Center of Mass and Work Problem

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SUMMARY

The discussion focuses on calculating the work done by laborers to position stone blocks in the construction of an ancient monument shaped like an isosceles triangle. The monument's dimensions are 17.6 m in height, 69.4 m in width, and 3.30 m in thickness, with a density of 3,174 kg/m³ for the stone blocks. The total mass of the monument is calculated to be 12,793,606.85 kg. The work is determined using the formula Work = (Mass * Gravity * Center of Mass), where the center of mass for a triangular shape is identified as the centroid.

PREREQUISITES
  • Understanding of basic physics concepts, specifically work and energy.
  • Familiarity with geometric properties of triangles, particularly centroids.
  • Knowledge of density calculations and mass determination.
  • Proficiency in using the formula for work: Work = (Mass * Gravity * Height).
NEXT STEPS
  • Study the concept of centroids in various geometric shapes.
  • Learn about the principles of work and energy in physics.
  • Explore density and mass calculations in real-world applications.
  • Investigate the effects of gravity on work done in different environments.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and work-energy principles, as well as educators looking for practical examples of geometric applications in physics.

JoeyM88
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Homework Statement



Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle . The monument is made from tens of thousands of small stone blocks of density 3 174 kg/m3. The monument is 17.6 m high and 69.4 m wide at its base and is everywhere 3.30 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. How much work did laborers do on the blocks to put them in position while building the entire monument?

Homework Equations


Work = (Mass*Gravity*Center of Mass)



The Attempt at a Solution


Volume=(17.6*69.4*3.30)=4030.752
Mass = (3174*4030.752)=12793606.85kg
Center of Mass=?
Work=(12793606.85kg*9.8*Center of Mass)
 
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your volume is what a rectangular shape would have (twice too large).
the center of mass for a triangle is the centroid.
 

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