How to play Block Tower
- Choose a stack and read the blocks' masses and how far each one sticks out past the one below.
- Work from the top down: the blocks resting on each edge must have their centre of mass over that edge.
- Find the bottom block's overhang that puts the whole stack's x_cm at the table's edge, or the counterweight that brings it back, and press Let go.
- Watch the marks: green means a centre of mass is over its support; orange means that part of the stack topples.
How far can a stack lean?
A stack of blocks stays put as long as, at every level, the centre of mass of everything above lies over the block or table below. One uniform block can stick out half its length, because its centre of mass is at its middle. With more blocks you can do better by working from the top down: the top block sticks out L/2 past the one below, the top pair sticks out L/4 past the next, then L/6, L/8, and so on. Each lower block carries more weight, so it can stick out less. With enough blocks the top one ends up more than a whole block length past the table, with nothing under it. A counterweight on the back end works the same way: it pulls the centre of mass back over the table.
A focused learning model
Blocks are rigid, uniform, 0.4 m long and 0.1 m high, so each one's centre of mass is at its middle; a counterweight is a point mass on the bottom block's back end. The stack stays put while, at every level, the centre of mass of everything above lies over the edge below, within 0.2 mm. Otherwise the part above the lowest failing edge turns from rest about that edge, θ = ½·α·t² with α = M·g·d ÷ I, and is drawn until it has turned 30°, found exactly. Plays in real time.