If momentum is conserved, must kinetic energy be conserved too?

No. Momentum can be conserved with partial energy loss to heat and sound. The textbook equal-mass elastic swap is a special case with e = 1.

Why do real cradles sometimes launch two balls?

Small gaps, angular wobble, and imperfect timing break the ideal simultaneous-contact assumption, redistributing momentum across neighbors.

Is this the same math as the 1D collisions lab?

Yes in spirit: sequential pairwise collisions with restitution laws. The cradle emphasizes wave-like impulse transfer through multiple contacts.

Does angular momentum matter here?

If spheres twist or strings apply torques, yes. Many didactic models freeze rotation and treat line-of-centers impacts only.

Newton's Cradle

Conservation of momentum and energy visualized with swinging balls.

Live graphs

About this model

Newton's cradle is the desk toy of suspended metal spheres that collide in a line. Ideal elastic collisions between identical spheres transfer momentum and energy in a way that launches one outgoing sphere when one incoming sphere strikes a stationary chain—an illustration of one-dimensional impulse propagation and approximate Hertzian contact mechanics. Real cradles deviate: dispersion in the balls and supports, slight misalignment, internal modes, and inelasticity cause secondary motion and imperfect single-sphere ejection. The simulator typically treats spheres as point masses or rigid bodies with a chosen coefficient of restitution, sometimes including small angles for visual flair but keeping the pedagogy one-dimensional. Students compare momentum-conserving limits with energy loss, discuss why the *last* ball pops out in the ideal story, and connect the demo to collision lessons in 1D and 2D simulators elsewhere in the catalog.

Who it's for: High school mechanics classes reinforcing impulse, momentum conservation, and coefficients of restitution after introducing Newton's laws.

Key terms

Impulse
Momentum conservation
Elastic collision
Coefficient of restitution
Hertzian contact
1D chain
Dispersion
Newton's cradle

How it works

Newton’s cradle idealizes equal masses in a line with elastic impacts. In 1D, two equal spheres in a head-on elastic collision exchange velocities. Here a small chain propagates that impulse; light damping models air and hinge losses so motion eventually stops.

Key equations

Elastic, equal masses: v₁′ = v₂, v₂′ = v₁ (head-on)

p = Σ mᵢvᵢ conserved in elastic collisions

Frequently asked questions

If momentum is conserved, must kinetic energy be conserved too?: No. Momentum can be conserved with partial energy loss to heat and sound. The textbook equal-mass elastic swap is a special case with e = 1.
Why do real cradles sometimes launch two balls?: Small gaps, angular wobble, and imperfect timing break the ideal simultaneous-contact assumption, redistributing momentum across neighbors.
Is this the same math as the 1D collisions lab?: Yes in spirit: sequential pairwise collisions with restitution laws. The cradle emphasizes wave-like impulse transfer through multiple contacts.
Does angular momentum matter here?: If spheres twist or strings apply torques, yes. Many didactic models freeze rotation and treat line-of-centers impacts only.

Continue with similar topics in this category — or all 85 in Classical Mechanics.

View category →

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Newton's Cradle

Live graphs

About this model

How it works

Key equations

Frequently asked questions

Related simulators

1D Collisions

2D Collisions

Wall Bounce

Oblique Wall Impact

Pendulum Collision

Energy Conservation

Newton's Cradle

Live graphs

About this model

How it works

Key equations

Frequently asked questions