Bed or Tiles — Same Fall, Different Stop
Why is a phone less likely to break when it lands on a bed than on a tiled floor, dropped from the same height? Two identical phones hang side by side, each the same height above its own surface — one over a bed, one over floor tiles. Press play to let them go together: the drop plays once, and the timeline can be dragged back to any moment. Sliders set the drop height, the phone's mass and how far the mattress gives. The fall is shown in slow motion, slowing further at the moment of impact, and two force–time graphs on one time axis record how each surface brings its phone to rest.
Como usar esta simulação
- Drop height h — 0.20 m to 2.00 m above each surface (default 1.00 m); both phones start this high above their own surface.
- Phone mass m — 0.10 kg to 0.30 kg (default 0.18 kg); the two phones are identical.
- How far the mattress gives d — 2 cm to 15 cm (default 8 cm): how deep the bed phone sinks before it stops.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion.
- Drag anywhere on the scene to look around.
O que observar
- Both phones reach their surfaces at the same moment and the same speed, so both have the same momentum to lose.
- The tile phone stops within about a millisecond; in slow motion the bed phone is still sinking into the mattress.
- The shaded areas under the two force–time graphs are equal — the same Δp — although the bed's pulse is low and wide and the tiles' pulse tall and narrow.
- The average-force card shows how many times harder the tiles push, and that number equals the ratio of the stopping times.
- At the default settings only the tile phone's screen cracks; a light phone dropped from low height survives even the tiles.
- Let the mattress give more: the bed's stopping time grows and its average force falls, while Δp stays the same.
A física por trás
Each phone reaches its surface at v = √(2gh) and stops without bouncing, so both lose the same momentum, Δp = mv: with the default 0.18 kg phone dropped 1.00 m, v = 4.43 m/s and Δp = 0.80 N s. What differs is the stopping time. In the model each surface pushes harder the faster the phone is still moving into it. The mattress lets the phone sink the chosen distance (8 cm by default) and stops it in about 0.050 s; the phone's case and the tiles give only about 1.3 mm between them and stop it in about 0.0008 s. Newton's second law in momentum form gives the average resultant force, F = Δp/Δt: about 16 N on the bed against roughly 1000 N on the tiles, some 60 times more. The graphs plot the resultant force — the surface's push minus the phone's weight — so the area under each pulse is exactly Δp: a low, wide pulse for the bed and a tall, narrow one for the tiles. A higher drop or a heavier phone raises Δp and both forces; a mattress that gives more lengthens the bed's stop and lowers its force. In the model the glass cracks when the push on it passes 700 N.