What is the relationship between diameter and mass per length in a steel wire?

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Homework Help Overview

The discussion revolves around the relationship between the diameter of a steel wire and its mass per unit length. Participants are exploring how the density of the material and the geometry of the wire interact in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to relate mass per volume to mass per length, questioning how to convert density into the desired mass per unit length. There is also a consideration of how diameter affects mass per length, particularly in the context of steel wires.

Discussion Status

Some participants have pointed out potential misunderstandings regarding the dimensions of mass per length versus mass per volume. There is an ongoing exploration of how changes in diameter might influence mass per length, with no clear consensus yet on the implications of these relationships.

Contextual Notes

Participants are working with the assumption that both wires are made of steel, thus sharing the same density, but are uncertain about how to apply this to their calculations regarding mass per length.

nesan
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Homework Statement



http://puu.sh/frpk5/eae7bce2e3.png

Homework Equations



v = sqrt(T / (m / L));

The Attempt at a Solution



7.86 g / cm^3 = 7860 kg / m^3

T = v^2 * m/L

T = 160 ^ 2 * 7860 which is a huge number

I have no idea where the diametre plays a part.
 
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m/L ≠ 7860 (check the dimensions)
 
Nathanael said:
m/L ≠ 7860 (check the dimensions)
I'm sorry I really don't understand what you're aiming at. Does it have to do with the m^3?

I know it's mass per unit length but how would I go from 7860 kg / m^3 to what I need? Thank you.
 
nesan said:
I'm sorry I really don't understand what you're aiming at. Does it have to do with the m^3?
You were given the mass per volume, but you want to know the mass per length. You used the mass per volume where you should have used the mass per length.

nesan said:
I know it's mass per unit length but how would I go from 7860 kg / m^3 to what I need? Thank you.
Consider a steel wire with a larger diameter. (They are both steel, so the density is the same.) Which one will have the larger mass per length? Or will it be the same? And why?
 

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