Final answer:
The ratio is known as the proportionality constant k, which varies based on material factors and dictates the amount of deformation in materials like wood under applied forces.
Step-by-step explanation:
The ratio that shows the amount that wood will bend in proportion to its load is known as the proportionality constant k. This constant depends on several material factors, such as the type of material, its dimensions, and the kind of force applied to it. For instance, a nylon guitar string stretches when a force is applied, and this elongation is proportional to the force, provided the deformation is small.
Thicker or steel strings have a larger value of k, meaning they stretch less for the same force, indicating a greater resistance to deformation. In structural engineering, similar principles apply to materials like wood, and k can be used to calculate how much a wooden pole bends or is compressed under load, helping in the design of structures such as buildings and utility poles.