Newton’s third law and interaction pairs

What you will learn

Equal and opposite forces on different bodies; transport examples.

Specification mapping: B2.6

Prerequisites: B2.1, B2.5

Physical principles

When two bodies interact, each exerts a force on the other. These forces have equal magnitude and opposite direction, act simultaneously and are the same type of interaction. They act on different bodies. Consequently they do not cancel on one object’s free-body diagram.

A driven tyre pushes the road backwards and the road pushes the tyre forwards. The forward road force can accelerate the vehicle. The equal opposite force acts on Earth; Earth’s huge mass gives it a negligible acceleration for everyday purposes. Different accelerations are consistent with equal interaction forces because masses differ.

An object’s weight is Earth’s gravitational force on it. The third-law partner is the object’s gravitational force on Earth, not the support normal acting on the object. Weight and normal can balance on the same object without being an interaction pair. A hand pushing a wall and the wall pushing the hand is a contact pair; a propeller pushing air back and air pushing the aircraft forwards is another.

Scientific diagram and interpretation

The force on the tyre points forwards (right); the force on the road points backwards (left). The equal opposite forces are drawn on separate bodies, not both on the vehicle.

Worked examples and applications

Different masses

Two skaters push apart with interaction force magnitude 60 N. A 40 kg skater has acceleration 1.5 m s⁻²; a 60 kg skater has 1.0 m s⁻² in the opposite direction. Equal forces do not imply equal accelerations.

Choose a system

For a vehicle-only force diagram include the road-on-tyre force. The tyre-on-road force belongs on a road/Earth diagram. Including both on the vehicle would incorrectly cancel its driving interaction.

Common misconceptions

Third-law forces act on different objects; balanced forces in the first law act on the same chosen object.

Examination technique

Name both bodies and write “A on B” and “B on A”.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.