All of the narcotics cause drowsiness. Other culprits include the phenothiazine derivative anti nausea drugs such as compazine and phenergan.
Drugs that do not cause drowsiness include Zofran and scopolamine for nausea, and Tylenol, ibuprofen, and Toradol for pain.
Here is the etymology of the word narcotic: narcotic (n.)
c.1385, from O.Fr. adj. narcotique (1314), from M.L. narcoticum, from Gk. narkotikon, neut. of narkotikos "making stiff or numb," from narkotos, verbal adj. of narcoun "to benumb, make unconscious," from narke "numbness, stupor, cramp," perhaps from PIE base *(s)nerq- "to turn, twist." Sense of "any illegal drug" first recorded 1926, Amer.Eng. The adj. is first attested 1601.
Morphine is definitely in that category. Here's the scoop on the derivation:
morphine
1828, from Fr. morphine or Ger. Morphin (1816), name coined in allusion to L. Morpheus, Ovid's name for the god of dreams, son of Sleep, lit. "the maker of shapes," from Gk. morphe "form, shape, beauty, outward appearance," perhaps from PIE *merph-, possible Gk. root meaning "form," of unknown origin. So called because of the drug's sleep-inducing properties.
Painting of Morpheus and Iris by baron Guérin
