Introduction
Connected particles problems appear in almost every 9709 Mechanics paper and are a direct extension of applying Newton's second law () to single objects. Instead of one body, two or more bodies are linked — by a string over a pulley, a tow-rope, or a rigid tow-bar — and share a common magnitude of acceleration. The key skill is writing separate equations of motion for each particle and then solving the system simultaneously to find both the acceleration and the tension (or thrust) in the connecting link.
Core Concept
Fundamental Assumptions (Model Conditions)
Every connected-particles question in 9709 is built on a standard set of modelling assumptions. Learn them and state them if asked:
| Model condition | Consequence |
|---|---|
| String is light (massless) | Tension is the same throughout the string |
| String is inextensible | Both particles have the same magnitude of acceleration |
| Pulley is smooth | Tension is the same on both sides of the pulley |
| Rope/tow-bar is light | Coupling force carries no weight |
Method: Two-body System
- Identify each body and all forces acting on it (weight, normal reaction, tension , friction if present, driving force, etc.).
- Choose a positive direction for each body consistent with the assumed direction of motion.
- Apply to each body separately, writing one equation per body.
- Add (or subtract) the equations to eliminate and find .
- Back-substitute to find (or thrust/compression for a tow-bar).
Rope vs Rigid Tow-bar
- A rope can only pull — it carries tension ().
- A rigid tow-bar can push or pull — it carries tension (tow-bar is taut, pulling trailer) or thrust/compression (tow-bar is compressed, pushing trailer when the car brakes hard).
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