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Pointe Shoe Physics



When I was a little girl learning to dance, I dreamed of the day that I would put on a pair of pointe shoes and twirl like Clara from Tchaikovsky's "The Nutcracker".  Little did I know that pointe shoes make dancing about a million times more difficult and more painful.  Besides the basic discomfort that a ballerina experiences when squeezing her foot into an unconventionally shaped and small shoe, there are also a great amount of physics that go with explaining why pointe shoes are not the dreamy things that they appear to be.  For starters, the pain is unbearable, and the reason why has to do with the combination of surface area and gravity.  When a person walks normally, they are displacing the force of their body (their mass multiplied times their acceleration), over their two feet.  When you think about, that is actually a relatively small surface to hold up a human's weight, but because human feet grow with weight as children mature into adults, holding up one's weight on two feet is not a burden; rather, it is quite natural.  When a ballerina first begins to dance, she learns to "twirl" and pirouette on "demi-pointe," or quite simply, on the ball of her foot.  Doing so divides the surface area for weight distribution in half, which makes it more difficult to oppose the force of gravity that may pull her off balance.  After years of strength build up, dancing on demi pointe becomes almost as natural as walking because the ballerina has gained the strength to hold up her same weight over a smaller surface area.  However, when a ballerina puts on her pointe shoes, she nearly quarters the surface area which she had to work with when she danced on demi pointe.  In pointe shoes, all of the ballerina's weight is centered on a surface area that is about one by two inches.  Even if the dancer's weight has not changed, because the surface area is reduced, the force of her weight is all on her toes, which in real life would have very little experience in holding up the weight of a human.  This strong force often times does work (W=Fd)  on the dancer's toes; gravity pushes the toes further down into the pointe shoe, and the friction between the shoes and toes does work on the toes as well, causing them to burn and bleed.  Also, because pointe shoes lower surface area, the ballerina must adjust her center of mass to be over her her toe so she does not fall, when naturally the center of mass of a human is more so centered over the middle of the foot.  Crazy to think that so much physics goes into just putting on and standing in a pointe shoe, let alone dancing in one, but for all little ballerinas, they dream of that moment.

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Yikes.  This scares me a bit.  Sure hoping my little one decides to switch from ballet to another activity before we get to the stage of pointe shoes...

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