Improving Accuracy in Spring Constant Measurements: Tips and Considerations

[Swamifez]

A student hangs masses on a spring and measures the spring's extension as a function of the applied force in order to find the spring constant k. Her measurements are:

Mass(kg): 200, 300, 400, 500, 600, 700, 800, 900
Extension (cm): 5.1, 5.5, 5.9, 6.8, 7.4, 7.5, 8.6, 9.4

There is an uncertainty of 0.2 inces in each measurment of the extension. The unccertainity in the masses is neglible. For a perfect string, the extension delta L of the spring will be related to the applied force by the relation kDelta L=F, where F=mg, and Delta L= L-L_0, L_0 is the unstretched length of the spring. Use these data and method of the least squares to find the spring constant k, the unstretched length of the spring L_0, and their uncertainties. Find Chi^2 for the fit and associated probability.

 

[dacruick]

what is Chi^2?

 

[Swamifez]

(χ2) or http://en.wikipedia.org/wiki/Pearson's_chi-square_test

 

[jrlaguna]

Do you know how to do the fit? Just least squares... Write the chi², just by writing down the sum of the squares of the distances from each point to the fitting line. Now, minimize for the fitting parameters.

For the associated probability, you have to put the resulting chi^2 into the appropriate chi^2 distribution... but I don't know yet where your real problem is...