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2.3 Newton’s Third Law

Syllabus
2024
Topic
2.3
Level
—

Learning objectives

2.3A—Describe the interaction of two objects using Newton’s third law and a representation of paired forces exerted…Describe the interaction of two objects using Newton’s third law and a representation of paired forces exerted on each object.• Newton’s third law describes the interaction of two objects in terms of the paired forces that each exerts on the other. - →- → =−FFAo nB Bo nA• Interactions between objects within a system (internal a system’s center of mass.• T ension is the macroscopic net result of forces that segments of a string, cable, chain, or similar system exert on each other in response to an external force.- i. An ideal string has negligible mass and does not stretch when under tension.- ii. The tension in an ideal string is the same at all points within the string.- iii. In a string with nonnegligible mass, tension may not be the same at all points within the string.- iv. An ideal pulley is a pulley that has negligible mass and rotates about an axle through its center of mass with negligible friction. forces) do not influence the motion of

Third-law forces are one interaction on two objects

Name the reciprocal forces

When objects AA and BB interact, each exerts a force on the other at the same time. The forces have equal magnitude and opposite direction: F⃗A on B=−F⃗B on A\vec F_{A\,on\,B}=-\vec F_{B\,on\,A}. They are a pair because they come from the same interaction.

Verify a true pair

Pair test Must be true
Interaction Both forces describe the same interaction
Objects One force acts on AA; the other acts on BB
Magnitude ∣F⃗A on B∣=∣F⃗B on A∣|\vec F_{A\,on\,B}|=|\vec F_{B\,on\,A}|
Direction The force vectors point oppositely
Timing Both forces exist simultaneously

Separate object and system views

Example: a book rests on a table. The table's upward force on the book pairs with the book's downward force on the table. The book's weight is not that partner; it pairs with the book's gravitational force on Earth. Third-law partners do not cancel on the book because each pair member acts on a different object. If both objects are inside one chosen system, the internal pair cancels in the system force sum and does not change the system's center-of-mass motion.

Choose the string model

Model Consequence for tension
Ideal string Negligible mass, does not stretch, and has the same tension at all points
String or chain with mass Tension may vary along its length; for a hanging chain it is greater nearer the top
Ideal pulley Negligible mass and negligible axle friction; it rotates about an axle through its center of mass

Avoid false pairs

Equal-and-opposite arrows on the same object are not a third-law pair. They may instead be balanced forces from different interactions. AP Physics 1 treats tension in a massive string qualitatively, and its noncontact interactions at a distance are limited here to gravity.