Hi All,

Would it be at all possible for someone to please advise me how the author arrived at this solution to the following question.

Question;

A linear spring, with a spring constant K = 100kN/m, is stretched a distance of 0.8m and attached to a paddle wheel. The paddle wheel then rotates until the spring is unstretched. Calculate the heat transfer necessary to return the system to its initial state.

Solution;

The work done by the linear spring on the system is given by;

W 1-2 = integration 0 to 0.8 Fdx = integration 0 to 0.8 100x dx = 100 x 0.8Sq / 2 = 32 N m

Thoughts

my problem stems around were 0.8sq / 2 came from

maybe I am misunderstanding the use of integration here or the author has used it but found the solution by a different method?

any help much appreciated

Additional info I worked out;

Using the integral 0 - 8 Fdx = inegral 0 - 8 100 x 2x dx 2 = 100 x 0.8sq / 2 = 32 N m

the 2x becomes x sq and then i divided both sides by the remaining 2 to conclude 0.8 / 2.

does this sound like I am getting the understanding correct.

Remember that,

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Where [LaTeX Error: Can't write to directory] is some constant produced by anti-differentiating.

[LaTeX Error: Can't write to directory]

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[LaTeX Error: Can't write to directory]

What's incorrect here?

__________________
"Dissent is the highest form of patriotism." - Thomas Jefferson.

"Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild

I study Mathematical Physics at the
University of Waterloo.

-DC

Hi Deco,

thanks for the info provided. Please advise on this part the denominator 2 were 100xsq / 2

so what i mean is;

100x dx = 100x sq / 2. Were did 2 originate from in that equation?

Like I said;

[LaTeX Error: Can't write to directory]

So, for example;

[LaTeX Error: Can't write to directory]

or

[LaTeX Error: Can't write to directory]

The coefficient of 100 is taken out of the integral because it's a constant.

__________________
"Dissent is the highest form of patriotism." - Thomas Jefferson.

"Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild

I study Mathematical Physics at the
University of Waterloo.

-DC

Please pardon my ignorance as I am learning the ropes.

you said;

intergral x power 3 dx = x power 4 / 4 +C

Can I work it out like this;

2x power 2 dx = 2x2 = 4 + (x) x (x) = x power 4 / 4 + C

Sorry to be a pain, it's just the method I want to understand?

Thanks

No, because the factor of 2 is constant.

[LaTeX Error: Can't write to directory]

If you are not familiar with integral calculus, I'd suggest you do some reading on the subject in order to keep up with the math.

__________________
"Dissent is the highest form of patriotism." - Thomas Jefferson.

"Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild

I study Mathematical Physics at the
University of Waterloo.

-DC

Hi Deco,

The subject area is new to me and as you advise I will have to do some research in Technician Mathematics that explains the subject. Where possible I do like asking for second professional opinions just in case I don't understand the books?

Thanks

David

I wouldn't mind answering some of your question if you pm me. Also, our sister forum, Math Help Forum, could also be a source of "second opinions".

__________________
"Dissent is the highest form of patriotism." - Thomas Jefferson.

"Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild

I study Mathematical Physics at the
University of Waterloo.

-DC

Hi Deco,

Thank you very much, most appreciated. Please allow me a little time this evening to do some research and the parts I can't or don't understand from the books I will PM you for advice.

Thanks

David