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A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to?
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A uniform chain is placed at rest on a rough surface of base length l ...
Understanding the Problem
In this scenario, we need to evaluate the minimum coefficient of friction required to keep a uniform chain at rest on a rough surface with a base length l and a height h.
Forces Acting on the Chain
- The weight of the chain acts downwards at its center of mass.
- The frictional force acts upwards along the slope to prevent slipping.
Components of Forces
- The gravitational force can be decomposed into components along the incline and perpendicular to it.
- The normal force acts perpendicular to the surface, opposing the chain's weight component.
Calculating the Minimum Coefficient of Friction
- The frictional force (F_f) must counterbalance the component of the weight pulling the chain down the slope.
- The condition for equilibrium dictates that the frictional force equals the downhill component of the weight.
Frictional Force Equation
- The frictional force can be expressed as F_f = μ * N, where μ is the coefficient of friction and N is the normal force.
- The normal force is influenced by the height (h) and the angle of the incline.
Conclusion
- To maintain equilibrium, the relationship between the forces must satisfy:
μ * N ≥ Weight component along the incline.
- The minimum coefficient of friction (μ_min) can thus be derived from the geometry of the setup, leading to the conclusion for the conditions under which the chain remains at rest.
This analysis provides the necessary insight to calculate the minimum coefficient of friction essential for keeping the uniform chain stable on the irregular surface.
In this scenario, we need to evaluate the minimum coefficient of friction required to keep a uniform chain at rest on a rough surface with a base length l and a height h.
Forces Acting on the Chain
- The weight of the chain acts downwards at its center of mass.
- The frictional force acts upwards along the slope to prevent slipping.
Components of Forces
- The gravitational force can be decomposed into components along the incline and perpendicular to it.
- The normal force acts perpendicular to the surface, opposing the chain's weight component.
Calculating the Minimum Coefficient of Friction
- The frictional force (F_f) must counterbalance the component of the weight pulling the chain down the slope.
- The condition for equilibrium dictates that the frictional force equals the downhill component of the weight.
Frictional Force Equation
- The frictional force can be expressed as F_f = μ * N, where μ is the coefficient of friction and N is the normal force.
- The normal force is influenced by the height (h) and the angle of the incline.
Conclusion
- To maintain equilibrium, the relationship between the forces must satisfy:
μ * N ≥ Weight component along the incline.
- The minimum coefficient of friction (μ_min) can thus be derived from the geometry of the setup, leading to the conclusion for the conditions under which the chain remains at rest.
This analysis provides the necessary insight to calculate the minimum coefficient of friction essential for keeping the uniform chain stable on the irregular surface.
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A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to?
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A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to?.
A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform chain is placed at rest on a rough surface of base length l and h on an irregular surface as shown in fig then the minimum coefficient of friction between the chain and the surface must be equal to?.
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