Physics 1600 7 Energy and Newtonian Mechanics

from Physics 1600 Review Plan Physics 1600 7 Energy and Newtonian Mechanics 7.1 Energy in one dimension (Page 176) 7.1.1 Work-energy theorem (Page 178)

• When the force F can be expressed as a single-valued function F(x) of x, the theorem holds.
  • It can be mathematically understood that if the force is F(x), the value of the integral dx will be conserved (blu3mo).
  • Implication:
    • Regardless of the path taken, if the start and end points are the same, the change in energy will be the same.
      • This leads to the concept of potential energy.
  • Friction force acts as a trap.
    • Although the magnitude remains constant, the direction of the force changes depending on the direction of motion, so it is not represented by F(x). 7.1.2 Conservative forces (Page 180) 7.1.3 Potential energy (Page 181)
• From the work-energy theorem, Work = ΔKE.
  • Using work, kinetic energy is produced.
• Potential energy is defined as Work = - ΔPotential E.
  • Work is produced using potential energy.
  • By using the negative sign, the consistency with kinetic energy is maintained, and it can be said that ΔKE + ΔPE = 0. 7.1.4 Energy diagrams (Page 184) 7.1.5 Motion near equilibrium points (Page 184)
• As noted above, the presence of a maximum or minimum means that dU/dx = 0, so there is no force on the particle at xm. 7.1.6 Work and potential energy for multiple forces (Page 186)
• Consideration is made by separating into conservative and non-conservative forces.

7.1.7 Energy conservation and non-mechanical forms of energy (Page 190) 7.2 Work-energy theorem in three dimensions (Page 191) 7.2.1 Conservative forces (Page 194) 7.2.2 Application of the three-dimensional work-energy theorem (Page 196) 7.2.3 Potential energy in three dimensions (Page 201) 7.2.4 Generalized energy conservation (Page 203) 7.2.5 Examples applying energy conservation (Page 203)

• This part is a must-read (blu3mo)(blu3mo)(blu3mo). 7.3 Potential energy, force, equipotential surfaces (Page 208)
• Partial derivative:
  • df/dt =
  • 
  • 

7.3.1 Functions of multiple variables (Page 208) 7.3.2 Force from gradient of the potential energy (Page 213) 7.4 Equipotential surfaces (Page 216) 7.5 Symmetry and potential energy (Page 219) 7.5.1 Inversion symmetries (Page 219) 7.5.2 Translational symmetries (Page 222) 7.5.3 Cylindrical symmetries (Page 223) 7.5.4 Spherical symmetries (Page 224)