Locate Newton’s third-law partners on different bodies

1. Orient: Locate Newton’s third-law partners on different bodies

An interaction produces a pair: the force of A on B and the force of B on A. Their magnitudes are equal and their directions opposite at the same instant. The labels reverse agent and recipient. The pair is not “a force and the motion it causes”; acceleration is a response, not the partner force.

2. Explain and derive

Equal interaction forces do not require equal accelerations. For one-dimensional motion with no other horizontal forces, a_left=F/m_left and a_right=−F/m_right. The less massive object changes velocity more rapidly. A large body can experience the same gravitational force as a small body yet have a much smaller acceleration.

A third-law pair cannot cancel on one object’s free-body diagram because its members act on different recipients. When both bodies belong to the chosen system, adding their force equations cancels that internal pair. Remaining external forces then determine center-of-mass acceleration.

Balanced forces on the same body are not automatically a third-law pair. A book’s upward table force and downward Earth force can balance, but their partners are the book’s force on the table and the book’s force on Earth. Matching magnitudes is insufficient; name the interaction and reverse agent/recipient.

3. Work an example

At a selected instant two objects attract with magnitude 12 N. With masses 2 kg and 4 kg, their accelerations are +6 and−3 m/s² along the chosen axis. Their mass-weighted acceleration sum is 2×6+4×(−3)=0, consistent with zero net external horizontal force on the pair.

4. Predict and investigate

Predict first: If only the right mass doubles while the stipulated interaction force is fixed, which force and which acceleration changes?

Compare equal masses and a 3:1 mass ratio. List each interaction force and the acceleration of its recipient. Multiply accelerations by their masses and verify cancellation for the whole system. Explain why this is not cancellation within either individual diagram. Use the lesson controls and record the settings with your evidence.

5. Transfer and explain

Try a new practice case

A 2 kg body experiences an isolated mutual force of 18 N toward its partner. Find the magnitude of its acceleration.

Your numerical result (m/s²) 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

Name the third-law partner of the track’s upward normal force on a cart. Why is the cart’s downward weight not that partner?

Retain your first answer, force diagram, equations, units, assumptions and a changed-case prediction. Public worked checks are practice, not independent mastery evidence. Supplied synthetic outputs do not certify actual laboratory skill.

Framework and source notes

Original teaching prose and numerical cases. College Board AP Physics 1 CED, Unit 2 topic mapping: 2.3; 2.5. Checked 30 October 2026. This is a content cross-reference, not AP authorization.