Permanent externsion of a wire. Watch

Zishi
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#1
Report Thread starter 7 years ago
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I'm sure that first part of this question is not required, but if you still want to see it, then I'll post it.

As for the area, see if I've shaded it correctly:



If it's incorrect, then don't bother to see the other part, but if it's correct, then please tell me about the next part:



I tried to divide it into 4 regions. The first region into triangle, and other three into trapeziums like this:


This gives my answer as 5.95 mJ, but mark scheme's answer is 6.4 +/- 0.2 mJ. Please take your time, and explain it. Thanks...
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Stonebridge
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Report 7 years ago
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You have to count the small squares. Each small square is then 2N x 0.02mm = 0.04mJ
When counting, count in any part square greater than a half and count out any less.
There are a lot of squares near the origin which are about half a square.
For example, the first row of small squares next to the origin has 4 whole squares and 2 halves.
I counted that as 5.
I must say, it's a bit hit and miss.
Their answer seems to imply there are about 160 small squares.
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Zishi
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Report Thread starter 7 years ago
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(Original post by Stonebridge)
You have to count the small squares. Each small square is then 2N x 0.02mm = 0.04mJ
When counting, count in any part square greater than a half and count out any less.
There are a lot of squares near the origin which are about half a square.
For example, the first row of small squares next to the origin has 4 whole squares and 2 halves.
I counted that as 5.
I must say, it's a bit hit and miss.
Their answer seems to imply there are about 160 small squares.
Wow, I didn't think that taking it as triangles, etc would give this much error. But thanks anyway, by 'small squares' method, I get exactly 6.4mJ. By the way I think I know why the shaded region would be the area between two curves, but I was just wondering if you could give your explanation about it - I may not be fully aware why I shaded that.
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Stonebridge
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The area under a force-extension graph is an amount of energy because force x distance is work done.
The area under the upper curve is work done extending the wire, and the area under the lower curve is the work recovered when the wire contracts.
The shaded area is the difference between the two and is the amount of energy lost in the process. In other words, you didn't get as much energy back when the tension was removed.
There will always be energy lost if the wire doesn't return to its original length because the second curve will be below the first.
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Zishi
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Report Thread starter 7 years ago
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(Original post by Stonebridge)
The area under a force-extension graph is an amount of energy because force x distance is work done.
The area under the upper curve is work done extending the wire, and the area under the lower curve is the work recovered when the wire contracts.
The shaded area is the difference between the two and is the amount of energy lost in the process. In other words, you didn't get as much energy back when the tension was removed.
There will always be energy lost if the wire doesn't return to its original length because the second curve will be below the first.
Hmm, yeah. My concept was right then. Thanks a lot!!
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