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

Answer:

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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