Final answer:
The design of tapered springs with the large diameter end down allows for a more even distribution of stress, aligning with Hooke's law by maintaining a proportional limit throughout the spring to avoid permanent deformation and ensuring that it can handle applied forces efficiently over a wider range of loads.
Step-by-step explanation:
The specific question about why tapered springs obey Hooke's law over the widest range of loads when suspended with the large diameter end down relates to physics, particularly the mechanics of materials and spring dynamics. The design of tapered springs allows for a more even distribution of stress throughout the spring when a load is applied. As Hooke's law states that the force exerted by a spring is proportional to its extension, it is important for the material of the spring to maintain its proportional limit to prevent permanent deformation.
When the larger end of the tapered spring is facing down, there's a gradual transition of stiffness from the wider to the narrower end, allowing the spring to handle the applied forces more efficiently. This helps prevent an uneven distribution of forces that could lead to premature failure of the spring. By maintaining a uniform stress distribution, the spring can exhibit linear elastic behavior, consistent with Hooke's law, over a broader range of forces before reaching the material's yield point or ultimate tensile strength.