In the Grey’s Anatomy episode , the "long piece" refers to a critical medical procedure involving Nick Hanscom (played by Seth Green) .

: Following the traumatic day, the interns (Meredith, Cristina, Lexie, Izzie, and George) gather at Meredith's house for an "impromptu dance party" to decompress. Crash Into Me Part 2 : r/greysanatomy - Season 4 Episode 10

After Nick's carotid artery unexpectedly bursts, is forced to use her bare hands to apply pressure to stop the bleeding while they wait for an operating room. The "long piece" of medical equipment she has to maintain pressure on is a large piece of gauze or a surgical pack used to stem the massive hemorrhage while she is literally holding his life in her hands. Key Plot Points of S4E10

: Nick Hanscom, a patient with a large tumor on his neck, suffers a catastrophic artery rupture. Lexie is the only one present and must hold the artery closed manually.

: Meredith continues her desperate attempt to save Ray, a paramedic trapped in an overturned ambulance.