# Newton's Third Law by David Halliday and Robert Resnick   Figure 5-10 (a) Book B leans against crate C. (b) Forces ${\stackrel{\to }{F}}_{\mathrm{BC}}$ (the force on the book from the crate) and ${\stackrel{\to }{\mathrm{-F}}}_{\mathrm{CB}}$ (the force on the crate from the book) have the same magnitude and are opposite in direction.

Two bodies are said to interact when they push or pull on each other-that is, when a force acts on each body due to the other body. For example, suppose you position a book B so it leans against a crate C (Fig. 5-10a). Then the book and crate interact: There is a horizontal force ${\stackrel{\to }{F}}_{\mathrm{BC}}$ on the book from the crate (or due to the crate) and a horizontal force ${\stackrel{\to }{F}}_{\mathrm{CB}}$ on the crate from the book (or due to the book).This pair of forces is shown in Fig. 5-10b. Newton's third law states that

• Newton's Third Law: When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.

For the book and crate, we can write this law as the scalar relation

FBC = FCB (equal magnitudes)

or as the vector relation

${\stackrel{\to }{F}}_{\mathrm{BC}}$ = ${\stackrel{\to }{\mathrm{-F}}}_{\mathrm{CB}}$ (equal magnitudes and opposite directions), (5-15)

where the minus sign means that these two forces are in opposite directions. We can call the forces between two interacting bodies a third-law force pair. When any two bodies interact in any situation, a third-law force pair is present. The book and crate in Fig. 5-10a are stationary, but the third law would still hold if they were moving and even if they were accelerating. Figure 5-11 (a) A cantaloupe lies on a table that stands on Earth. (b) The forces on the cantaloupe are ${\stackrel{\to }{F}}_{\mathrm{CT}}$ and ${\stackrel{\to }{F}}_{\mathrm{CE}}$. (c) The third-law force pair for the cantaloupe-Earth interaction. (d) The third-law force pair for the cantaloupe-table interaction.

As another example, let us find the third-law force pairs involving the cantaloupe in Fig. 5-11a, which lies on a table that stands on Earth. The cantaloupe interacts with the table and with Earth (this time, there are three bodies whose interactions we must sort out).

Let's first focus on the forces acting on the cantaloupe (Fig. 5-11b). Force ${\stackrel{\to }{F}}_{\mathrm{CE}}$ is the normal force on the cantaloupe from the table, and force ${\stackrel{\to }{F}}_{\mathrm{CT}}$ is the gravitational force on the cantaloupe due to Earth. Are they a third-law force pair? No, because they are forces on a single body, the cantaloupe, and not on two interacting bodies.

To find a third-law pair, we must focus not on the cantaloupe but on the interaction between the cantaloupe and one other body. In the cantaloupe-Earth interaction (Fig. 5-11c), Earth pulls on the cantaloupe with a gravitational force ${\stackrel{\to }{F}}_{\mathrm{CE}}$ and the cantaloupe pulls on Earth with a gravitational force ${\stackrel{\to }{F}}_{\mathrm{EC}}$. Are these forces a third-law force pair? Yes, because they are forces on two interacting bodies, the force on each due to the other.Thus, by Newton's third law,

${\stackrel{\to }{F}}_{\mathrm{CE}}$ = ${\stackrel{\to }{F}}_{\mathrm{EC}}$ (cantaloupe-Earth interaction).

Next, in the cantaloupe-table interaction, the force on the cantaloupe from the table is ${\stackrel{\to }{F}}_{\mathrm{CT}}$ and, conversely, the force on the table from the cantaloupe is ${\stackrel{\to }{F}}_{\mathrm{TC}}$ (Fig. 5-11d).These forces are also a third-law force pair, and so

${\stackrel{\to }{F}}_{\mathrm{CT}}$ = ${\stackrel{\to }{\mathrm{-F}}}_{\mathrm{TC}}$ (cantaloupe-table interaction).

Checkpoint Suppose that the cantaloupe and table of Fig. 5-11 are in an elevator cab that begins to accelerate upward. (a) Do the magnitudes of ${\stackrel{\to }{F}}_{\mathrm{CT}}$ and ${\stackrel{\to }{F}}_{\mathrm{TC}}$ increase, decrease, or stay the same? (b) Are those two forces still equal in magnitude and opposite in direction? (c) Do the magnitudes of ${\stackrel{\to }{F}}_{\mathrm{CE}}$ and ${\stackrel{\to }{F}}_{\mathrm{EC}}$ increase,decrease,or stay the same? (d) Are those two forces still equal in magnitude and opposite in direction?

Answers: (a) increase; (b) yes; (c) same; (d) yes

David Halliday was an American physicist known for his physics textbooks, Physics and Fundamentals of Physics, which he wrote with Robert Resnick. Both textbooks have been in continuous use since 1960 and are available in more than 47 languages.

Robert Resnick was a physics educator and author of physics textbooks. He was born in Baltimore, Maryland on January 11, 1923 and graduated from the Baltimore City College high school in 1939. He received his B.A. in 1943 and his Ph.D. in 1949, both in physics from Johns Hopkins University.  The 10th edition of Halliday's Fundamentals of Physics, Extended building upon previous issues by offering several new features and additions. The new edition offers most accurate, extensive and varied set of assessment questions of any course management program in addition to all questions including some form of question assistance including answer specific feedback to facilitate success. The text also offers multimedia presentations (videos and animations) of much of the material that provide an alternative pathway through the material for those who struggle with reading scientific exposition.

Furthermore, the book includes math review content in both a self-study module for more in-depth review and also in just-in-time math videos for a quick refresher on a specific topic. The Halliday content is widely accepted as clear, correct, and complete. The end-of-chapters problems are without peer. The new design, which was introduced in 9e continues with 10e, making this new edition of Halliday the most accessible and reader-friendly book on the market.

A Reader says,"As many reviewers have noted, this is a great physics book used widely in university technical programs as a first course in technical physics, with calculus. I find it is the one book I start with when trying to understand physical concepts at a useful but basic level. It has broad coverage and is well written . To go beyond this book requires specialized books on each topic of interest (electromagnetics, quantum mechanics, thermodynamics, etc.)."

Reader Frank says, "The treatment is sound, thorough, and clear. I've owned the early editions of Halliday and Resnick for years. I'm very happy that I updated my library with this 10th edition. The topics are covered in a very logical order. The study features and worked examples are outstanding. Don't hesitate to buy this book! Reading it is awesome on the Kindle app on the iPad."