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📐 Friction & Pulley System — Complete Theory
🔍 Core Concepts
When a block (m₁) on a horizontal surface is connected via a pulley to a hanging mass (m₂), friction opposes motion. The system's behavior depends on static and kinetic friction coefficients.
⚡ Key Formulas
Newton's Second Law: ΣF = m·a
Weight: W = m·g (g = 9.81 m/s²)
Maximum Static Friction: ƒs,max = μs · m₁·g
Kinetic Friction (moving): ƒk = μk · m₁·g
Tension Force: T = m₂·g (ideal pulley, no inertia)
Condition for Motion: m₂·g > μs·m₁·g
Net Force when moving: Fnet = m₂·g − μk·m₁·g
Acceleration of system: a = (m₂·g − μk·m₁·g) / (m₁ + m₂)
📈 Simulation Logic
If µₛ is high, system may not move. Once threshold exceeded, kinetic friction takes over and acceleration is computed. The pulley is massless & frictionless; rope is ideal.
At rest: a = 0, static friction adjusts up to μₛ·m₁·g
Moving: a = (m₂g − μₖ·m₁·g)/(m₁+m₂)
🌱 Real‑World Relevance
Understanding friction is essential in engineering (brakes, belts, clutches), transport, and everyday motion. This simulation visualizes the transition from static to kinetic friction.
🧪 Variables used
m₁ (kg), m₂ (kg), μₛ, μₖ. Sliders update real‑time physics and motion simulation.
