Question

Every rope has a safe working load. A rope should not be used to lift a weight greater than its safe working load. The table shows the safe working loads S (in pounds) for ropes with circumference C (in inches). Write an equation for the safe working load for a rope. Find the safe working load for a rope that has a circumference of 10 inches.

Answer 1

9514 1404 393

Answer:

• S = 180C²
• 18,000 lbs

Explanation:

Assuming the table attached with C in inches and S in pounds, we see that the first differences in S are ...

180, 540, 900

These are not constant, so the relation is not linear.

Second differences are ...

360, 360

These are constant, so the relation is quadratic. With a short trial, we find that a suitable equation is ...

S = 180·C²

__

The safe load for C=10 is then ...

S = 180·10² = 18,000 . . . pounds