How Many Centimeters of Wire Were Used Up? | Mu Alpha Theta Math Club Question"

  • Context: Undergrad 
  • Thread starter Thread starter Jameson
  • Start date Start date
  • Tags Tags
    Alpha Theta
Click For Summary

Discussion Overview

The discussion revolves around a math problem involving the calculation of the length of wire used when tightly wound around a cylindrical pole. The problem includes considerations of volume, cross-sectional area, and the geometry of the winding process, with a specific focus on the implications of having no gaps between layers of wire.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant suggests finding the volume of the cylindrical shell formed by the wire using an integral approach, specifically \(\pi\int_{0}^{1}(4+h)^2dh\).
  • Another participant raises a question about the meaning of "no gaps between layers," inquiring if this implies treating the winding as a solid shell.
  • A participant agrees with the assumption that the winding can be treated as a solid shell.
  • It is proposed that the volume of wire used can be calculated by equating the volume of the cylindrical shell to the product of the cross-sectional area of the wire and the length of the wire.
  • One participant expresses uncertainty about their setup of the problem and requests feedback on their work before proceeding with calculations.

Areas of Agreement / Disagreement

Participants generally agree on the approach to calculate the volume of the cylindrical shell and the implications of the problem's conditions, but there is some uncertainty regarding the interpretation of "no gaps between layers." The discussion remains unresolved as participants seek clarification and validation of their methods.

Contextual Notes

There are limitations regarding the assumptions made about the geometry of the wire winding and the interpretations of the problem's conditions. The exact setup of the problem and the calculations involved have not been fully established.

Who May Find This Useful

Students and participants interested in mathematical problem-solving, particularly in geometry and volume calculations, may find this discussion relevant.

Jameson
Insights Author
Gold Member
MHB
Messages
4,533
Reaction score
13
I don't know how many are familiar with this math club, I think it is mostly a southern thing, but here is a question which remains to stump me.

---------
Wire of 0.1cm is tightly wound (with no gaps in between layers) around a cylindrical pole of 3cm radius between heights of 0cm and 1cm. As a result, this part of the pole thickens, and the new radius is (4+h), where h is the height. How many centimeters of wire were used up?

(Hint: Length * Cross-sectional Area = Volume)
----------------

Ok, here are my few thoughts.

I guess you need to find the volume and the cross-sectional area, and thus divide to find the length.

For volume, an inegral of something along of the lines of [tex]\pi\int_{0}^{1}(4+h)^2dh[/tex] might find the volume.

For cross-sectional area, perhaps (3)(4+h).

Thanks,
Jameson
 
Physics news on Phys.org
what do they mean by no gaps between layers? Does this mean you can treat the winding as a solid shell?
 
I assume so. That's how I took it.
 
Okay, calculate the volume of that cylindrical shell the wire forms. You know the radius of the wire so you can find the cross sectional area of the wire. The volume of wire used, which is equal to the cross sectional area time the length of wire used, must be equal to that volume.
 
Those were my thoughts... can you look at my work before I calculate a wrong answer?

I don't know if I set the problem up correctly.
 

Similar threads

Graduate How Does Geometry Influence Our Understanding of the Universe?
  • · Replies 29 ·
Replies
29
Views
8K
What is the Mathematical Treatment of Thermal Stress and Strain?
  • · Replies 10 ·
Replies
10
Views
22K