Chapter 18, Problem 27A

A thick rope is stronger than a thin rope of the same material. Is a long rope stronger than a short rope?

To determine

To identify:Whether a long rope is stronger than a short rope.

Answer to Problem 27A

The long rope is not stronger than a short rope.

Explanation of Solution

Introduction:

Scaling is the study of how size affects the relation between weight, strength, and surface area.The proportions of things in nature are in accord with their size.

Weight depends on volume and strength from the cross sectional area.

As the linear dimensions increases, the weight and volume increases much faster than the cross sectional area with respect to the linear dimensions.

In general, the volume grows as the cube of linear dimensions, while area grows as the square of the linear dimensions.

In relation to the weight of the ropes, the long rope is weaker than the short rope

Conclusion:

Thus, the long rope is not stronger than a short rope.