Question

What do we call the two parts of lift that goes down a mine

Answer 1

The sheave wheel is a pulley wheel that sits above the mine shaft. The hoist cable passes over the sheave wheel and then down the shaft of the mine.
(copied from google)

Answer 2

The sheave wheel is a pulley wheel that sits above the mine shaft. The hoist cable passes over the sheave wheel and then down the shaft of the mine.