Final answer:
The normal force by the surface on a box over a rough horizontal surface is the force that the surface exerts on the box, perpendicular to the surface. It balances the object's weight and is related to the friction it experiences.
Step-by-step explanation:
When pulling a box over a rough horizontal surface, the normal force exerted by the surface on the box is defined as option (a): The force that the surface exerts on the box, perpendicular to the surface. The normal force is a supporting force that acts perpendicular to and away from the surface on which the object rests, symbolized by the letter N. This force is crucial because it balances the weight of the object, and is also related to the frictional force, as the frictional force is proportional to the normal force. The normal force can be calculated using Newton's second law and knowing the mass of the object, as shown in the equation w = mg, where w is the weight of the object, m is the mass, and g is the acceleration due to gravity. The normal force would be equal to the weight if the box is at rest on a horizontal surface and would differ on an inclined plane where only a component of the weight acts perpendicularly to the surface.