Forces & Newton's 2nd Law
Year 10 (IGCSE) 🚀 Forces & Motion Apply F = ma to calculate resultant force, mass or acceleration.
🚀 Resultant Force and F = ma
In real situations, multiple forces act on an object. The resultant force is the single force that has the same effect as all forces combined.
⚡ Newton's Second Law
$$F_{\text{resultant}} = ma$$
$F$ = resultant force (N) · $m$ = mass (kg) · $a$ = acceleration (m/s²)
🚗 Example: A 1200 kg car has engine force 3000 N and friction 600 N.
Resultant = 3000 − 600 = 2400 N.
a = F/m = 2400/1200 = 2 m/s²
Resultant = 3000 − 600 = 2400 N.
a = F/m = 2400/1200 = 2 m/s²
🪂 Terminal Velocity
As an object falls or moves through a fluid, drag (air resistance) increases with speed. Eventually drag equals the driving force — the object reaches terminal velocity.
🪂 Terminal Velocity Condition
$$F_{\text{driving}} = F_{\text{drag}} \rightarrow F_{\text{resultant}} = 0 \rightarrow a = 0 \rightarrow \text{constant velocity}$$| ⏱️ Stage | 📊 Forces | 🏃 Motion |
|---|---|---|
| Just started falling | Weight > Drag | Accelerates downward |
| Speed increasing | Weight > Drag (gap closing) | Accelerates, but less |
| Terminal velocity | Weight = Drag | Constant velocity |
A skydiver reaches about 55 m/s (200 km/h) before opening their parachute. With the parachute open, terminal velocity drops to about 6 m/s — safe to land!
⚖️ Free Body Diagrams
A free body diagram shows all forces acting on an object as arrows. Arrow direction shows force direction; arrow length shows force magnitude.
| 📝 Scenario | ⚖️ Forces | 🏃 Result |
|---|---|---|
| Book on a table | Weight = Normal force | Balanced → stationary |
| Car braking | Friction > Engine force | Unbalanced → decelerates |
| Rocket launching | Thrust > Weight + Drag | Accelerates upward |
Always check your free body diagram: if arrows balance exactly, acceleration = 0. If one side is bigger, acceleration is in that direction!
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