Ballistic Pendulum Calculator (Speed of a Projectile)

What this tool does

The ballistic pendulum splits a fast problem into two easy ones: the catch is a perfectly inelastic collision, where momentum is conserved but energy is not, and the swing that follows is an ordinary rise in which energy is conserved. Working back from the height gives the speed of the block, and from there the speed of the projectile. Most of the projectile's energy is lost in the impact, the share M ÷ (m + M), which for a light bullet in a heavy block is nearly all of it. That is why the block's swing looks tiny compared with the energy fired into it.

Formula

m v = (m + M) V · ½ V² = g h · h = L (1 − cos θ) · v = (m + M) ÷ m × √(2 g L (1 − cos θ))

Variables

Worked example

Limitations

• The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
• Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.