The Trolleys Stick — Where Did the Energy Go?
Two lab trolleys meet on a level track. Trolley A runs into trolley B, which waits at rest, and hook-and-loop pads on the facing ends make them stick. A phone on a small tripod films the collision at 240 frames per second beside a tape measure, and the scene plays eight times slower than real life, the way the slow-motion clip would. Three sliders set the mass of each trolley and A's speed; slotted masses appear on the trolleys as you add them. Press play and the clip runs once: the pads squash and glow, then the two trolleys roll on together, more slowly.
Como usar esta simulação
- Mass of trolley A, mA — 0.5 to 3.0 kg in 0.5 kg steps, starting at 1.0 kg: a bare trolley is 0.50 kg, and each step adds or removes a 0.50 kg slotted mass.
- Mass of trolley B, mB — 0.5 to 4.0 kg in 0.5 kg steps, starting at 1.5 kg.
- Speed of A before the collision, vA — 1.0 to 6.0 m/s, starting at 4.0 m/s. A change keeps the timeline where it is; a short clack sounds when the playing clip passes the impact.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion. At 1× the scene already runs eight times slower than real life, like a 240 fps clip played at 30 fps, so ⅛× shows the pads squashing 64 times slower.
- Drag anywhere on the scene to look around.
O que observar
- At the starting values the trolleys stick and move on at 1.6 m/s; the momentum reads 4.0 → 4.0 kg m/s while the kinetic energy falls from 8.0 J to 3.2 J.
- The energy bar keeps its full length after the collision: 3.2 J is still kinetic and 4.8 J has become internal energy and sound.
- Equal numbers of frame intervals are equal times: in the film strip the dots are 0.133 m apart before the impact and only 0.053 m apart after it.
- Take B from 0.5 kg to 4.0 kg: the share of kinetic energy lost rises from 33 % to 80 %, exactly mB/(mA + mB). Make A heavier and the share falls: 3.0 kg into 0.5 kg loses only 14 %.
- Halve A's speed from 4.0 to 2.0 m/s: the energy lost drops from 4.8 J to 1.2 J, but the share stays 60 %.
- At ⅛× watch the pads: they squash deeper the more energy is lost, glow, and stay squashed as the hooks grip.
- Drag the timeline slowly across the impact: the pads are squashed within about 0.006 s, the time it takes the two speeds to become equal, and the film strip fills in frame by frame.
A física por trás
Take the direction of A's motion as positive. The pads push the two trolleys with equal and opposite forces, so the total momentum cannot change: mA vA = (mA + mB) v′, and v′ = mA vA/(mA + mB). At the starting values, v′ = 1.0 × 4.0 / 2.5 = 1.6 m/s. The kinetic energy before is ½ × 1.0 × 4.0² = 8.0 J; after, ½ × 2.5 × 1.6² = 3.2 J, so 4.8 J, or 60 %, leaves the motion. It is not destroyed. In the model it is the work done squashing the foam pads, which the hooks hold squashed; in a real collision it ends up as internal energy of deformation, vibration and heating, plus a little sound. The share lost is mB/(mA + mB): a heavier B loses a bigger share, a heavier A a smaller one, and A's speed changes how many joules are lost but not the share. The film strip reads A's centre mark every 8th frame, 1/30 s apart, over the same number of frame intervals on each side of the impact: 0.400 m in 0.100 s gives 4.0 m/s before, and 0.160 m in 0.100 s gives 1.6 m/s after.