Topic · 3 games

Centre of mass: where the weight acts

Every object acts as if its whole weight pulled at one point, the centre of mass: x_cm = Σm·x ÷ Σm. Support it there and it balances; let it pass the edge of its support and it tips.

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3 games

PLAY NOW · 40

Balance Point: Find the Centre of Mass

Balance a loaded beam on a narrow support. Weight each position by its mass to find the centre of mass, include the beam's own weight, and place or choose a mass to move the balance point.

Centre of massBalance
Play Balance Point
Centre of mass
x_cm = Σm·x ÷ Σm
Level when
|x_cm − x_s| ≤ 1 cm

PLAY NOW · 41

Hanging Mobile: Level Every Rod

Build a mobile that hangs level. Find the balance point of each rod, work from the bottom up, and treat a whole lower mobile as a single mass hanging at the end of a rod.

Centre of massComposite objects
Play Hanging Mobile
Knot
x_k = Σm·x ÷ Σm
Lower mobile
M = m₁ + m₂ + …

PLAY NOW · 42

Block Tower: Reach Past the Edge

Stack blocks out past a table's edge without toppling. Keep the centre of mass of every part of the stack over the block below it, add a counterweight, and find out how far a stack can lean.

Centre of massToppling
Play Block Tower
Stays put while
x_cm ≤ x_edge
Three-block reach
L·(1/2 + 1/4 + 1/6)

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