Choose a system before conserving momentum
You will be able to: Use system boundaries and external impulse to decide whether total momentum is constant.
Whose momentum is conserved during a collision?
Cart A pushes cart B during a collision. A loses momentum while B gains it. A alone has an external push from B; the pair includes both sides of that interaction.
A useful starting point: Choosing a system →
Words and symbols before equations
- Internal force
- An interaction between two objects inside the chosen system.
- External force
- A force exerted by an object outside the boundary.
- Net external impulse J_ext
- The combined impulse crossing the system boundary.
- Conserved over an interval
- Has the same total value at the interval’s start and end.
What this picture assumes
Initially p_A=+6 and p_B=0 kg·m/s. Fixed mutual impulses: −4 N·s on A, +4 N·s on B. An outside agent additionally acts on B. Boundary choice changes the account, not the event.
Connect the picture to the physics
For two carts on a level low-friction track, draw a boundary around both. Their forces on each other are equal and opposite at every instant, so their internal impulses cancel in the sum. They act on different carts, not as balanced forces on either cart alone.
The general momentum balance is P_f−P_i=J_ext. Total momentum remains constant throughout an interval if the net external force is zero throughout. Equal initial and final totals only require zero net external impulse over that interval; momentum could vary in between.
During a short collision, external friction may be present but deliver a small impulse compared with collision impulses. State this approximation and use velocities immediately before and after. If an external push has appreciable impulse, include it instead of declaring the pair isolated.
A worked example, step by step
Initially p_A=+6 and p_B=0 kg·m/s. During a short collision, A gives B +4 N·s. First neglect outside impulses; then add an external +1 N·s push to B. Find the final momenta and totals.
- The impulse on A from B is −4 N·s; the impulse on B from A is +4 N·s.
- Without outside impulse: p_Af=6−4=2, p_Bf=0+4=4 kg·m/s; total remains 6.
- With an extra external +1 N·s on B: p_Af=2, p_Bf=5; P_f=7 kg·m/s.
- The pair’s total changed by exactly J_ext=+1 N·s. Internal transfer still canceled.
Momentum of one cart need not be conserved when the two-cart total is conserved. Name the boundary and interval.
Are equal and opposite collision forces a reason each cart’s momentum is constant?
Compare with an explanation
No. They act on different carts. Their impulses cancel only when the system contains both.
Predict. Change one thing. Explain.
Select A alone or A+B while varying the extra external impulse delivered to B. Track which impulse crosses each boundary and check ΔP=J_ext for that selected system.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
For A+B, ΔP=0 kg·m/s = external impulse 0 N·s. The mutual ±4 N·s impulses are internal and cancel.
Initially p_A=+6 and p_B=0 kg·m/s. Fixed mutual impulses: −4 N·s on A, +4 N·s on B. An outside agent additionally acts on B. Boundary choice changes the account, not the event.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a momentum or impulse relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionTwo carts start with total P=+8 kg·m/s. A transfers +3 N·s to B. An outside brake gives the pair −2 N·s. (a) State the impulse on A from B. (b) Find the sum of internal impulses. (c) Find final total momentum. (d) State why setting P_f=P_i fails.
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Compare with the answer and four-point rubric
- 1 point: −3 N·s, by Newton’s third law.
- 1 point: Zero: −3+3=0.
- 1 point: P_f=8−2=+6 kg·m/s.
- 1 point: The brake supplies a non-negligible external impulse during the chosen interval.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1General system momentum balance?
P_f−P_i=J_ext.
RECALL 2When do internal impulses cancel?
When both interacting objects are included.
RECALL 3What makes a short-collision approximation useful?
External impulse can be small over the short interval.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Choose a system before conserving momentum
- P_f=P_i+J_ext.
- Internal impulses cancel in the total for a system containing both interacting objects.
Remember: Momentum of one cart need not be conserved when the two-cart total is conserved. Name the boundary and interval.
Conditions: Initially p_A=+6 and p_B=0 kg·m/s. Fixed mutual impulses: −4 N·s on A, +4 N·s on B. An outside agent additionally acts on B. Boundary choice changes the account, not the event.
Refresh Kid · Unit 4 · Objectives 4.3.A, 4.3.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 4.3, objectives 4.3.A, 4.3.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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