The better component among a door, nail, or hinge is the hinge. While a door is the functional element that provides access or closure, and a nail is a fastener used to hold materials together, the hinge is the critical component that allows the door to open and close smoothly. Hinges are specifically designed to bear the weight of the door and facilitate its movement, making them the most crucial part of the trio.

Hinges are engineered with precision to ensure durability and reliability. According to a study by the Door and Hardware Institute, hinges are subjected to an average of 100,000 cycles of opening and closing over the lifespan of a door. This extensive use underscores the importance of hinges in maintaining the integrity of the door's operation. High-quality hinges are made from materials like brass, steel, or stainless steel, which are resistant to corrosion and wear, further enhancing their longevity.

Moreover, hinges are available in various designs and configurations to accommodate different types of doors and door frames. For instance, pivot hinges are suitable for heavier doors and can support up to 300 pounds, while butt hinges are ideal for lighter doors and are commonly used in residential settings. The versatility of hinges allows them to be used in a wide range of applications, from residential to commercial and industrial environments.

In contrast, while nails are essential for securing materials, they are not designed to bear the weight or facilitate the movement of a door. A single nail can easily be pulled out or bend under the stress of a door's weight, leading to a compromised structure. Additionally, nails do not provide the necessary precision or durability that hinges offer.

Furthermore, a door, while functional, is a static component that requires hinges to operate effectively. Without hinges, a door would be unable to open or close, rendering it useless. Therefore, while the door is the primary object, it is the hinge that enables its functionality.

In conclusion, the hinge is the superior component among a door, nail, or hinge due to its specialized design, durability, and versatility. Its role in enabling the door's operation and its ability to withstand the demands of frequent use make it the most critical element of the trio.