How to play Balance Point
- Choose a beam and read each mass and its distance from the left end on the card.
- Multiply each mass by its position and add them up: Σm·x. Count the beam's own mass at its middle.
- Divide by the total mass to find x_cm, or solve for the position or mass that puts x_cm over the support, and press Let go.
- Watch the green mark: if the centre of mass is over the support, the beam stays level; otherwise it tips toward it.
Where is the centre of mass?
Every object behaves as if its whole weight pulled down at one point, its centre of mass. For masses along a line it is the mass-weighted average position: x_cm = Σm·x ÷ Σm. Heavy pieces pull it toward themselves; light ones barely move it. A uniform beam's own centre of mass is at its middle, so the beam counts as one more mass placed there. An object resting on a support stays put while its centre of mass is above the support; once it is past the support's edge, its weight turns the object over that edge. That is why you can balance a ruler on one finger, and why a seesaw balances when Σm·x is the same on both sides of the pivot.
A focused learning model
The beam is rigid and 2 m long; masses are points at fixed positions, and a uniform beam's own mass acts at its middle. The support's flat top is 2 cm wide: the beam stays level while its centre of mass is over it. Otherwise the beam turns from rest about the support's nearer edge, θ = ½·α·t² with α = M·g·d ÷ I, until its lower end touches the table, found exactly. Plays in real time.