Question

The safe working load \(S\) (in tons) for a wire rope is a function of \(D\), the diameter of the rope in inches. Safe working load model for wire rope: \(4 \cdot D^{2}=S\) What diameter of wire rope do you need to lift a 9 -ton load and have a safe working load?

Short answer

A wire rope with a diameter of approximately 1.5 inches is required to lift a 9-ton load safely.

Step-by-step solution

Given information

We know that the safe working load model for the wire rope is given by \(4 \cdot D^{2}=S\) and \(S\), the safe working load is 9 tons.

Rearrange equation for Diameter D

The equation can be rearranged to get \(D\) if we divide both sides by 4: \(D^{2} = \frac{S}{4}\). So, \(D= \sqrt{\frac{S}{4}}\) is our formula to calculate the diameter of the wire necessary to lift a 9-ton load safely.

Solving for Diameter D

Substituting the value of \(S\) into the formula gives \(D= \sqrt{\frac{9}{4}} = \sqrt{2.25}\). So, \(D\) is approximately 1.5.