Math Problem Statement
Solution
The image displays two questions related to the properties of springs and the forces applied to them:
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Physical Law (Question 12):
- The question asks which law governs the relationship between the extension of a spring and the force applied to it.
- You have selected Hooke's Law, which is correct. Hooke's Law states that the force applied to stretch or compress a spring is directly proportional to the extension (displacement) of the spring, as long as the elastic limit is not exceeded. Mathematically, , where is the force, is the spring constant, and is the displacement.
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Type of Variation (Question 13):
- The question asks about the type of variation between force and extension in a spring.
- You have selected direct, which is correct. The relationship between the force applied to a spring and its extension is a direct variation because the extension increases linearly with the applied force, assuming the spring constant remains constant.
Would you like more details or explanations on these topics?
Here are 5 related questions to expand your understanding:
- How is the spring constant calculated in Hooke's Law?
- What happens to a spring if the force applied exceeds its elastic limit?
- Can Hooke's Law apply to materials other than springs?
- What are examples of systems where inverse variation is observed instead of direct?
- How would you calculate the force required to extend a spring by a certain length if the spring constant is known?
Tip:
In physics, recognizing whether relationships are direct or inverse variations helps in understanding how changing one quantity affects another in various physical systems.
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Math Problem Analysis
Mathematical Concepts
Direct Variation
Hooke's Law
Linear Relationships
Formulas
F = kx (Hooke's Law)
Theorems
Hooke's Law
Suitable Grade Level
Grades 8-10
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