Final answer:
The length of a nail is a straight measurement from its head to its tip, while the length of the threads on a screw is the unwrapped length of the inclined plane around the shaft, which is typically longer.
Step-by-step explanation:
The length of the threads on a screw refer to the combined length of the inclined plane wrapped around the screw's shaft. This length is typically longer than the nail because it is a spiral that extends from the tip of the screw to the head. For instance, if a screw has 10 threads and each pitch measures 1 mm.
The total length of the screw's threads will be much longer than 10 mm when unwrapped in a straight line because it includes the helical path. In contrast, a nail of the same height would measure exactly its height in length, say, 50 mm, without any additional length needed for threads because nails do not have threads.
Therefore, even for screws and nails of the same height, the length of the screw's threads will be longer than the length of a nail when the threads are envisioned as unwrapped into a straight line. Nails are simple straight shafts with no additional length due to spiraling threads.