When two particles are joined by a light inextensible string, they move with the same acceleration and the tension is the same along the string. Write F = ma for each particle separately, then solve the two equations together.
For particles over a smooth pulley, the heavier one goes down. For a car towing a trailer, treat the whole system to find the acceleration, then the trailer alone to find the tension in the towbar. Considering the whole system removes the tension, because it is an internal force.
Worked example
Masses of 8 kg and 3 kg hang over a smooth pulley. Find the acceleration. Use g = 9.8.
- Whole system: (8 − 3)g = (8 + 3)a.
- 49 = 11a.
Answer:a = 4.45 m/s²
Key words
- inextensible
- does not stretch
- smooth pulley
- no friction, same tension both sides
- internal force
- a force between parts of a system
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