Final answer:
The magnitude of the force of static friction acting on the box is exactly 12 N, as it must balance the horizontal force to keep the box at rest, following Newton's first law of motion.
Step-by-step explanation:
When a 12-N horizontal force is applied to a box on a horizontal tabletop and the box remains at rest, the magnitude of the force of static friction acting on the box is exactly equal to the applied force. This is because, according to Newton's first law of motion, if the box is not moving, the net force acting on the box must be zero. Therefore, the force of static friction must be providing an equal and opposite force to the applied force, preventing the box from accelerating. In this case, the static friction force must be exactly 12 N to balance out the applied force and keep the box at rest.
The subject in question is directly related to the principles of static and kinetic friction in Physics. An example scenario outlining static friction would be a 20.0-kg crate on a floor where the maximum force of static friction is calculated using the coefficient of static friction and the normal force. Applied forces less than or equal to this maximum do not move the object. Thus, if an applied force is equal to the force of static friction (as in the student's question), the object remains stationary.