Connected Particles and Pulleys
Two bodies joined by a string share one acceleration and pull on each other equally and oppositely. Write F = ma for each body, then solve the two equations together for the acceleration and the tension.
What a learner can do afterwards
- Write the equation of motion for each of two connected masses
- Solve the pair for the shared acceleration and the tension
- Explain why the tension is the same throughout a light string over a smooth pulley
1 · Read
Two bodies joined by a light string over a smooth pulley share one acceleration and one tension. The light string cannot keep any extra force and the smooth pulley adds no friction, so the pull matches all along. Write F = ma for each body with the same a and T, then solve the pair.
Hang 6 kg and 2 kg either side with g = 10: weights 60 N and 20 N. For the heavy side 60 - T = 6a, and for the light side T - 20 = 2a. Net pull 40 N on 8 kg gives a = 5 m/s squared, and T = 20 + 2 times 5 = 30 N.
Always start with one equation of motion per body, each with its own forces but shared unknowns. Adding the equations kills T and leaves a, then substituting back finds T. Take the direction of motion as positive for each body and keep it fixed.
Check answers by asking what each side feels: tension 30 N sits between 20 N and 60 N, holding the light side back and the heavy side up. If T ever lands outside the two weights, the algebra slipped. Equal sides would balance at zero acceleration.
Give each body its own F = ma with shared a and T, then solve the two equations together.
2 · Watch
Take it off screen
Where it sits
This opens up
Nothing builds on it yet.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.