Question

A book rests on the surface of the table. Consider the following four forces that arise in this situation: (a) the force of the Earth pulling on the book, (b) the force of the table pushing on the book, (c) the force of the book pushing on the table, and (d) the force of the book pulling on the Earth. The book is not moving. Which pair of forces must be equal in magnitude and opposite in direction even though they are not an interaction pair?

Short answer

Answer: The force of the Earth pulling on the book (F(earth on book)) and the force of the book pushing on the table (F(book on table)) meet the criteria of being equal in magnitude, opposite in direction, and not an interaction pair.

Step-by-step solution

Identify the four forces

We are given four forces: (a) Force of Earth pulling on the book (F(earth on book)) (b) Force of the table pushing on the book (F(table on book)) (c) Force of the book pushing on the table (F(book on table)) (d) Force of the book pulling on the Earth (F(book on earth))

Analyze the forces involved

The forces acting on the book are F(earth on book) and F(table on book), both of which act vertically. Since the book is in equilibrium (not moving), the sum of these forces must be equal to zero. Similarly, the forces acting on the table are F(book on table) and F(table on book), both of which also act vertically.

Identify the pair of forces that meet the required criteria

We need to find the pair of forces that are equal in magnitude and opposite in direction, but not an interaction pair. Let's examine each pair: (a) F(earth on book) & F(table on book) - They are an interaction pair so they won't meet our criteria. (b) F(book on table) & F(table on book) - They are an interaction pair, so they won't meet our criteria either. (c) F(earth on book) & F(book on table) - F(earth on book) is the gravitational force acting on the book, while F(book on table) is the force of the book acting on the table. Since the book is not moving, we can deduce that F(earth on book) must be equal to F(book on table) in magnitude and opposite in direction. (d) F(earth on book) & F(book on earth) - They are an interaction pair according to Newton's third law, so they don't meet our criteria.

Conclusion

Based on our analysis, the only pair of forces that meet the criteria of being equal in magnitude, opposite in direction, and not an interaction pair are F(earth on book) and F(book on table). The force of the Earth pulling on the book is equal in magnitude and opposite in direction to the force of the book pushing on the table.