Simulation · Dynamics
Pulley and rope laboratory
Compare five ideal rope-and-pulley systems, observe their geometric constraints, and test how masses, tension, and friction determine motion.
Physical model
Newton's second law and rope constraints
Each body has its own FBD, while inextensible ropes link their accelerations. Compare five geometries without confusing tension, net force, and constraint.
The rope does not stretch and each ideal pulley only redirects tension; the movable pulley receives two segments with tension T.
2D Canvas · laboratory
Ropes, pulleys, and constrained motion
The scene preserves geometric connections while readings and equations remain outside the canvas.
Playback stopped at the apparatus geometry limit. The state immediately before impact is shown; the collision is not modeled.
The selector switches among five systems: table and hanging mass, Atwood, movable pulley, a three-pulley 3:1 system, and double Atwood. Text readings describe positions, velocities, accelerations, and tensions.
Positive coordinates point downward, except m₁ on the table, whose positive direction points toward the edge.
Live readings
Physical state
- Instant t
- 0 s
- State of m1
- Δq 0 m · v 0 m/s · a 0 m/s²
- State of m2
- Δq 0 m · v 0 m/s · a 0 m/s²
- State of m3
- Δq 0 m · v 0 m/s · a 0 m/s²
- State of mL
- Δq 0 m · v 0 m/s · a 0 m/s²
- State of mC
- Δq 0 m · v 0 m/s · a 0 m/s²
- State of pulley
- Δq 0 m · v 0 m/s · a 0 m/s²
- Tension T
- 30.58 N
- Tension TA
- 0 N
- Tension TC
- 0 N
- Friction on m₁
- 17.64 N
Body-by-body analysis
Separate free-body diagrams
Each card isolates one body or assembly. Every T is a real segment force: two arrows support the 2:1 movable pulley, three support the 3:1 pulley system, and in the double Atwood T_C balances the two T_A forces on the ideal moving pulley.
Current model
Live Newton equations
T = 0 N · f = 0 N · a = 0 m/s²
T = 0 N · a₁ = 0 · a₂ = 0 m/s²
T = 0 N · aL = 0 · aC = 0 m/s²
T = 0 N · aL = 0 · aC = 0 m/s²
TA = 0 N · TC = 0 N
a₁ = 0 · a₂ = 0 · a₃ = 0 m/s²
Inextensible geometry
Rope constraint
m₁ advances toward the edge by exactly the distance m₂ descends.
The two masses travel equal distances in opposite directions.
The free end travels twice the distance of the moving load.
The counterweight travels three times the load displacement in the opposite direction.
The two ropes link all three accelerations and the center of the movable pulley.
Numerical constraint residual: 0
Graphs
Last ten seconds
Connected displacements
Position history
- q₁
- q₂
- q₃
Paused
Exploration guide
What to observe
- 01
Begin with the table system and compare the actual static friction with its maximum value.
- 02
Balance an Atwood machine, then change one mass and track the sign of both accelerations.
- 03
In the movable-pulley system, compare the load displacement with the free-end displacement.
- 04
In the 3:1 pulley system, verify that the counterweight travels three times the load displacement in the opposite direction.
- 05
Use the symmetric double Atwood case before exploring an asymmetric set of three masses.
- 06
For every scenario, compare the free-body diagrams, Newton equations, and rope constraint with the animation.
Scope
Model limits
One-dimensional translational model with ideal massless inextensible ropes, massless pulleys, frictionless axles, and uniform gravity. Visible wheel rotation is only a kinematic cue derived from rope displacement: rotational inertia, torque, impact, and rebound are not solved.