Final answer:
The correct option for a (64.4) lb plate resting on a smooth tabletop is b) Normal force equals gravitational force because the normal force is equal to the weight of the object, leading to a state of equilibrium where the object does not accelerate, and hence, the net force is zero.
Step-by-step explanation:
When a 64.4 lb plate rests on a smooth tabletop, we must consider the forces acting on the plate to understand its state of equilibrium. A key force is the normal force, which is the force that the surface (in this case, the tabletop) applies to the plate. This normal force supports the weight of the plate and acts perpendicular to the surface. According to Newton's third law of motion, for every action force, there is an equal and opposite reaction force. Therefore, the normal force exerted by the table on the plate is equal in magnitude to the gravitational force, or weight, acting on the plate.
If the plate is not moving, there is no net force acting on it, which implies that the normal force is equal to the gravitational force, and their effects cancel each other out, resulting in no acceleration. This situation also means that the friction force is either absent or not relevant since the plate is not sliding or being moved across the tabletop. Similarly, a tension force typically acts along a rope, string, or cable and is not applicable to an object resting on a surface without any such attachments.
Therefore, the correct option based on the given information is: b) Normal force equals gravitational force. This identifies the key concept that, for objects at rest on a horizontal and non-deformable surface, the upward normal force balances the downward force of gravity. The use of the word 'smooth' in this context suggests that there is no noticeable friction between the plate and the table, further validating that option b is the correct answer. The idea that the net force is zero when there is no acceleration, and the normal force is equal to the weight of the object, are central themes in this analysis.