The preposition in question is "on", and its purpose is to show you where the dog chewed. You can remove the preposition to form the sentence "The brown dog chewed the rawhide bone." You can also rearrange it to find the preposition, "on the rawhide bone, the dog chewed" in what is commonly known as the Yoda technique.
Subject- The longest, most boring day of his life
Predicate- ended with a thud.
