Math Problem Statement
Solution
Let's delve into solving these two problems from the image:
Question 13:
We are dealing with floating objects in a liquid with a density of . The key here is Archimedes' principle, which says:
- Objects less dense than water (less than ) will float.
- Objects with equal density will be submerged but not sink.
- Objects denser than water (more than ) will sink.
From the diagram:
- Object floats at the surface, so its density is less than .
- Object is submerged but does not sink, so its density is equal to .
- Object sinks, so its density is greater than .
Thus, the answer is: A. .
Question 14:
This is a hydraulic jack problem, where Pascal's principle applies: Here:
Rearranging for : Substitute values:
Thus, the answer is: A. .
Do you want further explanations or clarifications? Here are 5 related questions for practice:
- How does Archimedes' principle apply to irregularly shaped objects?
- Can you derive Pascal's principle using fluid mechanics laws?
- What is the impact of temperature on fluid density in buoyancy problems?
- How does the area ratio affect force in hydraulic systems?
- What are practical applications of hydraulic jacks in engineering?
Tip: Always check the units when working with density, force, or area in fluid dynamics problems!
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Math Problem Analysis
Mathematical Concepts
Archimedes' principle
Pascal's principle
Density calculations
Hydraulics and pressure
Formulas
Buoyancy: Density = Mass / Volume
Hydraulics: F1 / A1 = F2 / A2
Theorems
Archimedes' Principle
Pascal's Principle
Suitable Grade Level
Grades 10-12