Newton’s Cradle
Pull back one or more balls and release. Watch momentum transfer through a chain of elastic collisions — the same number of balls swing out on the opposite side, conserving both momentum and kinetic energy.
How it works
Newton’s cradle demonstrates the nearly elastic transfer of momentum and kinetic energy through a series of contacting spheres. When one ball strikes the row, it decelerates to a stop while the ball on the far end launches away at nearly the same velocity. The intermediate balls barely move — they transmit a compression wave through direct contact, much like a pulse traveling through a line of springs.
The key insight is that two conservation laws — conservation of momentum and conservation of kinetic energy — together uniquely determine the outcome of an elastic collision between equal masses. If you pull back one ball, exactly one must swing out the other side. Pull back two, and two swing out. No other partition of velocities among the balls satisfies both conservation laws simultaneously when all masses are equal.
When masses are unequal, the picture changes. A heavier ball striking a lighter one will continue forward (though slower), while the lighter ball flies off faster. A lighter ball striking a heavier one bounces back. The general formulas for one-dimensional elastic collisions are v′₁ = (m₁ - m₂)v₁/(m₁ + m₂) and v′₂ = 2m₁v₁/(m₁ + m₂). Try adjusting the mass ratio slider to see how unequal masses break the clean “same number in, same number out” behavior.
Real Newton’s cradles lose energy to heat and sound at each collision, which is why the swings gradually diminish. The damping slider lets you control this dissipation. At zero damping, the cradle swings forever — a perpetual motion machine that exists only in idealized physics.