How Much Weight Can a Cardboard Boat Hold?

  • Context: Mathematica 
  • Thread starter Thread starter vondutchgurl
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Discussion Overview

The discussion revolves around determining the maximum weight that a boat made from a single sheet of cardboard (4 feet by 8 feet) can hold when folded and shaped appropriately. The scope includes design engineering principles, mathematical reasoning, and practical application of buoyancy concepts.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant, Brooke, seeks assistance in calculating the maximum weight a cardboard boat can hold and emphasizes the need to prove the solution.
  • Another participant claims to have calculated a maximum weight of 1010.31 pounds but expresses uncertainty about the cutting and folding methods required to validate this claim.
  • A different participant argues that the boat will sink quickly, suggesting that it may not hold any weight effectively.
  • Another contribution discusses the complexity of the problem if any shape is allowed, proposing that if confined to box shapes, the problem simplifies to maximizing volume with a given surface area, using calculus of variations and Lagrange multipliers.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of the cardboard boat holding weight, with some suggesting it can hold significant weight while others believe it will sink quickly. There is no consensus on the maximum weight or the methods to achieve it.

Contextual Notes

Participants have not resolved the assumptions regarding the shape of the boat and the implications of surface area on weight capacity. The mathematical approach proposed involves specific conditions that may not be universally accepted.

Who May Find This Useful

This discussion may be useful for students in design engineering, individuals interested in buoyancy and material properties, and those exploring practical applications of mathematical optimization in engineering contexts.

vondutchgurl
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i was given an assignment in my design engineering class...it goes as follows:

What is the maximum amount of weight that can float in a boat made out of 1 sheet of cardboard 4 feet by 8 feet in size...when flat but it can be folded and cut and glued in any shape you choose.



**you also have to be able to prove your solution**

if anyone could help me figure this out i would really appreciate it

thanks---
brooke
 
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if i did my calculation correct...then the maximum weight it could hold is 1010.31 pounds...im jst not sure how i would cut or fold the 8' by 4' sheet of cardboard to be able to prove my solution
 
I vote none since the boat will sink after a very short time after being introduced to the water.
 
If the cardboard is allowed to take any shape, then this is a very complicated problem involving the calculus of variations. If we are confining ourselves to box shapes, the problem becomes much more managable. Call the dimentions x, y, and z. You have to find the box of maximal volume with a given surface area. (This will be the box that holds the most weight since the amount of weight an object can have before sinking is the wieght that water of an equivalent volume has.) The thing to notice is that the top of the box does not need to be covered and shouldn't be in the box of maximal volume since it would be a waste of surface area. If x is the length, y is the hieght, and z is the other dimension, then one of the xz surfaces does not need to be there. So you must maximize
[tex]f(x,y,z)=xyz[/tex]
subject to
[tex]2xy + 2yz + xz=32[/tex]
The standard way of doing this would be the method of Lagrange multipliers.
 

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