Physics: Absolute Potential Energy

Chapter 1

Core concepts and definitions

1

Potential energy U vs potential (per unit mass/charge)

2

Absolute vs relative potential energy

2 subtopics

3

What “absolute” means (and when it’s physically meaningful)

4

Choosing the zero level: reference points and constant offsets

5

Work, energy conservation, and potential energy

2 subtopics

6

Key relation: W_conservative = −ΔU

7

Path independence and when a potential function exists

Chapter 2

Mathematical foundations (calculus & vectors)

8

Gradients and line integrals for potentials

2 subtopics

9

From potential to force: F = −∇U (1D and 3D)

10

Compute ΔU via line integral: ΔU = −∫ F · dl

11

Potential functions and additive constants (gauge freedom basics)

12

Units, signs, and dimensional checks for potential energy

Chapter 3

Conservative forces and reference choices

13

Conservative vs non-conservative forces

2 subtopics

14

Tests for conservativeness: closed-loop work and curl criteria

15

Non-conservative examples: friction and drag (why U fails)

16

Gauge freedom: adding a constant to U and what stays invariant

1 subtopics

17

Why only differences in U matter for forces and motion

18

Potential energy landscapes and stability

2 subtopics

19

Equilibria from U(x): stable/unstable/neutral points

20

Small oscillations: relate curvature d²U/dx² to frequency

Chapter 4

Absolute potential energy in common physical systems

21

Near-Earth gravity: U = mgh and choosing h = 0

22

Newtonian gravity: U(r) = −GMm/r

2 subtopics

23

Reference at infinity and “absolute” gravitational potential energy

24

Binding energy and escape speed from gravitational potential energy

25

Spring (elastic) potential: U = ½kx² and reference at x = 0

26

Electric potential energy: U = qV

2 subtopics

27

Electric potential V and choices of zero (ground vs infinity)

28

Multi-particle potentials: pairwise sums and avoiding double-counting

Chapter 5

Measurement, computation, and visualization

29

Experimental determination of potential energy differences

1 subtopics

30

Measure F(x) and integrate to get ΔU (lab workflow)

31

Numerical computation of U(x) from force or data

2 subtopics

32

Discrete integration methods (trapezoid, Simpson) for ΔU

33

From noisy data: fitting U(x) and estimating uncertainty

34

Visualizing potentials and predicting motion qualitatively

1 subtopics

35

Read U(x) plots: turning points, allowed regions, and barriers

Chapter 6

Advanced and modern perspectives

36

General relativity: limits of defining gravitational potential energy

1 subtopics

37

Why gravitational potential energy isn’t globally defined in GR

38

Quantum mechanics: potentials and energy reference levels

2 subtopics

39

Potential offsets in Schrödinger’s equation: what changes and what doesn’t

40

Model potentials: infinite well, harmonic oscillator, Coulomb

41

Field energy and gauge potentials (electromagnetism)

2 subtopics

42

Energy stored in fields (e.g., ½ε₀E²) vs particle potential energy

43

Gauge potentials in EM: scalar potential V and vector potential A