werg-
“to work, to do”work, make, do
Root for working, yielding English work, Greek ergon, German Werk, organ.
Discussion
The PIE root *werg- (to work, to do, to make) produced the vocabulary of labour, creative production, and physical energy across the major branches — connecting the craftsman's workshop, the physicist's formula, and the priest's liturgy through a single concept of purposeful activity.
Greek érgon (ἔργον, "work, deed, action") is the most productive Hellenic reflex: energy (en-ergeia, "the working-within" — Aristotle's term for the actualisation of potential, adopted by physics for the capacity to do work), synergy (syn-ergeia, "working together"), allergy (allo-ergeia, "other-working" — an immune response to a foreign substance), surgery (kheir-ourgía, "hand-working"), organ (órganon, "a working tool" — then a body part, then a musical instrument), and liturgy (leit-ourgía, "public working" — the work done for the community, later the church service).
The scientific use of energy deserves emphasis: when Young and Helmholtz adopted the Greek word in the 19th century for the physical quantity measured in joules, they chose a PIE root for "work" — making E=mc² etymologically a statement about mass and work.
German Werk (work, opus) and English work (OE weorc, from PGmc *werką) continue the root natively: workshop, workman, handiwork, and the combining form -wright (wheelwright, playwright — the worker, the maker). The surname Wright is literally "worker."
The Old English word wrought (past participle of wyrcan, "to work") preserves an archaic form: wrought iron is "worked iron," iron that has been shaped by the blacksmith's labour.
Avestan vərəz- (to work, to do) confirms the Indo-Iranian reflex.
Notes
Pokorny 1168-1169. English work, wrought, energy, organ, surgery.