We are going to consider a series of measurements to determine a spring constant

Question

We are going to consider a series of measurements to determine a spring constant using the expression |F|=kx where |F| is how much force is exerted on a spring to pull it a distance x. The value of the spring constant can be found by determining the slope on a graph of |F| vs. x Make a graph with the following data (Force on the vertical, x on the horizontal axis), and place error bars on the two endpoints I've included a picture of my graph to help you (no calculations). Some comments, your best line of fit is not simply connecting the endpoints. The best line (trend line) brings the line closest to all the data points. The slope of the line will be "k" the spring constant. It is not a connection to the two endpoints alone (throwing out the rest of the data is not what we want). I've drawn a "best line" from which I will determine the slope k. Then I have drawn a line with maximum slope and minimum using only the endpoints to determine the slop in the slope. You should be able to use your own graph to determine k and the uncertainty in k. Do so. k(max)= k(min)= k =_ plusminus _N/m

Explanation / Answer

k(max) = F/x

=71.9/2.19

= 32.83 N/m

k (min) = 15/0.57

=26.32 N/m

k = [kmin+kmax]/2 = [32.83+26.32]/2 = 29.575 N/m

now for uncertainty , F =kx

ln F = ln k + ln x

dF/F = dk/k + dx/x

dk/k = dF/F - dx/x

dk/29.575 = 5/((11.7+15+28.5+46.3+71.9+93.5)/6) +0.10/((0.38+0.57+0.92+1.48+2.19+2.99)/6)

dk = 29.575*0.183 = 5.4 N/m

hence k = 29.6 (+-) 5.4 N/m

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