Equilibrium of a stiff plate on inclined planes

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SUMMARY

The discussion centers on the equilibrium of a thin, stiff rectangular plate resting on two inclined planes with angles α and β, where α + β = 90°. The participants analyze the forces acting on the plate, including normal forces and gravitational forces, while attempting to determine the conditions for static balance. Key insights include the relationship between the angles and the stability of the system, emphasizing that the normal force (NA) is perpendicular to the plate and that the angle θ, which the plate makes with the horizontal, is critical for stability. The conclusion is that the system's stability depends on the specific angles α and β, and whether a suitable angle θ exists for equilibrium.

PREREQUISITES
  • Understanding of static equilibrium and forces acting on bodies.
  • Familiarity with inclined planes and normal force concepts.
  • Knowledge of basic trigonometry, particularly involving angles and triangles.
  • Ability to analyze free-body diagrams and apply Newton's laws.
NEXT STEPS
  • Study the principles of static equilibrium in mechanics.
  • Learn how to draw and analyze free-body diagrams for inclined planes.
  • Explore the concept of stability in mechanical systems.
  • Investigate the role of angles in determining the equilibrium of rigid bodies.
USEFUL FOR

Students in physics or engineering disciplines, particularly those studying mechanics, as well as educators and tutors looking to enhance their understanding of equilibrium conditions in rigid body dynamics.

  • #31
Well the first problem is α+β = 90.
IT is the exact same problem.
Do i really need to start a new thread for the same question.
 
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  • #32
aang said:
Well the first problem is α+β = 90.
IT is the exact same problem.
Do i really need to start a new thread for the same question.
aang said:
and where α=45,β=60.
Those don't add to 90.
But more importantly, as with a new thread in a homework forum, you should show some attempt. A diagram employing the advances already made in this thread would be a good start.

Edit: aang has now started a new thread at https://www.physicsforums.com/threads/equilibrium-of-a-stiff-plate-on-inclined-planes.1004932/
 

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