The book on the table (forces and pairs)

Problem

The book on the table. A book rests on the table. Identify the forces acting on the book, stating for each the body that exerts it and the one with which it forms an action-reaction pair.

Solution

Forces acting on the book. Circling the book as the system, we identify two forces applied to it:

1. The weight force $\vv{P}$, directed downward, exerted by the Earth (gravitational attraction on the book).
2. The normal reaction $\vv{N}$, directed upward, exerted by the table (the supporting surface pushes upward on the book).

The book is in equilibrium, so these two forces have equal magnitude and opposite direction: $\vv{P} + \vv{N} = 0$. Careful: although equal and opposite, $\vv{P}$ and $\vv{N}$ do not form an action-reaction pair, because they act on the same body (the book). Their balancing is a consequence of the second law (zero resultant on a stationary body), not of the third.

The action-reaction pairs (the “twins”). By the third law every force has a twin acting on the other body in the interaction:

• The twin of the weight $\vv{P}$ (Earth → book) is the gravitational attraction of the book on the Earth: $\vv{P}' = -\vv{P}$, applied at the Earth’s centre, directed upward.
• The twin of the normal reaction $\vv{N}$ (table → book) is the force the book exerts on the table, directed downward, pressing on the supporting surface: $\vv{N}' = -\vv{N}$.

Interaction diagram (sketch). Circling the book, two “squiggly links” emerge: one toward the Earth (gravitational interaction) and one toward the table (contact interaction). Each squiggly link represents a pair of equal and opposite forces applied to the two interacting bodies.

$\ev{\text{On the book: weight (Earth) and normal (table). Twins: book}\to\text{Earth and book}\to\text{table.}}$

Links

Topics: Dynamics Concepts: Newton’s third law Skills: Interaction diagram