A ballistic pendulum needs two separate models

01
The tempting model
Using momentum conservation through the entire swing, or energy conservation through the collision.
02
Why it feels right
The problem has one object sequence, so one conservation law feels enough.
03
Where it breaks · how to catch it
You conserve kinetic energy in the sticky collision or conserve momentum during the upward swing.
04
The correct model
During the short collision, momentum is conserved and kinetic energy is not. During the swing after sticking, mechanical energy is conserved if losses are negligible.
05
Repair · see it, then test it
worked example A bullet embeds in a block, then the block rises. Which laws apply?
Tempting move
Energy conserved from bullet before impact to top of swing.
Correct move
Momentum for collision; then energy for the post-collision rise.
Test the repair MOM-09 · transfer

A dart sticks in a cart; the joined pair then compresses a spring. Which sequence is valid if external impulse during impact is negligible?
Energy through impact, then momentum during compression Momentum through impact, then mechanical energy during compression Momentum through both stages Mechanical energy through both stages

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R24Ballistic pendulum sequenceadds: Use momentum for the collision, then energy for the swing.