulum.
A nifty device to measure the speed of a projectile by converting kinetic energy to potential energy
A beautiful application of both momentum and energy conservation
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7. Elastic Collisions in One Dimension
When momentum and kinetic energy are both conserved, we have two powerful handles for describing a collision.
The best practical examples would be billiard balls or air-hockey pucks
The normal force and gravity are equal so the main external forces sum to zero.
Friction is essentially zero.
We ignore rotational motion because at the instant of collision unimportant.
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8. The Setup Although the figure has objects with
positive velocity, the discussion is general
and describes motion in either direction
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11. Special Case 1: Equal Masses
A billiard ball of mass m moving with speed v1 collides head-on and elastically with a second ball of equal mass.
What are the speeds after the collision, assuming:
both balls are in motion
the second ball is initially at rest v2=0.
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13. Special Case 2: Unequal Masses Target at Rest
MINERnA Main INjector ExpeRiment for v-A
In fixed target particle physics experiment, a projectile of mass m1 strikes a motionless target, v2=0, of mass m2.
For a head-on elastic collision, derive eqs. for final velocities, v’1 and v’2
Determine the final velocities in the limit of a infinitely massive projectile and an infinitely massive target. g n g
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14. A Dread Derivation!
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18. An Example: Proton Scattering
A proton of mass 1.01u moving at 3.6x104m/s elastically collides with a 4.00u Helium atom.
What are the final velocities of the two particles?
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20. To Finish Up
Next well finish collisions and then we’ll focus on the center of mass.
Remember
No class Friday!
Quiz April 6th
See you next week.
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