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.
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:
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).