Equal force pairs, different accelerations
You will be able to: Identify a third-law pair and explain why it does not balance on one object.
Why can two objects push equally but move differently?
Two skaters push apart. A 40 kg skater and an 80 kg skater feel equally strong pushes from one another. The lighter skater changes velocity faster.
A useful starting point: Free-body diagrams →
Words and symbols before equations
- Interaction pair
- A-on-B and B-on-A forces from the same interaction.
- Equal and opposite
- Same force magnitude, opposite directions, at the same time.
- Acceleration a
- Rate of velocity change, measured in m/s².
What this picture assumes
Skater A is 40 kg. The interaction pair is always 80 N. Horizontal resistance neglected; positive is right. This is a force snapshot, not an animated collision.
Connect the picture to the physics
Newton’s third law connects two forces acting on two different recipients. If A pushes B right with 80 N, B simultaneously pushes A left with 80 N. Neither force occurs first.
They do not cancel in a free-body diagram of A alone: only B-on-A belongs there. They do cancel internally if the chosen system contains both A and B.
Equal force does not mean equal acceleration. The same net force produces a smaller acceleration for a larger mass. This remains true in a collision between a small car and a large truck.
| Feature | Third-law pair | Balanced forces |
|---|---|---|
| Recipients | Two different objects | Same chosen object or system |
| Example | Earth-on-book and book-on-Earth | Desk-on-book and Earth-on-book |
| Consequence | Equal/opposite interaction forces | Zero net force if these are the complete force list |
A worked example, step by step
A 40 kg skater A pushes an 80 kg skater B with 80 N right. Ignore horizontal friction. Compare forces and accelerations.
- B receives +80 N from A; A receives −80 N from B.
- Using a=F_net/m, A has −80/40 = −2 m/s².
- B has +80/80 = +1 m/s².
- The forces are equal in magnitude. The accelerations differ because the masses differ.
Weight and normal force on a resting book are not a third-law pair: both act on the book.
What is the partner of Earth pulling a book downward?
Compare with an explanation
The book gravitationally pulling Earth toward the book. It is not the desk’s normal force.
Predict. Change one thing. Explain.
Hold the interaction at 80 N. Increase B’s mass from 40 to 80 kg. Explain why the force arrows stay equal while B’s acceleration halves.
The forces stay 80 N each. A accelerates at −2 m/s²; B at +1 m/s². Each force arrow uses 1.25 drawing units/N.
Skater A is 40 kg. The interaction pair is always 80 N. Horizontal resistance neglected; positive is right. This is a force snapshot, not an animated collision.
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 questionA 2 kg cart and a 6 kg cart push apart with 12 N interaction forces. (a) Label the pair, (b) find each acceleration magnitude, (c) compare directions, and (d) explain the system’s horizontal center-of-mass acceleration if no external horizontal force acts.
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Compare with the answer and four-point rubric
- 1 point: A-on-B and B-on-A, each 12 N.
- 1 point: Magnitudes 6 m/s² and 2 m/s².
- 1 point: Accelerations point oppositely.
- 1 point: Center-of-mass acceleration is zero because the net external horizontal force is zero.
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 1Do third-law forces act on one body?
No, on different recipients.
RECALL 2Do they require objects to be at rest?
No, the law applies during motion and collisions.
RECALL 3Equal forces imply equal accelerations?
Only if the relevant masses and other forces make that true.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Equal force pairs, different accelerations
- F_A on B = −F_B on A (vectors).
- A force pair has different recipients; balanced forces share one recipient.
Remember: Weight and normal force on a resting book are not a third-law pair: both act on the book.
Conditions: Skater A is 40 kg. The interaction pair is always 80 N. Horizontal resistance neglected; positive is right. This is a force snapshot, not an animated collision.
Refresh Kid · Unit 2 · Objectives 2.3.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.3, objectives 2.3.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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