when does ariel sing part of your world
Before she meets Eric
Part of Your World
Set prior to most of the film's action, "Part of Your World" is the second proper song in "The Little Mermaid", and takes place in Ariel's grotto before she meets Eric. 
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Part of Your World [SEP] Sequence and use in "The Little Mermaid"
Set prior to most of the film's action, "Part of Your World" is the second proper song in "The Little Mermaid", and takes place in Ariel's grotto before she meets Eric. A character song used to progress the plot, "Part of Your World" resembles a monologue in which Ariel expresses her desire to become part of the human world while reveling in her expansive collection of discarded human items and artifacts. Singing about her interest in exploring the human world and learning as much as she can about it, Ariel performs the ballad while gazing up towards the surface longingly, wishing that she could be human herself and live among other humans, and refusing to believe that they are as horrible as her father describes them.