Physics 1600 7 Energy and Newtonian Mechanics

7.1 Energyinonedimension ......................176

7.1.1 Work-energytheorem....................178

FがF(x)としてxのsingle val funcで表せる時、theoremが成り立つ

integral F(x) dx= W

implication

経路に関係なく、スタートとエンドが一緒ならenergyの変化は同じ

ここからpotentialみたいな概念が導けるのか

friction forceはトラップで、

magnitudeは一定でも、移動方向によってforceの方向が変わるのでF(x)ではない

7.1.2 Conservativeforces.....................180

7.1.3 Potentialenergy.......................181

work e theoremで、Work = ΔKE

workを使うとKEが生える

potential Eは、Work = - ΔPotential E

Potentialを使ってWorkが生まれる

ここで-を使って定義することで、KEとの整合性が取れて、ΔKE + ΔPE = 0と言える

7.1.4 Energydiagrams ......................184

7.1.5 Motionnearequilibriumpoints..............184

As noted above, the presence of a maximum or minimum means that dUdx = 0 so there is no force on the particle at 4928 xm.

7.1.6 Work and potential energy for multiple forces . . . . . . 186

conservativeとnon-conservativeに分けて考える、みたいな

7.1.7 Energy conservation and non-mechanical forms of energy190

7.2 Work-energy theorem in three dimensions . . . . . . . . . . . . 191

7.2.1 Conservativeforces.....................194

7.2.2 Application of the three-dimensional work-energy theorem..............................196

7.2.3 Potential energy in threedimensions . . . . . . . . . . . 201

7.2.4 Generalizedenergyconservation . . . . . . . . . . . . . 203

7.2.5 Examples applying energy conservation . . . . . . . . . 203

7.3 Potential energy, force, equipotential surfaces . . . . . . . . . . 208

partial deriv.

df/dt =

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7.3.1 Functionsofmultiplevariables . . . . . . . . . . . . . . 208

7.3.2 Force from gradient of the potential energy . . . . . . . 213

7.4 Equipotential surfaces .......................216

7.5 Symmetry and potential energy ..................219

7.5.1 Inversionsymmetries....................219

7.5.2 Translationalsymmetries..................222

7.5.3 Cylindricalsymmetries...................223

7.5.4 Sphericalsymmetries....................224