Solve Hanging Blocks Homework: Find Max Height

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SUMMARY

The discussion focuses on solving a physics homework problem involving stacking blocks to determine the maximum height before the tower topples. Each block has a mass (m) and length (l), with the second block offset by 0.15L from the first. The key equation involves the center of mass, where the condition for toppling is that the center of mass must extend beyond the edge of the first block. The participants explore the arithmetic series formed by the incremental offsets and seek to establish a mathematical model for the center of mass as more blocks are added.

PREREQUISITES
  • Understanding of center of mass concepts
  • Familiarity with arithmetic series
  • Basic knowledge of physics principles related to equilibrium and stability
  • Ability to set up and solve equations
NEXT STEPS
  • Study the principles of center of mass in multi-body systems
  • Learn how to derive and manipulate arithmetic series
  • Explore stability conditions for stacked objects in physics
  • Investigate practical examples of equilibrium in engineering contexts
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Students in physics or engineering courses, educators teaching mechanics, and anyone interested in understanding stability in stacked systems.

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Homework Statement



How many blocks can you stack on top of each other before the tower falls? Each block has a mass m and a length l. The first block is on the table. The second block is stacked on top of the first but moved by 0.15L to the right. This pattern continues

Homework Equations



Distance to centre of mass multiplied by total mass is the summation of each individual mass multiplied by distance from reference point .

The Attempt at a Solution



For the tower to topple , centre of mass has to be beyond the edge of the first block so I can say that 0.5L(n)(m) = some form of arithmetic series due to the increments of 0.15L but I don't know how to set up the equation
 
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So start working it out. Where is the center of mass for 1 block on top, for 2, for 3 ? Do you see a pattern ?
 

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