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What are the differences between the two mine winches shown here?

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Answer

18.85 m\text{18.85 m}

Step-by-step solution

6 steps

1.12:
The main differences between the two mine winches are:

  • The winch on the left uses one sheave wheel and directly connects the cage to the winding drum.
  • The winch on the right uses two sheave wheels and incorporates a counterweight to balance the cage.

1.13:
A counterweight in a mine winding system helps to balance the load of the cage, significantly reducing the amount of force or energy required to lift the cage. If winding by hand, it would make the task much easier as you would only need to overcome the difference in weight between the cage and the counterweight, rather than the full weight of the cage.

1.14:

  1. Identify the given diameter of the drum.

    The diameter of the drum is D=6 mD = 6 \text{ m}.

  2. Calculate the circumference of the drum.

    For each single rotation, the cage will drop a distance equal to the circumference of the drum.
    The formula for circumference is C=πDC = \pi D.

    C=π×6 mC = \pi \times 6 \text{ m} C=6π mC = 6\pi \text{ m}

  3. Calculate the numerical value.

    C≈6×3.14159 mC \approx 6 \times 3.14159 \text{ m} C≈18.85 mC \approx 18.85 \text{ m}

    The cage will drop approximately 18.85 m\boxed{\text{18.85 m}} for each single rotation of the drum.

    1.15:

  4. Identify the given diameter of the drum.

    The diameter of the drum is D=6 mD = 6 \text{ m}.

  5. Calculate the circumference of the drum.

    For each single rotation, the counterweight will lift a distance equal to the circumference of the drum, as it is connected to the same drum.
    The formula for circumference is C=πDC = \pi D.

    C=π×6 mC = \pi \times 6 \text{ m} C=6π mC = 6\pi \text{ m}

  6. Calculate the numerical value.

    C≈6×3.14159 mC \approx 6 \times 3.14159 \text{ m} C≈18.85 mC \approx 18.85 \text{ m}

    The counterweight will lift approximately 18.85 m\boxed{\text{18.85 m}} for each single rotation of the drum.

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