ATWOOD
Two masses, one rope, one pulley — the tension tells the truth.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Two masses hang from a massless rope over a frictionless pulley. m₂ is heavier. When the system is released, what acceleration do the masses share — and what is the tension in the rope?
Forces
Isolate each mass. Weight pulls down; rope tension pulls up. One taut rope over a massless pulley means the same T on both sides; one inextensible rope means both masses share the same acceleration magnitude a.
Solve
Add the two equations: tension cancels, leaving (heavier − lighter)×g = (m₁ + m₂)a. Solve for a, then substitute back for T. The imbalance in weight drives the combined inertia of the system.
Motion
Released from rest, the system moves with constant acceleration: s = ½at², v = at. The forces do not change during the motion — the vectors hold constant length as the heavier mass falls and the lighter rises.
Impact & Energy
The heavier mass lands at v = √(2ah). Check the books: potential energy released, (heavier − lighter)gh, equals kinetic energy gained, ½(m₁ + m₂)v². The audit balances — the dynamics are confirmed.