A book is sitting at rest on a horizontal desk. Which statement best describes the normal force acting on the book?

• A. The normal force is equal in magnitude and opposite in direction to the gravitational force acting on the book, so $N=mg$.
• B. The normal force is less than the gravitational force acting on the book, so $N<mg$.
• C. The normal force is zero because the book is not accelerating.
• D. The normal force is greater than the gravitational force acting on the book, so $N>mg$.

Answer: (A)

Verified step by step guidance

1. Identify the forces acting on the book: the gravitational force (weight) acting downward and the normal force exerted by the desk acting upward.
2. Since the book is at rest and not accelerating, apply Newton's first law which states that the net force on the book must be zero.
3. Set up the force balance equation in the vertical direction: the upward normal force \(N\) must balance the downward gravitational force \(mg\), where \(m\) is the mass of the book and \(g\) is the acceleration due to gravity.
4. Express this balance mathematically as \(N = mg\), indicating that the normal force is equal in magnitude and opposite in direction to the gravitational force.
5. Conclude that the normal force is neither less than nor greater than the gravitational force, but exactly equal, ensuring the book remains at rest on the desk.