Breaking Point for a Copper Wire

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Homework Help Overview

The discussion revolves around determining the maximum load that can be suspended from a copper wire, given its dimensions and material properties, specifically its elastic limit and tensile strength. The subject area includes concepts from material science and mechanics, particularly related to stress and strain in materials.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to convert units and clarify the relationship between stress, strain, and the elastic limit. There is an exploration of the definitions of key terms such as elastic limit, tensile strength, and breaking point. Some participants express confusion about how to derive the breaking point and calculate the maximum weight.

Discussion Status

The discussion is ongoing, with participants offering guidance on unit conversions and definitions. There is an acknowledgment of the relationship between stress and the elastic limit, but no consensus has been reached on the specific calculations or methods to apply.

Contextual Notes

Participants note that the problem assumes the elastic limit corresponds to the breaking point, which may influence the approach to solving the problem. There is also a mention of the need for clarity on the definitions of stress and its application in this context.

Ike
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What is the maximum load that could be suspended from a copper wire of length 1.9 m and radius 1.2 mm without breaking the wire? Copper has an elastic limit of 2.9 x 10^8 Pa and a tensile strength of 4.3 x 10^8 Pa. Give your answer in Newtons (N).


Any thoughts? I'm completely lost.
 
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Well you may want to start by converting the Pascals to its other SI units (part of it is in Newtons...). That should make it a bit more apparent.
 
My main problem here is this...
When a wire is stretched, it will return to it's original length if the weight is removed. This is true, unless the elastic limit has been reached, in which case the wire will be permanently stretched. Before this point, the proportional limit is met, in which the tensile strain and the tensile stress are no longer proportional. Further beyond the elastic limit is the point of ultimate strength. I assume this is the same as tensile strength. Further beyond this point is the breaking point.

I have no idea how to derive the breaking point at all, nor how to find the maximum weight before that point for that matter.
 
Oh yes, and one Pascal is the same as one Newton per square meter.

1 Pa = 1 N/m^2
 
Since you are only given the elastic limit (yield point) the problem assumes that the onset of yielding will be the breaking point.

You should start looking at what the definition of stress is. If you set the stress in the wire equal to the elastic limit...
 

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