Density of Wood

This isn't much - really it is part of another post I am working on. The point of this post is to calculate the density of this piece of wood.

Really, there is a reason for this. I saw this little stick (sticklette?) and noticed that it was very cylindrically shaped. So, what if I just pretend it is a cylinder to calculate the volume? This way I won't have to get it wet or anything (because I might need this stick later).

First the mass

Yes, there is some uncertainty in the mass - but it is small. I put the stick on balance and I will use a value of m = 28.9 g or 0.0289 kg.

Volume

The volume of a cylinder is:

And from my estimates, I get a length and diameter of:

To determine the volume (and the uncertainty in the volume) I am going to use the "max-min" method for uncertainty. The basic idea is that I will calculate the maximum value the volume could be and the minimum and base the uncertainty on these.

And for the minimum volume:

Note: I put too many digits in these number because at this point, I don't know how many to keep. Now for the uncertainty in the volume, I will just take the average change from max to average and average to min:

Putting this all together, I get a volume of:

Density

Now to do the same thing with the density. The maximum density is:

Here I divided by the minimum volume to get the maximum density. And the min volume:

This gives a density of:

I am pretty happy with this. This density is less than water (1000 kg/m³) so that means this wood would float (along with very small rocks and gravy).