Distinguish internal recoil from an external impulse

1. Orient: Distinguish internal recoil from an external impulse

The change in total momentum of a chosen system equals the net external impulse on that system. Internal interaction impulses occur in equal and opposite pairs and cancel when the members’ momentum changes are summed. They do not cancel on each individual object, whose momentum can change substantially.

2. Explain and derive

Choose the boundary before applying conservation. For one recoiling cart, the force of its partner is external. For both carts together, that same interaction is internal. A short interaction time can make an external impulse negligible compared with collision impulses, but “short” is not proof; estimate force times duration or compare measurements.

The model starts two objects at rest. A virtual internal stored-energy release gives the 2 kg object impulse−J and the 3 kg object impulse+J. If external impulse is zero, they acquire opposite momenta and the center remains at rest. The increase in kinetic energy comes from stored internal energy, so it does not violate energy conservation.

An additional external impulse on the first object changes the total momentum. Write Δp 1=Jexternal−J and Δp 2=J; their sum is Jexternal. Internal release still redistributes momentum, but it cannot erase the external contribution. No physical release device, pressure apparatus or energetic-material procedure is required; these are supplied virtual ledgers.

3. Work an example

With internal impulse 3 N s and no external impulse, final velocities are−3/2=−1.5 m/s and+3/3=+1 m/s. Their momentum sum is zero. Adding external impulse+2 N s to the first object changes its final momentum to−1 kg m/s; total final momentum is+2 and center velocity 2/5=0.4 m/s.

4. Predict and investigate

Predict first: Can an internal stored-energy release change total momentum from zero without any external impulse?

Hold internal impulse at 3 N s and compare external impulses−2,0 and+2 N s. Verify the sum of individual momentum changes. Then hold external impulse fixed and change internal impulse; identify which system quantity stays the same. Retain settings and raw evidence in the lesson notebook.

5. Transfer and explain

Try a new practice case

A system starts with momentum−3 kg m/s and receives external impulse+8 N s. Find final system momentum.

Your numerical result (kg m/s) Check number

Reveal worked check (practice, not mastery)

This extra practice is not saved and does not award mastery. Record your first answer, explanation and whether you revealed help in the lesson notebook. Use the lesson’s saved question separately.

6. Reflect and retain evidence

A cart collides with a wall. Why is momentum of cart alone not conserved, and how would enlarging the system to include the wall and Earth change the accounting?

Retain the first answer, signed component sums, scalar energy totals, bounds, assumptions and one changed-case prediction. Public worked checks are practice, not independent mastery evidence. Synthetic readings are not a performed physical experiment.

Framework and source notes

Original teaching prose and numerical cases. College Board AP Physics 1 CED, Unit 4 topic mapping: 4.2; 4.3. Checked 30 October 2026. Two-dimensional cases use component setup and simple separate relations, not a general simultaneous-angle solver. This is a framework cross-reference, not AP authorization.