A ballistic pendulum needs two separate models

The mistake

Using momentum conservation through the entire swing, or energy conservation through the collision.

Why it feels right

The problem has one object sequence, so one conservation law feels enough.

How to catch it

You conserve kinetic energy in the sticky collision or conserve momentum during the upward swing.

The first principle

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.

worked mini-example

A bullet embeds in a block, then the block rises. Which laws apply?

Common wrong move

Energy conserved from bullet before impact to top of swing.

Correct

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.