phy53 lecture  			dr. brown		23 Sept 2010

energy -- graph of potential energy --> force

then center of mass frame and many particle system

	F_x = - \frac{dU}{dx}

		N2 in "desguise [sp]"

\vec{F} = - \vec{\Delta} U    gradient {direction of steepest decent}

equilibrium
	stable
	unstable 
	"neutral"

	F_x = - \frac{dU}{dx} = 0

consider spring potential [harmonic oscillator]  
   "     neg. of spring potential 
   "     general 

K >= 0   so, plot total mech energy to find classically forbidden and allowed regions [turning points] 

near all stable equilib ~~ parabolic potential -- oscillators

reiterate arbitrary choice for U_o   -- physics (force) depends on the change in potential

have been treating objects as "particles" -- can define a point in space as location -- etc.  NOW --

many particle systems!

go from microscopic to macroscopic description of matter

center of mass 

momentum

calculate center of mass for 3 discrete masses