Ballistic Pendulum Calculator

Ballistic Pendulum Calculator computes the initial velocity of a projectile that strikes a pendulum bob, causing it to swing to a maximum angle. The collision is modeled as perfectly inelastic, with momentum conserved during the collision and energy conserved during the swing. Enter the projectile mass, pendulum mass, pendulum length, and maximum swing angle to view detailed results for the equation mv₀ = (m + M)v.

How to Use Ballistic Pendulum Calculator:

1. Enter the projectile mass (m), pendulum mass (M), pendulum length (L), and maximum swing angle (α) using the keypad or direct input; use “Next” to switch fields.
2. Select appropriate units for masses (kg, g), length (m, cm), and angle (degrees).
3. Click “Calculate” to see step-by-step results for the projectile’s initial velocity.
4. Use “Share Result” to get shareable text or “Copy Result” to copy to clipboard.

Formulas:

Conservation of Momentum (inelastic collision):

Conservation of Energy (post-collision swing):

Maximum Height:

Initial Velocity of Projectile:

Where: m = projectile mass (kg), M = pendulum mass (kg), L = pendulum length (m), α = max angle (degrees), h = max height (m), v = velocity post-collision (m/s), v₀ = initial projectile velocity (m/s), g = 9.8 m/s²

Important Notes:

• Inputs for masses and length must be positive. Angle must be between 0° and 90°.
• Assumes a perfectly inelastic collision and negligible friction/air resistance.
• Results are rounded to four decimal places for clarity.
• Clipboard access requires a secure context (HTTPS). If copying fails, try accessing over HTTPS or copy manually.