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