Final answer:
Mechanics has numerous formulas because they are developed for specific conditions and can be derived from general principles or empirical laws. The complexity of solving Newton's laws can lead to the use of more general principles like the work-energy theorem, and the refinement of theories as seen with Einstein's general relativity. Successful problem-solving in physics also involves understanding known variables, performing algebraic manipulations, and maintaining consistent units like in Boyle's Law.
Step-by-step explanation:
The question 'Why does mechanics have so many formulas for the same thing?' can be explored by understanding the nature of physics and its empirical laws. For instance, static and kinetic friction are governed by formulas that, although useful, have their limitations and are not accurate under conditions like lubricated surfaces or at high speeds. Formulas are created based on logical statements and can be derived to suit specific conditions and tasks at hand.
Moreover, in physics, the application of Newton's laws often involves the solving of complex differential equations which might not have analytical solutions, leading to reliance on more general principles such as the work-energy theorem. Similarly, assumptions like those in Newton's law of gravitation are consistent with experimental results but are further refined by theories like Einstein's general relativity, which deals with the geometry of space-time rather than forces.
When working with mathematical problems in physics and chemistry, understanding the known quantities and their units, performing algebraic manipulations, and ensuring consistent units are crucial tactics. For example, Boyle's Law in chemistry requires both pressure variables to have the same unit of measurement. These strategies not only aid in solving complex problems but also develop quantitative thinking and estimation skills, which are valuable across various fields.