Currency of the Universe

NODE 01

The Idea of Energy

→

• Capacity for physical change/work.
• Moves between systems, changes form.
• Conserved in isolated systems.

NODE 02

The Idea of Work

• Force produces displacement.
• Component along the force matters.
• W = F s cosθ.

NODE 03

Positive Work

• Force component in SAME direction as displacement.
• E.g., Pushing forward, gravity falling.

NODE 04

Negative Work

• Force component OPPOSES displacement.
• E.g., Friction, air resistance, braking.
• Removes energy from system.

NODE 05

Zero Work

• No displacement, or force perpendicular.
• E.g., Centripetal force in UCM.
• cos(90°) = 0.

NODE 06

Work by Variable Force

• When force changes with position.
• W = ∫F dx.
• Area under Force-Position graph.

NODE 07

Work-Energy Theorem

W_net=ΔK

• Net work = change in kinetic energy.
• Wnet = ½mv² − ½mu².
• Unifies force, motion, and energy.

NODE 08

Kinetic Energy

• Energy associated with motion.
• K = ½mv².
• Depends heavily on speed (v squared).

NODE 09

KE in Rotation

• Connects to Realm 05.
• K_rot = ½Iω².
• Combined: K = ½Mv² + ½Iω² (Rolling).

NODE 10

Potential Energy

• Energy associated with configuration/position.
• Requires choice of reference level.
• Energy differences matter, not absolute zero.

NODE 11

Gravitational PE

U = mgh

• Near Earth's surface: U = mgh.
• Depends on mass, height, gravity.
• Prepares for deeper gravitation in Realm 07.

NODE 12

Elastic PE

• For an ideal spring: U = ½kx².
• Depends on spring constant & extension.
• Energy stored in deformation.

NODE 13

Spring Work

• Force changes with extension: F = kx.
• W = ½kx².
• Area of the force-extension triangle.

NODE 14

Conservative Forces

• Work is path independent.
• Closed-path work = 0.
• E.g., Gravity, Ideal spring force.

NODE 15

Non-Conservative

• Friction, Drag, Dissipative effects.
• Mechanical energy decreases (becomes heat/sound).
• Leads toward Thermodynamics.

NODE 16

Cons of Mech Energy

K + U = C

• When ONLY conservative forces do work.
• K₁ + U₁ = K₂ + U₂.
• Roller coasters, pendulums, springs.

NODE 17

Transformations

☀️→🌿→🔋

• Potential ↔ Kinetic, Chemical → Mechanical.
• Electrical → Thermal/Mechanical.
• The civilization-scale view of Physics.

NODE 18

Power

• Energy tells how much. Power tells how quickly.
• P = W/t. Instantaneous: P = dW/dt.
• P = F·v (Translation), P = τω (Rotation).

NODE 19

Units of Power

WATT

KILOWATT

MEGAWATT

HORSEPOWER

• W, kW, MW, hp.
• Distinguish: kW (Power) vs kWh (Energy).

NODE 20

Electrical Energy Preview

• Electrical power → energy consumed over time.
• Energy = power × time.
• Prepares for Realm 16.

NODE 21

Efficiency

• Useful output / Total input × 100%.
• Accounts for waste/dissipated energy (thermal/friction).

NODE 22

Machines & Mech Adv

• Lever, pulley, wheel/axle, inclined plane.
• Mechanical advantage, velocity ratio.
• Connects force mechanics to engineering.

NODE 23

Collisions (Energy View)

• Elastic: Momentum & KE conserved.
• Inelastic: Momentum conserved, KE decreases.
• Momentum can be conserved when KE is not.

NODE 24

Explosions

• Reverse-collision viewpoint.
• Internal energy release → KE increases.
• Momentum remains conserved. Recoil/Fragmentation.

NODE 25

COM Energy View

• Translational energy of system + Internal motion.
• Relative motion decomposition.
• Bridge toward advanced system mechanics.

NODE 26

Energy in Rot Systems

• Torque → angular displacement → rotational work.
• W = ΔK_rot.
• Completes translation-rotation symmetry.

NODE 27

Energy Diagrams

• Visual representations (Bar charts, PE graphs).
• Potential energy wells/curves.
• Gateway to advanced mechanics/quantum.

NODE 28

P-t & E-t Graphs

Area=E

Slope=P

• Power vs Time: Area = Energy transferred.
• Energy vs Time: Slope = Power.

NODE 29

Real-World Energy

• Power plants, turbines, solar, batteries, motors.
• Where did energy come from, where did it go?
• How efficiently was it transformed?

NODE 30

Experiment Lab

• Work moving load, Spring energy.
• Conservation on roller coasters/pendulums.
• Machine efficiency, Power measurement.

NODE 31

Misconceptions

• "Energy gets used up" → No, transferred/transformed.
• "Rest = no energy" → No, potential/internal.
• "Negative work = negative energy" → No.

NODE 32

Solving Engine

• SYSTEM? → STATES? → FORCES? → WORK?
• CONSERVED? → EXTERNAL TRANSFER?
• Equation → Solve → Check Units.

NODE 33

Conservation Map

↔

→

• Work → Energy Transfer.
• Kinetic ↔ Potential → Thermal/Internal.
• Forms change, accounting remains.

NODE 34

Three Languages

F = maΔp = JW = ΔE

• Newton's Language.
• Momentum Language.
• Energy Language. (Know when to use each).

NODE 35

Currency Metaphor

• Work = Transfer mechanism.
• Energy = Account being tracked.
• Power = Rate. Conservation = Accounting law.