Newton's Cradle

Conservation of Momentum

Newton's Cradle is one of the most elegant demonstrations of the conservation of linear momentum. When a ball on one side is lifted and released, it swings down and strikes the next ball. The momentum is transferred through the chain of contacting balls and emerges on the far side, launching the end ball outward.

The key insight is that momentum ($p = mv$) must be conserved in every collision. Since all balls have equal mass, the velocity of impact is fully transferred to the last ball. If two balls are pulled back, two balls swing out on the opposite side — preserving both total momentum and kinetic energy.

Elastic Collisions

Newton's Cradle relies on nearly elastic collisions — collisions where both momentum and kinetic energy are conserved. In a perfectly elastic collision between identical masses, a moving object striking a stationary one transfers all its velocity — the striker stops and the target moves.

Real steel balls are not perfectly elastic. With each impact a small fraction of energy converts to heat and sound. This is why the cradle eventually comes to rest. The Elasticity slider in this simulator lets you explore how different levels of energy loss affect the system.

Pendulum Physics

Each ball in the cradle swings on a string, making it a simple pendulum. At the highest point the ball has maximum potential energy; at the lowest point all energy has converted to kinetic energy. The gravitational acceleration (g) determines how quickly the ball swings down.

For small angles, the period of a pendulum depends only on the string length and gravity: $T = 2\pi\sqrt{L/g}$. This means that changing gravity in the simulator accelerates or decelerates the swings without affecting the collision dynamics.

Energy Dissipation

In a real Newton's Cradle, several non-conservative forces dissipate energy:

• Air resistance — a drag force proportional to velocity
• String friction — loss at the pivot point
• Sound energy — the characteristic "click" carries energy away
• Deformation — slight compression of steel on impact

The Damping control simulates these combined losses. Set it to 1.000 for an ideal, lossless cradle.