Ballistic Pendulum: Muzzle Speed
A bullet of unknown speed embeds in a hanging block. Measure the maximum swing angle at several cord lengths and recover v₀ from momentum and energy.
Goal
Determine the hidden muzzle speed v₀ from θ_max: after a perfectly inelastic collision, V = √(2gL(1−cos θ)) and v₀ = (M+m)V/m. Average several runs at different L.
Equipment
- Ballistic pendulum (embedded shot)
- Protractor
- Known masses m, M
- Metre scale (L)
Experiment
Theory
Embedded (perfectly inelastic) impact conserves momentum: m v₀ = (M+m) V. The block-plus-bullet then rises; energy gives V² = 2 g L (1−cos θ_max). Combining, v₀ = (M+m)/m · √(2gL(1−cos θ_max)). The bench hides v₀ and the post-impact speed; you only read the protractor.
Procedure
- m, M and g are known. The muzzle speed is fixed and hidden. You only change the cord length L.
- Fire; read θ_max on the protractor. Small angular noise is added.
- The notebook computes v₀ from V = √(2gL(1−cos θ)) and v₀ = (M+m)V/m.
- Repeat for at least 6 different lengths between about 0.80 m and 1.60 m.
- Take the mean of the derived v₀ column and compare with the reference.
Conclusion
The mean recovered muzzle speed agrees with the hidden value within tolerance. Main uncertainties: protractor noise, treating the collision as perfectly inelastic, and neglecting support friction.