Physics Help Forum F-dL Graph Help!

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 Nov 4th 2009, 09:06 AM #1 Junior Member   Join Date: Nov 2009 Posts: 6 F-dL Graph Help! Hi, I need to plot a graph of F=kx for my lab report. By measuring x, displacement of spring for every mass (20g, 40g,50g) we found k. Now i need to draw F-x graph. I put my F and x data on graph w/o any problems. But when it comes to draw the line of F=kx i get stuck. Using the line's slope i need to find theoritecal k and calculate the error. I need to have a graph like this: http://phoenix.phys.clemson.edu/tuto...h/labgraph.gif This is my second lab report so i need help to get started and learn how to draw properly.
 Nov 4th 2009, 09:17 AM #2 Senior Member   Join Date: Sep 2009 Location: india Posts: 409 i dont know if u are needing this to find k from F x graph, draw a triangle(anywhere) and of any size with the straight line u have got by plotting F-x as ur hypotenuse and the other sides of ur triangle are parallel to x and y axes.measure these sides with your scale, (convert them to actual values)and take ratio to get tan theta which gives u the slope and hence k. to find error, take log and differentiate.
 Nov 4th 2009, 09:37 AM #3 Junior Member   Join Date: Nov 2009 Posts: 6 Imageshack - adszzx thanks, but my problem is i dont know how to get my straight line from F=kx. I dont know k so i cant give values and draw. Is the best fit line that im supposed to draw?
 Nov 4th 2009, 10:55 AM #4 Senior Member   Join Date: Sep 2009 Location: india Posts: 409 you draw the line so that it passes through the maximum number of points. also make sure that the number of unused points above this line equals the no of unused points below this line. then find k by my method.
 Nov 4th 2009, 11:38 AM #5 Junior Member   Join Date: Nov 2009 Posts: 6 alright, thanks for help.
Nov 4th 2009, 12:11 PM   #6
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 Originally Posted by Nrt Imageshack - adszzx thanks, but my problem is i dont know how to get my straight line from F=kx. I dont know k so i cant give values and draw. Is the best fit line that im supposed to draw?
,
 Originally Posted by r.samanta you draw the line so that it passes through the maximum number of points. also make sure that the number of unused points above this line equals the no of unused points below this line. then find k by my method.
I may disagree with r.samanta (depending of the following). One of the most used method for interpolating datas in physics are the least squares method (see http://en.wikipedia.org/wiki/Least_squares or just type it in google and look how to get the equation y=ax+b, where a is the slope. Basically you've found y's and x's, it remains to find out a and b precisely by the Least squares method). Now let me ask you a question Nrt : Have you been introduced to the Least square method? If no, then maybe the tip of r.samanta is good enough. If yes, then you'd have to apply what you've been introduced!
Sidenote : In fact what r.samanta proposed seems something similar to the least square method, but many times the line won't pass by any points. I've made many lab reports and I don't remember a single one in which the line passed by a point I had measured. I even wrote a program (with my friend) in Fortran 90 in order to calculate "a", "b", their errors (or uncertainties) and many more things related to this.

Edit: Maybe take a look at http://www.shodor.org/unchem/math/lls/leastsq.html in order to plot your data to compare with what you did. Search for "linear least squares".
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Last edited by arbolis; Nov 4th 2009 at 12:17 PM.

Nov 4th 2009, 01:53 PM   #7
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 Originally Posted by arbolis , Nrt : Have you been introduced to the Least square method? If no, then maybe the tip of r.samanta is good enough. If yes, then you'd have to apply what you've been introduced! Edit: Maybe take a look at Linear Least Squares Regression in order to plot your data to compare with what you did. Search for "linear least squares".
They showed advanced methods like least square, regression but told us that we don't have to use it on our reports.

So, that is the way i've done it.

Error: Lists do not contain expected number of data points. Check the number of data points in the lists against the number in the top field.

 Nov 4th 2009, 02:04 PM #8 Senior Member     Join Date: Apr 2008 Posts: 815 Your graphic looks good. I tried some points in http://www.shodor.org/cgi-bin/cchem/leastsq.pl and all worked fine. It seems you entered wrongly the number of points you have or you forgot a to enter a data in the table. If the number of points coincide with what you entered then all should work fine in my opinion. __________________ Isaac If the problem is too hard just let the Universe solve it.
 Nov 4th 2009, 04:20 PM #9 Junior Member   Join Date: Nov 2009 Posts: 6 Thanks for help. I'm about to finish my work. I think i'll have time to sleep :P.
Nov 4th 2009, 04:27 PM   #10
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 Originally Posted by Nrt Thanks for help. I'm about to finish my work. I think i'll have time to sleep :P.
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