Core answer: Newton's second law: F = ma — force equals mass times acceleration. A 1,000 kg car accelerating 0→100 km/h (27.8 m/s) in 8 s averages 3.5 m/s², so the net driving force is 3,500 N. Weight is just gravity's force: W = mg, so a 70 kg person weighs 686 N on Earth and only 114 N on the Moon (g = 1.62 m/s²).
The three laws in one minute
- Inertia — a body keeps its velocity unless a net force acts. Seatbelts exist because your body keeps moving at 60 km/h when the car stops.
- F = ma — net force produces acceleration in proportion to mass.
- Action–reaction — forces come in pairs; a rocket pushes exhaust down, exhaust pushes the rocket up.
Forces you compute every day
| Force | Formula | Example |
|---|---|---|
| Weight | W = mg | 70 kg × 9.8 = 686 N |
| Friction (dry) | F = μN | μ = 0.6 rubber on dry asphalt |
| Spring | F = kx | k = 500 N/m spring stretched 0.1 m → 50 N |
| Centripetal | F = mv²/r | 1,000 kg at 20 m/s around r = 50 m → 8,000 N |
| Drag | F = ½ρCdAv² | doubles with speed squared |
Worked examples
Example 1 — Elevator "weight change". A 70 kg person on a scale in an elevator accelerating up at 2 m/s²: scale reads m(g + a) = 70 × 11.8 = 826 N ≈ 84 kg equivalent. Accelerating down, it reads 70 × 7.8 ≈ 56 kg. Your mass never changed — the apparent weight did.
Example 2 — Braking distance force. A 1,200 kg car braking from 30 m/s to 0 over 45 m: deceleration a = v²/(2s) = 900/90 = 10 m/s², needing F = 12,000 N of tire grip. On wet asphalt (μ ≈ 0.4) the maximum friction is μmg ≈ 4,700 N — not enough, so braking distance stretches beyond 100 m.
Common mistakes and myths
- "Heavier objects fall faster" — Galileo refuted this: neglecting air drag, everything falls at g. A hammer and feather fall together on the Moon (Apollo 15 demonstrated it).
- Confusing mass and weight — mass (kg) is invariant; weight (N) depends on the local g. Your luggage allowance is mass; the scale infers it from weight assuming g = 9.81.
- Thinking motion needs force — motion needs no force; *changing* motion does. A spaceship coasts forever with engines off.
- Forgetting net force — two tug-of-war teams pulling equally produce huge tension but zero acceleration; only the imbalance accelerates anything.
- Adding action–reaction to the same body — the pair acts on different bodies and never cancels on one free-body diagram.