Dot Physics

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.

i-86a33f6ac5bc53ddf7455f7690c4fd94-2010-03-30_vid00865mp4.jpg

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:

i-c75d3b194ce7ade4a64404dcee3642e7-2010-03-30_la_te_xi_t_1_2.jpg

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

i-f5fc3f8152189ff869db1d1b69893284-2010-03-30_la_te_xi_t_1_3.jpg

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.

i-9d078b1cc47875dbb3a69d2604fb84bd-2010-03-30_la_te_xi_t_1_6.jpg

And for the minimum volume:

i-f8bcef8135b79ed4fa49ffc5129f4f9d-2010-03-30_la_te_xi_t_1_5.jpg

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:

i-b4839213335c2cfa8e34f64a0425856c-2010-03-30_la_te_xi_t_1_7.jpg

Putting this all together, I get a volume of:

i-e5fb30744568f08e6fd599dfe9e284e5-2010-03-30_la_te_xi_t_1_8.jpg

Density

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

i-4ca80543496952ebca088e3c45d6a9d0-2010-03-30_la_te_xi_t_1_9.jpg

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

i-f6fd5de998a2886a6eb7fb190a6e0a95-2010-03-30_la_te_xi_t_1_10.jpg

This gives a density of:

i-46b329c673031b178d6ab936c5afa7de-2010-03-30_la_te_xi_t_1_11.jpg

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).

Comments

  1. #1 DrA
    March 30, 2010

    Generally we calculate the specific gravity, dividing the density of the wood by the density of water, to yield a unitless value, which if less than 1 means the wood floats.
    Twigs are trickier because you have both bark (phloem plus cork) and pith tissues which generally are less dense than xylem, so by using the whole twig’s mass you under estimate the density of the wood. Also generally you dry out the wood in a warm oven (50 C) to remove any water present.

  2. #2 Sam K.
    March 30, 2010

    why not just submerge the piece of wood to figure out the volume?

  3. #3 Rhett Allain
    March 30, 2010

    @Sam,

    This way was more fun and less messy.

  4. #4 Mu
    March 30, 2010

    Hmm, how do you get from the second Vmax of 3.972 to the Vmin of 4.9 you use in the density calculation?

  5. #5 rob
    March 31, 2010

    cider!

  6. #6 Josh R.
    March 31, 2010

    What else floats aside com witches?
    Which begs the question: “Can you determine the density of a witch?”
    (even if it is a false nose?)

  7. #7 Frank Noschese
    April 4, 2010

    Churches!

  8. #8 Johnny
    October 18, 2010

    ughhhh im just a kid how am i gunna no how 2 read this???

  9. #9 navid
    February 24, 2011

    hi. density of wood (iron wood & box wood) ?thanks.

  10. #10 Santosh
    May 19, 2011

    Why a piece of wood floats on water and needle sinks into the water even needle has less density

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