Pull-down resistor value for FSR's voltage divider circuit connected to Arduino
The cynic in me says that everyone uses a 10kΩ resistor because under the technical data section of the FSR above, a chart is given with output voltages specified with 5V supply and a 10k pull-down resistor. I have copied the chart below for reference:
\$\begin{array}{}
Force (lb)&amp; Force (N)&amp; \begin{matrix}FSR\\ Resistance\end{matrix} &amp;(FSR + R) Ω&amp;\begin{matrix}\text{Current thru}\\ FSR+R\end{matrix} &amp;\begin{matrix}Voltage\\ \text{across }R\end{matrix} \\
\hline
None&amp; None&amp;\infty&amp;\infty&amp;0 mA&amp;0V\\
0.04 lb &amp;0.2 N &amp;30kΩ&amp;40 kΩ&amp;0.13 mA&amp;1.3 V\\
0.22 lb &amp;1 N &amp;6 kΩ&amp;16 kΩ&amp;0.31 mA&amp;3.1 V\\
2.2 lb &amp;10 N &amp;1 kΩ&amp;11 kΩ&amp;0.45 mA&amp;4.5 V\\
22 lb &amp;100 N &amp;250 Ω&amp;10.25 kΩ&amp;0.49 mA&amp;4.9 V
\end{array}\$

So we can see that a 10kΩ gives us a reasonable amount of range over the operation of the sensor. If we wanted to have better resolution with the smaller force ranges, we could increase the pull-down resistance. We could also decrease the pull-down resistance to improve the resolution at higher force ranges, although that would also come at a cost of greater current draw.