💡 Understand Energy

The science of what makes things happen

📍 Overview 🔍 Observe 💡 Understand ✏️ Practice

📐 The Science of Energy

🔍 Connecting to observations: Remember the pendulum, bouncing ball, roller coaster, food, and rubber band. Each shows energy transforming from one form to another.
1. What is Energy?
Definition: Energy is the ability to do work or cause change. It comes in many forms and can transform from one to another.
SI Unit: Joule (J)
1 J = 1 kg·m²/s²

📌 Key Insight:

  • Moving objects have energy (kinetic)
  • Stored energy exists (potential)
  • Energy can't be created or destroyed - only transformed
2. Kinetic Energy (KE) - Energy of Motion
KE = ½mv²
where m = mass (kg), v = velocity (m/s)
Key Insight: Kinetic energy depends on both mass and velocity. Doubling mass doubles KE. Doubling velocity quadruples KE!

📌 Connecting to Observations:

  • Pendulum bottom: Maximum KE, minimum PE
  • Roller coaster bottom of hill: Fastest point = maximum KE
  • Rubber band after release: Elastic PE → KE
3. Potential Energy (PE) - Stored Energy
Gravitational PE: PE = mgh
where m = mass (kg), g = gravity (10 m/s²), h = height (m)

Elastic PE (Spring): PE = ½kx²
where k = spring constant, x = displacement

📌 Connecting to Observations:

  • Pendulum at highest point: Maximum PE, minimum KE
  • Ball held above ground: Gravitational PE stored
  • Stretched rubber band: Elastic PE stored
  • Roller coaster at top of first hill: Maximum PE
4. Law of Conservation of Energy
Total Energy = KE + PE + Thermal + ... = constant
Energy cannot be created or destroyed, only transformed
For a falling object (no friction):
mgh (top) = ½mv² (bottom)
v = √(2gh)

📌 Connecting to Observations:

  • Bouncing ball: Energy converts to heat and sound on each bounce
  • Pendulum: KE ↔ PE continuously, but friction slowly converts to heat
  • Roller coaster: First hill gives total energy; can't go higher than start
🧠 Think Deeper: In real systems, energy is always conserved, but some becomes "less useful" forms (heat, sound). This is why perpetual motion machines are impossible!
5. Work-Energy Theorem
Work = ΔKE = ½mv² - ½mu²
Work done = Change in kinetic energy

Work = Force × distance (when force is constant)
W = F × d (in direction of force)

📌 Example:

A 10 N force pushes a box 5 meters. Work done = 10 × 5 = 50 J. This increases the box's kinetic energy by 50 J.

6. Power - Rate of Energy Transfer
Power = Work / Time = Energy / Time
SI Unit: Watt (W) = 1 J/s

📌 Example:

Lifting a 10 kg mass 2 meters in 2 seconds vs 4 seconds:

  • Work = mgh = 10 × 10 × 2 = 200 J (same for both)
  • Power (2 sec) = 200/2 = 100 W
  • Power (4 sec) = 200/4 = 50 W
📊 Forms of Energy
Energy Type Description Example
Kinetic Energy of motion Moving car, running person
Gravitational Potential Energy due to height Ball held above ground
Elastic Potential Stored in stretched/compressed objects Rubber band, spring
Chemical Stored in chemical bonds Food, batteries, fuel
Thermal Heat energy Hot objects, friction
Electrical Energy of electric charges Lightning, circuits
Nuclear Stored in atomic nucleus Sun, nuclear power
📊 Quick Reference
Quantity Formula Unit
Kinetic Energy KE = ½mv² Joule (J)
Gravitational PE PE = mgh Joule (J)
Elastic PE PE = ½kx² Joule (J)
Work W = F × d Joule (J)
Power P = W/t Watt (W)
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