4.4.4—Connected-particle models

For linked particles, an inextensible string over a smooth pulley gives equal magnitude accelerations and tension throughout the string. Newton’s second law is written separately for each mass.

Draw one diagram per particle, choose a common positive direction and use the string constraint only after writing the force equations.

A hanging mass and a block on a smooth table have the same acceleration; their combined equations can eliminate the internal tension.

Equal tension does not mean equal net force or equal mass; the particles can accelerate together with different forces.