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Ballistic pendulum
Intermediate
Measures bullet speed using momentum and then energy conservation.
v = (m+M)/m √(2gh)A bullet embeds in a hanging block. Momentum conservation gives the speed just after, and energy conservation then gives the swing height: v = ((m + M)/m)√(2gh).
m = 10 g, M = 2 kg, h = 5 cm: v ≈ 200 m/s.
Don't use energy conservation across the collision, it's inelastic.
In more detail
A ballistic pendulum measures a projectile's speed by letting it embed in a block that swings upward. Momentum conservation gives the projectile's speed, and energy conservation gives the swing height.
Real-world uses
- Historical method for measuring bullet speeds in physics labs.
- Teaching lab experiment that combines momentum and energy.
- A ballistic pendulum was used in the past to measure bullet speed by catching the bullet in a swinging block.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Which conservation law applies to the collision?
Momentum, since the collision is inelastic and energy is not conserved.
Which applies to the swing?
Energy, since the pendulum swings with no further losses in the ideal case.
How does the ballistic pendulum work?
Momentum conservation gives the speed of the block after impact, and energy conservation then gives its height of rise.
Related topics in Momentum & Collisions
Reduced mass · Collisions in two dimensions · Billiard ball collisions · Bouncing ball · Centre of mass · Velocity of centre of mass