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.
How to use this simulation
- 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.
What to look for
- 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.
The physics behind it
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.