Final answer:
The gerund in the sentence is 'mowing', which functions as the object of the preposition 'after', and it acts as an adverbial phrase in the sentence.
Step-by-step explanation:
The gerund in the sentence 'Micheal, please sweep the front sidewalk after mowing.' is mowing. A gerund is a verb form ending in -ing that functions as a noun in a sentence. In this case, 'mowing' is acting as the object of the preposition 'after', which makes it part of a prepositional phrase (after mowing). Thus, it is functioning as an adverbial phrase, providing more information about when Micheal should sweep the front sidewalk.