Bulllshine. When a falling ball hits the ground it doesn't require any NEW energy EITHER to change direction OR to proceed upwards. Did you seriously study physics? You must be kidding me? When the keybed stops the motion, there is no new energy. You are assuming energy is directional. It most certainly is not. It is based on MAGNITUDE of an instant of velocity and is an absolute that is not in any way linked to direction. Two instants of 10m/s (as you presented) equals the energy level times two (assuming zero conservation in the "bounce"- which does not happen in a piano action, the mechanism actually stores some of that energy, so it's not even double). I'm stunned that you actually studied physics, if you really did. I'm even more stunned that you'd seriously pretend such simple physics is in question, rather than admit to your gaffe. Sorry, but this is simply absurd. Also, keep your talk of "plugging and chugging" physics formulas to yourself. I am referring to the calculations YOU presented in the context that YOU presented them.
Your hand is not a ball.
Forces
are vectors not *scalars* (they are not called "magnitudes"). This means it IS directional. It is the forces and velocities, which are both vectors, which create the squaring effect.
You are still talking about the energy *of* the finger rather than the *"energy required to move the finger"* Which was your mistake I pointed out in your previous posts.
If the finger bounced you would not need to put in this extra energy, but since hands are non-rigid they are incapable of bouncing, so you must exert that force yourself by kinetic-linking...in your own words. Or you could simply lift up but that would be too simple wouldnt it?
If you "plug and chugged" my formula I gave, correctly, you would end up with quadruple the energy. The change in velocity is 20 m/s, it's a single equation not 2. And this isn't a conservation of energy solution either.
And when it reaches the bottom of the key? What happens then? Stop arguing like a lawyer and think like a bloody scientist, for God's sake. Scientists don't duck inconvenient questions.
Well a scientist would say, what state is the finger in? If it's rigid it will bounce. Depending on how much energy is put into making the finger rigid.
I think you're mistaking the careful placement of my words as ducking questions. When in fact my cautiousness is due to my knowing the delicacy of such problems. It comes from experience.
And scientists dodge questions all the time, mostly because the person asking the question clearly has no understanding of the subject and the effort is futile. Maybe I should act more like a scientist and stop responding to you and give you some fun fact you can go home and think about...making yourself feel more scientific.
That's without even going into any of the other inaccurate assumptions that you have leapt to. If you're going to make any more replies, stop leaping to your ridiculous assumptions about what I said and read what I DID say. When I referred to pressing AWAY from the keybed (not into it) how could that possibly lead you to think I'm involving momentum of the whole arm? Quite the contrary. Any arm momentum compresses you IN and not AWAY from the keybeds. To press away It just involves the arms inertia to resist reaction forces as the key moves. I'm not going to spend any more time replying to seemingly random misattributions that I never stated nor even implied. Also, your explanation of kinetic linking is collossally simplified. If energy is sourced in the finger, the ONLY linking with the arm is with regard to the braking effect of the arm's inertia. It doesn't involve a jot of additional momentum. You have massively oversimplified the idea- to the point of factual inaccuracy.
If you're pressing away from the keyboard that tells me you are using your fingers to lift your fingers by pressing down. And considering you were using that statement to "dispel" that you weren't pressing *into the keybed*...I don't see how you could interpret it any other way. Which might I remind you pressing into the keybed is an absolute waste of energy. Atleast when pressing "away" you are doing some sort of work. Albeit that work is useless aswell atleast your moving something.
There is momentum on both the way down and the way up, pressing up is simply converting your momentum into negative (in the opposite direction) momentum.
I really pity you for having to explain this for a 4th or 5th time, but the arm isn't actually connected to the finger for the application of "rigid-body physics" until the muscles are tensed. This is why if I were to come grab your idle index finger and move it 45 degrees, you arm would hardly move with it. Now if you were to flex and make it rigid I could probably move your arm very well.
And you never explained to me why a paddle ball in an airplane isn't harder to play?
.05(310^2) = 4805 Joules
.05(300^2) = 4500 Joules
= 305 Joulesvs
.05 (10^2) = 5 Joules
.05(0^2) = 0 Joules
= 5 JoulesA difference of 6100%, that seems high?
(.1 kg ball, 10 m/s, on a 300 m/s airplane)