Technologies K–10 · Years 7–8
Paper columns: how length changes the buckling load
Materials and Production Processes focus area (NSW Technology 7–8, 2023); Design and Technologies: Knowledge and understanding, Technologies context: Materials and technologies specialisations (ACARA v9)
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
A slender column that fails by bowing sideways (buckling) holds a load that falls with the square of its length, so doubling the length of a buckling tube quarters its load, while a short, stocky tube crushes instead at a load set by the strength of the paper.
What you need
- A4 copy paper, 80 gsm, 10 sheets per group (1 sheet per tube for the 9 tubes, plus 1 spare)
- A 2.0 cm diameter dowel to roll the tubes, sticky tape
- Scissors and a ruler
- A light card platform and a container that can be filled with sand or slotted masses; kitchen scale reading to 1 g
How to do it
- Roll 9 identical tubes around the dowel along the paper's long side and tape the seam.
- Trim 3 tubes to 10.0 cm, 3 to 20.0 cm and keep 3 at the full 29.7 cm.
- Stand a tube upright, place the platform on top and add sand slowly until the tube fails. Weigh the load.
- Note how each tube failed: bowed sideways (buckling) or crushed at an end.
- Test all 9 tubes and find the mean failure load for each length.
- Take the longest tubes that bowed sideways as the reference. Compare the mean loads of the other tubes that bowed sideways with the ratios predicted by the square of the lengths, and list the lengths that crushed instead.
What you should see
The buckling rule compares only tubes that fail by bowing sideways. If the 29.7 cm tubes buckle, a 20 cm tube that also buckles should hold (29.7 ÷ 20)² = 2.21 times their load, so a 29.7 cm tube holds 0.453 of a buckling 20 cm tube's load. A tube that crushes or crumples at an end fails at a load set by the paper's strength, which does not depend on length, so crushed tubes hold less than the rule predicts and their loads sit closer together. The 10 cm tubes are the stockiest and the most likely to crush, which is why the longest tubes, not the shortest, are the reference. Recording the failure mode of every tube shows which rule governs each length. The learner knows it worked when all 9 failure loads and modes are recorded and they can explain, from the modes, where the measured ratios follow 1 ÷ length² and where they do not.
What changes
- What you change
- tube length (10.0, 20.0, 29.7 cm)
- What you measure
- failure load (g) and failure mode
- What you keep the same
- the same paper and dowel
- the same taping
- load added slowly at the centre
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Columns fail by being squashed (slender columns bow sideways first).
- Twice the length halves the load (it quarters it for slender columns).
- A column fails at the top where the load is (buckling bows the middle).
Safety card
Hazards
- Sand spills
Controls
- Test inside a tray
Note
No chemicals or heat.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Technology 7–8 Syllabus (2023), NESA. Current: taught from 2026. Code read from the outcomes page on 2026-09-22.TE4-MSC-01TE4-DES-01
- Technology Mandatory 7–8 Syllabus (2017), NESA. Outgoing: replaced by the Technology 7–8 Syllabus (2023) from 2026 and not available after December 2027. Code read from the official syllabus document (DOCX) on 2026-09-22.TE4-9MATE4-8EN
- Australian Curriculum v9AC9TDE8K06AC9TDE8P02
Sources
The pages the author read to write this activity.