Re: How does the deflection of a cantilever [dowel] vary with mass/length etc..

Mr. Stevenson,

The best way to find out about the dependence of deflection on temperature 
is to do the experiment.  Take a cantilever and measure the deflection when 
a specific force is applied at two temperatures.  My guess is that you are 
correct.  At lower temperatures the cantilever will be stiffer and so will 
require more force for a given displacement.

Wood is not a crystalline structure, so the theory would be quite 
difficult, but it should have some of the same general properties of a 
metallic material.  At lower temperatures the atoms tend to occupy lower 
energy states, so there is less freedom of motion.  The atomic bonds are 
stiffer at lower temperatures and the whole structure becomes more 
difficult to bend.  This is related to atomic motion, but is not quite the 
same.  The atomic motion becomes greater at higher temperatures through 
this same mechanism, but atomic motion is not directly the cause of the 
stiffness of the cantilever.

As for how to measure the displacement, you can either measure the vertical 
displacement or the angular displacement.  However you do it, you should do 
it consistently.  The cantilever should (to a certain point) have a linear 
dependence between force and displacement.  If your cantilever only 
displaces by small angles (5 to 10 degrees) then the veritcal displacement 
is nearly proportional to the angular displacement.

For information about solid state atomic bonds you might refer to a general 
chemistry textbook, or to a solid-state physics text.  The latter will be 
quite advanced, so start with the chemistry text.  You can find a more 
general discussion of springs (a cantilever is, broadly speaking, a type 
of spring) in any general physics text.