The Bridge-Building Contest
A science club must build a paper bridge spanning a 30 cm gap that holds as much mass as possible. Rules: only paper and tape may be used; the bridge may not touch the gap's base; the load is placed at the centre. Two teams test designs.
Team Flat builds a single flat sheet of paper across the gap. It sags and holds 50 g. Team Fold builds the same sheet folded into a corrugated (zig-zag) shape. It holds 400 g.
A third team, Team Tube, rolls the paper into tight cylinders and tapes them under the deck. It holds 900 g but uses twice as much paper as the others. The contest scores mass held per gram of paper used, not total mass.
1. Apply the principle behind Team Fold's success to explain why Team Tube also does well, and predict which team scores highest.
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The underlying principle is shape, not material, resists bending. A flat sheet bends easily because its material sits close to the middle, so it has little resistance to folding. Folding into corrugations or rolling into tubes moves paper away from the middle line, which greatly increases stiffness - the same reason a flat ruler flops but a rolled one is rigid.
So Team Fold and Team Tube both win by changing shape, not by adding strength to the paper itself.
Scoring (mass per gram of paper):
- Flat: 50 g for 1 unit of paper = 50 per unit.
- Fold: 400 g for 1 unit = 400 per unit.
- Tube: 900 g for 2 units = 450 per unit.
Prediction: Team Tube edges it at 450 per unit, just ahead of Team Fold at 400. The principle explains why both beat Flat, but the scoring rule decides between them - and Tube's extra paper is nearly, but not quite, paid back by its greater strength.
2. Team Tube wants to improve its score without changing its tube design. Suggest one change and predict its effect using the scoring rule.
Read the worked answer
The score is mass held ÷ paper used, so Team Tube can raise its score either by holding more mass with the same paper, or by using less paper for the same mass.
Best single change: remove one of the tubes (use less paper) while keeping the rest of the structure, provided the bridge still holds a good load.
Prediction: If using 1.5 units of paper still holds, say, 750 g, the score becomes 750 ÷ 1.5 = 500 per unit - beating both the old Tube score (450) and Team Fold (400).
The reasoning: because the score is a ratio, trimming paper helps even if the absolute mass held drops, as long as the mass does not fall faster than the paper. A student who only tries to add more mass, ignoring paper used, has missed that the contest scores a ratio, not a total.