[ME statics] Papus' theorem - find required height of cup

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Discussion Overview

The discussion revolves around determining the height of liquid required to fill a cup such that it contacts half of the internal surface area. The problem is framed within the context of a homework assignment, involving geometric considerations and calculations related to surface area.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents a mathematical approach to find the height of liquid in the cup, referencing a specific equation for surface area.
  • Another participant questions the clarity of the initial post, asking if there is a specific question associated with the provided work.
  • A different participant expresses confusion regarding the calculation, particularly about whether the area of the bottom of the cup was considered in the total surface area.
  • One participant suggests that the problem is ambiguous and discusses the implications of including the bottom area in the calculations.
  • Another participant agrees that the bottom area should be accounted for in determining the "wanted" surface area, indicating that it contributes to the total area covered by the liquid.

Areas of Agreement / Disagreement

Participants express differing views on whether the bottom area of the cup should be included in the calculations for the surface area. There is no consensus on how to interpret the problem statement regarding the inclusion of the bottom area.

Contextual Notes

The discussion highlights potential ambiguities in the problem statement and the assumptions made regarding the surface area calculations, particularly concerning the bottom of the cup.

Feodalherren
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Homework Statement


Hibbler_ch9_p111.jpg
Determine the height h to which liquid should be poured into the cup so that it contacts half the surface area on the inside of the cup. Assume that r=11mm and l= 60mm . Neglect the cup's thickness for the calculation.

Homework Equations


Surface Area = 2πXL

where X is the distance to the center of mass from the axis of rotation and L is the length of the line that is rotating.

The Attempt at a Solution


IMG_20141023_013835.jpg


Link to my solution:

https://www.wolframalpha.com/input/?i=4243.57=2pi(11+((.317h)/2))sqrt(h^2+++(.317h)^2)
 
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Is there a question or something to go with your working?
 
It's in the problem statement. You can't see it?
 
I followed it up to the "want" (4243.57). Then I expected you to subtract the area of the bottom. I didn't try to follow your math passed that point, but I'm wondering if you took that "free bottom" into account.
 
I added the area of the bottom to the area of the side, then divided that total area by half. The question is kind of ambiguous and I don't know if they want me to account for the area of the bottom or not. I'm assuming yes since they only state "surface area" and the bottom certainly has some surface area.
 
That gave you the correct target area. ("wanted")
But as soon as you put half a drop into the container, you cover the bottom - and that contributes to your "wanted" area. So, to compute how much you need to take from the sides, subtract the surface area of the bottom from your "wanted" number.
 
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