Using individual pairs of measurements is **bad**,
and here's why.

Suppose your data show this:

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

The values of **k** derived from each individual pair of measurements
are definitely not the same. There's a clear trend. Should
you just take the average, and say **k = 0.80 N/m**?
Should you also say that "this spring does not obey Hooke's Law,
because the value of k isn't the same for each measurement?"

No!

If you were to make a graph of this data, you would see it looks like this:

If you look at this graph, it's clear that the data DOES lie
on a nice, straight line. So this method of analysis
DOES imply that the spring obeys Hooke's Law. Moreover, the
graph's slope yields a value of **k = 1.1 N/m**, which
is different than ANY of the individual values of **k**
derived from individual measurements.

What's going on?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.