Martial Science

“Magical” Pencil Balancing

I have heard a quote going around lately that says something along the lines of “the difference between science and just screwing around is weather or not you have someone writing it down.” I find this quote to be oddly satisfying because it accurately represents what I do on a daily basis. I spend a lot of time learning through experimentation and screwing around, and it is a jolly good time!

However, today I will not be screwing around, but instead I will be doing actual science by writing it down. In my English class, I found that by bending a piece of paper by just a bit I can give that paper enough stiffness to hold up two pencils by their little tabs. What made me so proud of this little structure is that I actually knew a bit of the martial physics at play here even though I did not actively recognize them.

One of my mentors in robotics, Mr. Coulombe (only one letter away from the name of the Law!) works as a programmer and structural engineer, and it his jobs to run massive computer simulations of individual atoms in materials acting upon each other. He is the smartest person I know, and has given me the honor of having mini-lessons on this particular science.

Basically, to make this work I had to slightly alter the martial properties of the paper so the paper would stand up on its own. When a piece of paper comes out of the factory, the cellulose molecules that compose it form a fairly imperfect lattice. By rolling the paper into a circle and back out again, I was working out those imperfections so that the lattice would slowly become more and more perfect. This causes the paper to become more and more brittle (and less ductile), and this brittleness makes the paper tend to form in a certain shape that is more stiff than otherwise. Because the paper rests in a stiffer and curved shape, it is able to be put onto its side without falling over. In addition, the added brittleness allows the paper to support slighly more weight before it starts to fail. This extra ability to bear weight allowed me to place the two pencils onto the paper without the paper caving in on itself.

However, the paper’s ability to hold the pencils weight is only one part of the mechanics at play here. The other part can be assessed by asking: How does the weight from the pencils not cause the structure to fall over? The answer to this question is far more simple, as it has to simply do with the idea of center of mass and the position of the pencils. In the picture, the pencils can be seen to be on the inside part of the curved paper. This would typically case the paper to fall in the same direction that the more massive part of the pencil is on, but it does not do this due to the support given by the outer parts of the paper curved in the same direction that the pencils are applying the sideways force. The pencils are safe on the inside of the curve, but would cause the paper to top if they were on the outside of the curve.

The application of the rules at play here go beyond balancing pencils on pieces of paper; they are used in architecture, mechanical engineering, and even aviation. By learning and applying the knowledge science has recorded, humanity had engineered the most amazing devices that are taken for granted every day.


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