Building Sand Castle Walls: Force vs. Exponential

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SUMMARY

The discussion centers on the effectiveness of slanted versus flat walls in building sand castles to withstand high tide. One participant argues that a slanted wall distributes water force exponentially better than a flat wall, while another contends that the difference is proportional. The consensus is that the angle of the wall does not change the total force exerted by the water but does affect the wall's resistance due to its larger base. The need for equational proof regarding the relationship between wall angle and water force distribution is highlighted.

PREREQUISITES
  • Basic understanding of physics concepts such as force and pressure
  • Familiarity with the principles of fluid dynamics
  • Knowledge of geometry, particularly regarding angles and surface area
  • Experience with mathematical modeling or proof techniques
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  • Research the principles of fluid dynamics and how they apply to slanted surfaces
  • Study the mathematical modeling of force distribution on inclined planes
  • Explore the concept of pressure distribution in fluids
  • Learn about the geometry of shapes and their impact on structural integrity
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This discussion is beneficial for physics students, engineers, and anyone interested in understanding the mechanics of force distribution in fluid dynamics and structural design.

russell16
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I am at a beach with my family and we were building a sand castle and we wanted to build a wall around it so it would last longer against high tide. I said to my cousins that the wall should be slanted in order to decrease the force of the water instead of being flat because then the wall would take the full force and it would not be distributed as well. And i used the term exponentially because i knew it was greater than a proportional difference and i wanted it done my way. another cousin said that he thinks it wouldn't be exponentional. he does agree that would better distribute the force but thinnks it would be a proportion. I just decided for sake of arguing to keep my side and say exponential. If anyone can provide equational proof that force of water flowing on to a slanted surface is exponential or proportional it would be apprieciated.
 
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The force hitting a wall does not depend at all upon its being slanted. What is true is that a slanted wall has a larger base than a non-slanted wall of the same amount of material and so resists that force better.
 

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