View source for Potential Energy EX 6

{| border="1" cellpadding="2" style="text-align:center"
|-
! # Particles
! System
! # Pairs
! Total Potential Energy
|-
! 3
| [[image:Helena_Pot_Energy_Ex_6_3part.png|TOP]]<br><br>
| 3
| <math>U = U_{12} + U_{13} + U_{23}</math>
|-
! 4
| [[image:Helena_Pot_Energy_Ex_6_4part.png|TOP]]<br><br>
| 6
| <math>U = U_{12} + U_{13} + U_{14} + U_{23} + U_{24} + U_{34}</math>
|-
! 5
| [[image:Helena_Pot_Energy_Ex_6_5part.png|TOP]]<br><br>
| 10
| <math>U = U_{12} + U_{13} + U_{14} + U_{15} + U_{23} + U_{24} + U_{25} + U_{34} + U_{35} + U_{45}</math>
|-
! 6
| [[image:Helena_Pot_Energy_Ex_6_6part.png|TOP]]<br><br>
| 15
| <math>U = U_{12} + U_{13} + U_{14} + U_{15} + U_{16} + U_{23} + U_{24} + U_{25} + U_{26} + U_{34} + U_{35} + U_{36} + U_{45} + U_{46} + U_{56}</math>
|}
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'''(c)''' For <math>n</math> interacting particles, there are <math>\frac{1}{2} n(n - 1)</math> pairs of interactions and therefore, there are that many terms in the expression for the total gravitational potential energy.