What is the required h for equilibrium in a body with two center of masses?

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SUMMARY

The discussion focuses on determining the required height (h) for equilibrium in a system with two centers of mass. The key insight is that the center of mass (CoM) of the combined bodies must align vertically with the point of support to maintain balance. Participants emphasize the importance of using geometry, trigonometry, and moment summation to derive the necessary relationships and expressions for solving the problem. The conversation highlights the need for a proactive approach in attempting the problem to facilitate constructive feedback.

PREREQUISITES
  • Understanding of center of mass (CoM) concepts
  • Familiarity with geometry and trigonometry
  • Knowledge of moment summation principles
  • Basic algebra skills for expression manipulation
NEXT STEPS
  • Study the principles of center of mass in combined bodies
  • Practice problems involving moment summation in equilibrium
  • Explore trigonometric relationships in geometric configurations
  • Review algebraic techniques for solving equations related to physical systems
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Students in physics, particularly those tackling mechanics and equilibrium problems, as well as educators looking for effective teaching strategies in these concepts.

Axe199
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Homework Statement



problem attached

Homework Equations





The Attempt at a Solution


i had no problem with part i and ii , iii on the other hand, i simply don't know what i should do , i figured out that the required h will be the one making the center of mass of the whole body on the vertical from the point it's standing on ( moments from both center of masses will be equal )
but i have no idea how to get that
 

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Axe199: It is just geometry and trigonometry, and the moment summation you mentioned in post 1 ... and algebra. And arithmetic. Just start by drawing and labeling the trigonometry; any and everything you know. Eventually, you will build relationships, and be able to write expressions. Just start, and try something. If you do not try something, and do not make a valid attempt, then we cannot check your math and give you hints on where you went wrong.
 
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