com/us/definition/american_english/at#at may be relevant here: Emphasizing the directing of an action toward a specified object However, native speakers (speaking personally, anyway) tend to treat many such verb + preposition combinations as idiomatic; so they just "know" that a preposition such as "at" goes with a particular verb to create a particular meaning, rather than consciously being aware of the individual meaning of the preposition. In this case I would say that "get at" is fully idiomatic, while "tug at" is partially so.
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