|MadSci Network: Physics|
Strength does not depend upon length. When the strength of a material is characterized, it is done with respect to "force per unit area". For a given rope material (natural fibers or man-made) strength will increase as the cross-section of the rope increases. Regarding the "horizontal or vertical", you are correct; the weight of the rope enters the equation as additional load. However, for most problems, you can assume that the weight of the rope is negligible with respect to the load. When thinking about the strength of the rope in real-life situations, the rate at which the force is applied is very important. Consider the following experiment: you have two identical ropes with a bucket tied to the end of each one. You add water very slowly to the bucket on the first rope, and add it very quickly to the second. The first rope will apperently hold much more weight (appear to be stronger) because of how the force was applied. One factor where the length of the rope will matter is it's ability to absorb the shock of a rapidly applied load. The rope will have some amount of elasticity (springiness). Your 100 foot rope is 100 times "springier" than your 1 foot rope just becuase of the added length. This added length will allow it to withstand a greater shock before breaking, but this ability is a function of the "design", not the underlying "material strength". Christopher M. Seaman ALCOA Technical Center
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