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Connected bodies
Intermediate
Bodies linked by strings share acceleration in the same direction of motion.
For bodies joined by a rope, they share the same acceleration magnitude. Write ΣF = ma for each body separately, or for the whole system when the internal tensions can be ignored.
A 4 kg block pulls a 2 kg block with 12 N: a = 12/6 = 2 m/s², tension on the second block 4 N.
Don't forget that the tension acts on both bodies in opposite directions.
In more detail
When bodies are connected by a string or rod, they share the same acceleration along the connection. Forces on each body are found separately and then combined.
Real-world uses
- Train carriages are connected, so they accelerate together under the locomotive's force.
- Towing a trailer involves connected bodies with a shared acceleration.
- Railway carriages linked by couplings accelerate together, so the engine must pull the total mass of the train.
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Frequently asked questions
How do I treat connected masses?
Draw a free-body diagram for each, write F = ma for each, and solve the set of equations together.
Why do connected masses share an acceleration?
Because the connection keeps the distance between them constant, so their accelerations must match.
Does the coupling force change along the train?
When the train accelerates, the force in each coupling depends on the mass it pulls, so it changes along the chain.
Related topics in Newton's Laws & Forces
Net force and equilibrium · Tension · Atwood machine · Elevator problems · Pulley systems · Motion on an inclined plane