Up to what vertical height can a particle remain at rest inside a hollow sphere of radius r with a friction coefficient -rr___________________?
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Answer: D. 0.134 r
Explanation
A particle remaining at rest inside a rough hollow sphere is limited by friction. Mathematical analysis of equilibrium forces and friction coefficients yields the height limit. The vertical height restriction depends directly on the sphere radius and surface friction properties. Static equilibrium requires gravitational, normal, and frictional forces to balance perfectly. Resolving forces along tangential and normal directions determines the maximum stable inclination angle. Standard mechanics problems of this type utilize trigonometry and friction cone principles.
Spherical containers and bowl mechanisms in manufacturing utilize friction limits for parts feeding. Mechanical engineering students solve these physics problems to master static equilibrium and friction. Understanding particle stability on curved surfaces is essential for designing material handling hoppers. Other geometric fractions like r/2 or r/4 do not satisfy the exact static equilibrium equations. Fractional values derived from incorrect trigonometric assumptions fail to match rigorous force balances. Standard derivations for spherical friction boundaries specifically yield the 0.134 r height limit.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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