Ballistic Pendulum

This interactive simulator explores Ballistic Pendulum in Classical Mechanics. Bullet hits block: embedded vs e; ω₀ = v/L, θ_max, energy graph. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Classical Mechanics.

Key terms

  • ballistic
  • pendulum
  • ballistic pendulum
  • mechanics
  • classical

Live graphs

How it works

A bullet strikes a hanging block at the lowest point of the arc so the impulse is approximately horizontal along the pendulum’s tangent. In the classic fully inelastic case the bullet embeds, momentum gives (M+m)V = mv₀, and the subsequent swing conserves mechanical energy in this ideal model (no drag). With a nonzero restitution e we treat a one-dimensional impact along the same line: the block picks up v₂′ = (1+e)mv₀/(m+M) while the bullet rebounds with v₁′ = v₀ − (1+e)Mv₀/(m+M); only the block is attached to the string, so its initial angular speed is v₂′/L. Compare predicted maximum angle from ½Mv₂′² = MgL(1−cos θ_max) with the live simulation.

Key equations

Embedded: (M+m)V = mv₀  ·  ½(M+m)V² = (M+m)gL(1−cos θ_max)
General: v₂′ = (1+e)mv₀/(m+M)  ·  ω₀ = v₂′/L