Choosing a system: internal & external forces
You will be able to: Identify which interactions cross a chosen system boundary.
Where should you draw the boundary?
Two students push two touching carts together. Cart A pushes cart B. If you study B alone, that push comes from outside. If you study both carts together, the same interaction is inside your boundary.
A useful starting point: Scalars, vectors and direction →
Words and symbols before equations
- System
- The object or collection of objects we choose to study.
- Environment
- Everything outside that boundary.
- External force
- A push or pull exerted by something outside the system; measured in newtons (N).
- Acceleration
- Change in velocity per second, in m/s². A force divided by mass in kg gives acceleration.
What this picture assumes
Both carts move together on a frictionless horizontal track. Masses: A 2 kg, B 3 kg. Hand push: 10 N right. Vertical weight and support balance and are omitted in this horizontal view.
Connect the picture to the physics
A boundary is a modeling choice, not a physical wall. Name every object inside before listing forces. Include only forces ON your chosen system when finding its net external force.
For the two-cart system, A-on-B and B-on-A are internal. For cart B alone, A-on-B is external. Changing the boundary changes the bookkeeping; it does not change what the carts actually do.
An extended object can be treated as a particle when its shape and rotation do not matter to the question. A system may exchange energy or mass with its environment. The fixed-mass models here do not describe fuel leaving a rocket.
A worked example, step by step
A 2 kg cart A pushes a 3 kg cart B on a level frictionless track. A hand pushes A with 10 N right. The contact force on B is 6 N right. Compare the force lists for B and for A+B.
- Choose B: external horizontal force is A-on-B, 6 N right. Its weight and the track’s support balance vertically.
- Choose A+B: the 6 N contact pair is internal. The only horizontal external force is the hand’s 10 N push.
- The two descriptions agree: B accelerates at 6/3 = 2 m/s²; the pair accelerates at 10/(2+3) = 2 m/s². Newton’s second law will explain this calculation in Topic 2.5.
Internal does not mean nonexistent. It means both interacting objects lie inside the chosen boundary.
Does the track’s upward force become internal when both carts are selected?
Compare with an explanation
No. The track remains outside either cart system.
Predict. Change one thing. Explain.
Switch between cart B and both carts. Keep the physical 10 N push fixed. Predict which arrow becomes internal; explain why the total external horizontal force changes.
External horizontal force 6 N right; selected mass 3 kg; acceleration 2 m/s² right. Horizontal force arrows: 8 drawing units per N.
Both carts move together on a frictionless horizontal track. Masses: A 2 kg, B 3 kg. Hand push: 10 N right. Vertical weight and support balance and are omitted in this horizontal view.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a force or motion 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 questionFor the worked example, (a) name the objects in system A+B, (b) classify the cart-cart interaction, (c) identify the horizontal external force, and (d) explain what changes if only B is selected.
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Compare with the answer and four-point rubric
- 1 point: A and B, with total mass 5 kg.
- 1 point: Cart-cart forces are internal to A+B.
- 1 point: The hand supplies 10 N right externally.
- 1 point: A-on-B is now external, 6 N right; the physical interaction did not change.
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 1What makes a force external?
Its source is outside the chosen system.
RECALL 2Does changing a boundary change reality?
No. It changes which interactions enter the system analysis.
RECALL 3When is a particle model appropriate?
When size, rotation and internal structure do not affect the question.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Choosing a system: internal & external forces
- Classify each interaction using its source and recipient.
- Use net EXTERNAL force for the motion of a fixed-mass system’s center of mass.
Remember: Internal does not mean nonexistent. It means both interacting objects lie inside the chosen boundary.
Conditions: Both carts move together on a frictionless horizontal track. Masses: A 2 kg, B 3 kg. Hand push: 10 N right. Vertical weight and support balance and are omitted in this horizontal view.
Refresh Kid · Unit 2 · Objectives 2.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.1, objectives 2.1.A. 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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