Why bother with graphs? (Part 3)

One more way to see the difference: if you use one pair of measurements at a time to calculate the spring constant, like this:

            This table doesn't include force due to pan

      mass added   Force      distance stretched         derived k
        (kg)        (N)            (m)                     (N/m)
    -----------------------------------------------------------------
        0.005      0.049          0.081                    0.61               
	0.010      0.098          0.125                    0.78
	0.015      0.147          0.169                    0.87
	0.020      0.196          0.214                    0.92

then you are assuming that the force equals zero when the distance stretched equals zero; in other words, you are measuring the slopes of each of the dashed lines in the graph below:

But what you really want to do is to measure the change in distance stretched with respect to the change in force, the derivative of the relationship. And for that, you should measure the slope of the line which passes through all the data. Note that this does NOT pass through the origin.