One of the sweetest gifts a student gave me years ago was a poem she had a written for an English class titled "The Music Machine." It was not about how the piano works, which we had discussed in lessons, but showed how much the student loved music and related to the piano.
On a more practical level, the piano is a machine, and it does require an understanding of how the machine works and how good body mechanics can help a musician play the piano easier and better.
I always discuss with students that the keys on the piano are levers (one of the simple machines most students learn in elementary school). You press a key which flips a hammer up to strike strings that vibrate and create sound. How fast the key goes down determines whether you end up with a strong (forte) or soft (piano) sound. This is how the piano machine works.
While most (competent) piano teachers emphasize good hand position, I am not sure all of them understand why and how it affects the lever/machine aspect of playing the piano. The fulcrum (the point where force is transferred from the key/lever to the hammer) is hidden under the fallboard of the piano. The farther away from the fallboard/fulcrum that the fingers push down on the keys/levers, the more control you have over the keys/levers. If you try to push down a key close to the fulcrum/fallboard, it is very difficult to do so with any control.
So why do we curl our fingers. trying to get approximately a 90 degree angle from our middle joint to our fingertips? This is body mechanics and the machine working together. The curled fingers allow each of our fingers to push the keys at approximately the same distance/angle from the fulcrum and creates a more uniform sound. Some music lesson books say to lay your thumb's side on the keys, but that means your thumb is approaching the keys from a different angle than the rest of your fingers, and will make your thumb whack the key! Laying the side of your thumb on the key will also pull down the rest of your curled fingers, ruining your angles. You CAN lift your thumb and curl it so it does come towards the key more like the other fingers, creating the more desired uniform sound.
Why do we keep our elbows away from our body and wrists level (no dipping or arching)? Two reasons. First is to support the curled finger position of our hands. Second, so we can move quickly across the keys without any unnecessary up and down motion of our hands or elbows. This allows us to play faster and with more dynamic control.
As a pianist and piano teacher, I love music and love teaching. But I also love science. Understanding basic science can help me and my students play our music machines better!