The Air-Table Collision — Momentum in Two Directions
An air-hockey table seen almost from above, its field left plain, with x and y axes painted in one corner. Puck A slides along x towards puck B, which waits at rest; both are made of the same plastic, so the heavier puck is the wider one. Five sliders set the two masses, A's speed, where A strikes B — the angle φ between A's path and the line joining the centres at the instant they touch, from 0° (head-on) to 70° (a glancing blow) — and how bouncy the collision is. Press ▶ and the run plays once: it leaves strobe dots every 0.1 s, the pink line of centres and the angle φ on the table, and stops just before a puck reaches a rail, so you can read the directions and compare the momenta.
Bu simülasyon nasıl kullanılır
- Mass of A, mA — 0.10 to 1.00 kg, starting at 0.20 kg. A puck's radius grows with the square root of its mass.
- Mass of B, mB — 0.10 to 1.00 kg, starting at 0.80 kg.
- Speed of A, uA — 0.5 to 3.0 m/s, starting at 2.0 m/s.
- Where A strikes B, φ — 0° (head-on) to 70°, starting at 30°. It shifts A's path sideways by b = (rA + rB) sin φ.
- Bounciness (restitution) e — 0 to 1, starting at 0.67 (2/3). A change re-computes the run and keeps the moment on screen; the collision spot is chosen so that both pucks have room to glide.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion (at 1× the scene runs four times slower than real life; the strobe dots stay 0.1 s of real time apart).
- Drag anywhere on the scene to look around.
Nelere dikkat etmeli
- B always leaves along the pink dashed line joining the two centres at the moment of contact, at the angle φ to A's first path.
- At the starting values A turns through 90° and moves off at 1.15 m/s, while B goes 30° the other way at 0.58 m/s.
- The balance card: along x, 0.40 before = 0.00 + 0.40 after; along y, 0 before = +0.23 − 0.23 after. In the triangle the two after-arrows, end to end, land exactly on the tip of A's momentum before.
- Set both masses to 0.50 kg and e to 1: whatever φ you choose, A and B leave at right angles to each other.
- At φ = 0° the collision stays on one line: a light A bounces back, a heavy A carries on, and with equal masses and e = 1, A stops dead while B takes all of its speed.
Arkasındaki fizik
The pucks are smooth, so the only push between them acts along the line joining their centres. B, at rest, can only leave along that line; A keeps its velocity across it. Along the line, the coefficient of restitution e sets how much of the approach speed comes back as separation speed: e = 1 is perfectly elastic, while e = 0 means the pucks move on together along the line. Momentum is a vector, so it is conserved separately along x and along y. At the starting values (0.20 kg at 2.0 m/s into 0.80 kg, φ = 30°, e = 0.67): x: 0.20 × 2.0 = 0.80 v′B cos 30°, so v′B = 0.58 m/s; y: 0 = 0.20 v′A − 0.80 v′B sin 30°, so v′A = 1.15 m/s, at 90° to A's first path. The x-row reads 0.40 = 0.00 + 0.40 and the y-row 0 = +0.23 − 0.23. Head-on (φ = 0°) A rebounds at 0.67 m/s and B moves on at 0.67 m/s. With equal masses and e = 1 the two pucks always leave at right angles to each other.