Is this a reliable way to measure an arc

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Discussion Overview

The discussion revolves around methods for measuring the outer and inner radii of a brass rod with a 90-degree bend. Participants explore the reliability and accuracy of using a string to measure these radii and consider alternative measurement techniques.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes using a string to measure the outer and inner radii by straightening it out for linear measurement.
  • Another participant agrees that the method could be reliable but questions its accuracy, suggesting that measurements may vary each time.
  • A participant inquires about more accurate methods, considering the use of a graduated flexible curve.
  • Another suggestion involves measuring the volume of the bent piece by submerging it in water and calculating the length of an unbent rod with the same volume.
  • Alternatively, calculating the length of an unbent rod based on the weight of the bent piece is also proposed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reliability and accuracy of the initial method. Multiple competing views on measurement techniques are presented, and the discussion remains unresolved regarding the best approach.

Contextual Notes

Limitations include potential variability in measurements with the string method and assumptions about the density and volume calculations for alternative methods.

camacru
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I have a brass rod with a 90 degree bend. I want to measure the outer and inner radii by placing a piece of string along both of them, and then straightening the string out to determine the linear measurement. Is this an accurate method?
 
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Reliable? Yes (depending on how well you keep the "string" on the line of the outer radius).

Accurate? No. At least not to the tolerances you stated in your previous post, if that's what you're getting at. But feel free to try. I'll bet you get a different measurement each time.

https://www.physicsforums.com/showpost.php?p=2411590&postcount=1
 
That's what I thought. What would be a more accurate method? I thought about using a graduated flexible curve...
 
Why don't you measure the volume of the bent piece (say, by submerging it underwater in a big graduated cylinder). Then calculate the length of an unbent rod with the same volume.

Or, if you know the density, simply calculate the length of unbent rod that has the same weight as your bent piece.
 

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