Act Two: To Stick a Landing
In my last article, we talked about how pliés are like springs that store potential energy, and that this potential energy can be used to start jumps, turns, and rises. Now, let’s talk about ending those moves, particularly jumps, in a plié and how pliés let us land smoothly.
If you have ever tried landing a jump with straight legs, you would immediately feel the impact rattling your ankles and knees and maybe even all the way up to your shoulders. But, when we land our jumps in a plié like our teachers told us, we feel less impact upon landing. But why does this happen? And what’s the physics behind it?
First of all, we have to see that the center of mass on a standing person is slightly underneath their belly button [1]. However, when we go into a plié, because of the action of bending our knees and shortening the length of our legs, we lower our center of mass [2].
When we go from a jump into a landing, we are basically creating a change in our velocity, from whatever it had been before we land, into a zero-velocity state with respect to the earth. And because our mass remains the same, this change in velocity causes a change in momentum.
p= mv (1)
with p being momentum, m being mass, and v being velocity
This change in momentum is called impulse and is defined as
J=∆p= F ∙∆t (2)
with J being impulse, F being force, and ∆t being the change in time
You might think that landing with straight legs and landing in a plié would have the same amount of force going through our body. After all, if we have the same velocity at the moment before landing and the same velocity after landing (that is, zero), we should have the same change in momentum, and therefore the same impulse and amount of force going through our body when we land, right?
Fortunately for our knees, no. As said above, going into a plié lowers our center of mass, therefore, when we land into a plié, even though our body is no longer moving with respect to the earth, our center of mass is still moving. It only stops moving when we finish our plié.
I have a confession to make. I’ve withheld a little piece of information from you when I defined momentum. The velocity in that definition of momentum (1) is the velocity of the center of mass, and since our center of mass still has a non-zero velocity, we have a non-zero momentum for a longer period of time, mainly, the time that it takes to finish our plié. Therefore, even though we have the same change of momentum between landing in a plié or landing on straight legs, we have different periods of time for our momentum to go to zero. Therefore, we would have a different amount of force going through our bodies.
As we can see from the definition of impulse (2), the longer the time, aka. the bigger the ∆t, to have the same impulse would require less force, and therefore when we land in a plié, there is less force going through our body, leading to a smoother landing and one that will not wreak havoc on our knees.
References
[1] Stephanie Gambino, Michael Mirochnik, Scott Schechter. Edited by Glenn Elert. 2005. “Center of Mass of a Human”. The Physics Factbook. Available on: https://hypertextbook.com/facts/2006/centerofmass.shtml . Accessed on 4th January 2022
[2] Emily Coates and Sarah Demers. 2019. “Physics and Dance”. New Haven and London: Yale University Press.