Stability and toppling sim

What the sim shows

Model: an object topples when the vertical line through its centre of gravity G (the weight line) passes outside its base; with xg the distance across from the downhill edge to G and h the height of G, that happens when tan θ > xg ÷ h, which is (b ÷ 2) ÷ h for a symmetric object. Blocks are wood of 0.6 g/cm³, 40 mm deep; block S has its bottom 10 mm in steel (7.9 g/cm³), so its G is 18.9 mm up instead of 40 mm. The model bus (60 mm across its tyres) is 300 g with G 40 mm up, plus 200 g on a deck (30 or 75 mm up); the bottle is 320 g of glass with G 62 mm up, plus damp sand (1.6 g/cm³); a solid cone's G is a quarter of its height up. The board tilts in 1° steps from 0° to 60°; the protractor, centred on the hinge, reads to 1°. In the practical each try goes over within ±1.2° of the prediction (seeded, so it repeats on every load). The fall uses g = 10 N/kg and a uniform block's moment of inertia. Idealised: the sandpaper never lets anything slide (a real short, wide block may slide first), the objects are rigid with sharp edges, the sand does not shift, and the bus's and bottle's own masses and G are chosen values, not measured.

• The object on the board: the part to watch
• Hinged board on a peg and stand, protractor, sandpaper strip, foam pad
• G and the weight line; the base turns red when the line is outside it

Use it in your lessons

• Try it here: anyone can unlock 2 figures free, and a free account unlocks up to 5. Runs on a laptop, a Chromebook or a phone; nothing to install.
• Present it and share student links with the teacher plan, from US$5 a month, billed yearly.
• Put it on your own website or LMS for US$9, paid once, or every sim from US$29 a month.

Free guide: 12 practicals as sims, and how to run one in a lesson →

Need a version for your exact set-up? Have one made: US$49 a figure in an order of 5.