if the mine winch drum diameter is 6 m, calculate how far the cage will drop for each single rotation of the drum

The depth to which the cage will drop for each single rotation of the drum is approximately 18.85 m.

Explanation:

The mine winch drum consists of a drum around around which the haulage rope is attached

Therefore, given that the diameter of the winch drum = 6 m

The length of rope unwound by each rotation = How far the cage will drop for each single rotation of the drum

The length of the rope unwound by each rotation = The rope that goes round the circumference of the winch drum, once

∴ Since the rope that goes round the circumference of the winch drum, once = The circumference of the winch drum, we have;

The length of the rope unwound by each rotation = The circumference of the winch drum = π × The diameter of the winch drum

The length of the rope unwound by each rotation = π × 6 m = 6·π m

The length of rope unwound by each rotation = How far the cage will drop for each single rotation of the drum = 6·π m

How far the cage will drop for each single rotation of the drum = 6·π m ≈ 18.85 m

The depth to which the cage will drop for each single rotation of the drum ≈ 18.85 m.

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