Weight and normal force are two essential concepts in physics that describe different types of forces acting on an object.

Weight is defined as the force exerted on an object due to gravity. It is always directed toward the center of the Earth (or another celestial body). The weight of an object can be calculated using the formula:

where $W$ represents weight, $m$ is the mass of the object, and $g$ is the acceleration due to gravity, approximately $9.8 \, \text{m/s}^2$ on Earth. Importantly, weight is a vector quantity, meaning it has both magnitude and direction. The value of weight is influenced by the gravitational field strength of a given location; for example, an individual’s weight would be less on the Moon than on Earth due to the Moon’s weaker gravitational force.

Normal force, in contrast, is the force exerted by a surface to support the weight of an object resting on it. This force acts perpendicular (or ‘normal’) to the surface. The normal force is crucial in preventing solid objects from passing through one another. For instance, when a book is placed on a table, the table exerts an upward normal force that balances the downward force of the book’s weight, thereby preventing the book from falling through the table.

The magnitude of the normal force can vary depending on the orientation of the surface. When an object is positioned on an inclined plane, the normal force will be less than the object’s weight because only a component of the weight acts perpendicular to the inclined surface.

In summary, while both weight and normal force are forces acting on an object, they differ in their origins and directions. Weight is generated by gravity and always acts downward, whereas normal force arises from a surface resisting an object’s weight and is directed perpendicular to that surface. Understanding the distinction between these two forces is essential for solving problems related to forces and motion.