Difference between revisions of "Forest UCM EnergyIntPart"
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| Line 26: | Line 26: | ||
;Conservation of Momentum | ;Conservation of Momentum | ||
| − | : <math>\left ( p_1 + p_2 \right ) _{initial} = \left ( p_1 + p_2 \right ) _{final}</math> | + | : <math>\left ( p_1 + p_2 \right ) _{\mbox{initial}} = \left ( p_1 + p_2 \right ) _{\mbox{final}}</math> |
:Conservation of Energy | :Conservation of Energy | ||
| − | : <math>\left ( T + U \right ) _{initial} = \left ( T + U \right ) _{final}</math> | + | : <math>\left ( T + U \right ) _{\mbox{initial}} = \left ( T + U \right ) _{\mbox{final}}</math> |
When the initial and final states are far away fromthe collision point | When the initial and final states are far away fromthe collision point | ||
| − | + | :<math>U_{\mbox{initial}} = U_{\mbox{final}} = 0 =</math> arbitrary constant | |
[[Forest_UCM_Energy#Energy_of_Interacting_Particles]] | [[Forest_UCM_Energy#Energy_of_Interacting_Particles]] | ||
Revision as of 12:52, 28 September 2014
Energy of Interacting particles
Translational invariance
One potential for Both Particles
Both forces from same potential
just take appropriate derivative
Total work given by one potential
Elastic Collisions
Definition
BOTH Momentum and Energy are conserved in an elastic collision
- Example
Consider two object that collide elastically
- Conservation of Momentum
- Conservation of Energy
When the initial and final states are far away fromthe collision point
- arbitrary constant