Question

The hoisting system of a drilling rig contains seven ideal sheaves with hook load of \(3.0 \times 10^5 \, \text{kg}\). The static derrick load is ............ \(\times 10^5 \, \text{kg}\) (rounded off to one decimal place).

Hint:

For ideal sheaves, the static derrick load is always twice the hook load, since both the traveling and crown blocks carry the load.

Answer 1

Step 1: Understand hoisting system mechanics.
In a drilling rig hoisting system, the block and tackle arrangement with \(n\) sheaves produces \(2n\) supporting lines (because the rope runs through both crown and traveling blocks). Step 2: Given parameters.
Number of sheaves = 7. Therefore, the number of supporting lines = 2 × 7 = 14. Step 3: Derrick load relation.
The hook load is carried by all lines, but the static derrick load = Hook load + Dead line load. For \(n\) lines: \[ \text{Derrick Load} = 2 \times \text{Hook Load}. \] Step 4: Substitution.
Hook load = \(3.0 \times 10^5 \, \text{kg}\). \[ \text{Derrick load} = 2 \times (3.0 \times 10^5) = 6.0 \times 10^5 \, \text{kg}. \] Final Answer: \[ \boxed{6.0 \times 10^5 \, \text{kg}} \]