You have some confused terms here. "Cop" and "Cope" are two entirely different terms.
COP is as follows:
Entry from June 04, 2006
Cop ("copper” badge myth)
"Cop" (policeman) probably comes from "cop," meaning to "nab" a suspect.
One myth suggests that "cop" comes from "Constable On Patrol." This has no factual basis.
Another myth suggests that "cop" comes from "copper," the copper badge that the police wore. (See the 1976 article, below.) Again, there is no factual basis for this.
(Oxford English Dictionary)
north. dial. and slang.
[Perh. a broad pronunciation of CAP v.2 (OF. caper to seize); in nearly all North Eng. glossaries; and now of general diffusion in the slang of schoolboys, criminals, policemen, etc.]
a. trans. To capture, catch, lay hold of, 'nab'.
1704 E. WARD Dissenting Hyp. 30 If the Cruel Stork should come, He'd Tyrannize and Cop up some [Frogs]. 1844 tr. Eugene Sue's Myst. Paris III. xi, Waiting until the patrol should pass to commence my robbery..in order to be copped. 1868 Daily Tel. 7 Sept., The privileged driver, on dropping his fare..almost invariably 'cops' a job on his way back.