Connected particles
Pulleys, lifts, cars-and-trailers. Same acceleration; tension or contact force connects.
Y12 Mechanics. Two or more bodies connected by a string, rod, or contact. They share an acceleration. Apply F = ma to each separately, then solve simultaneously.
Worked examples
Pulley: m1 hanging, m2 on table. T = m2a (table); m1g − T = m1a (hanging).
Car (m1) towing trailer (m2); driving force F: a = F/(m1+m2); coupling tension = m2a.
Lift with passenger: passenger weight + lift weight = lift cable tension − total mass × a.
Frequently asked questions
Smooth vs rough strings?
Smooth: tension uniform throughout. Rough: not on this syllabus.
Light, inextensible string?
Mass-less and doesn't stretch. Lets us use a single tension and shared acceleration.