YES! Could I have made any more clear that this is exactly what I am saying? That momentum is REDIRECTED to be absorbed into inertia instead of sent into impact and compression?
As for the nonsense about 4 times the energy (calculations that YOU constructed), I'm not even going to bother (particularly considering your strawman pretence that I claimed forces are not directional- I said that ENERGY is not directional. Feed words into somebody else's mouth.). If you feel it takes new energy input for something to have its velocity changed by hitting the ground, then feel free to base calculations around that (and then presumably pretend that I'm the one to blame for that error too).
Energy is scalar because it includes energy created by things such as heat. Inside scalar quantities you can have vectors. Otherwise we wouldnt be able to use force and velocity to calculate energy.
The momentum is not "redirected" without unnecessary energy input by you. You said so yourself the key lifts your finger when it is relaxed. So why bounce like this when you have a free energy source (after it's depressed) of the weight of the hammer.
When two objects collide they act a *force* on eachother depending on each's momentum. It is not magic, there are forces. In the case of the piano player, to *use* this force requires an energy input to make the body rigid so the energy is not dissipated. Being that the body is so non-rigid, essentially 0 rigidity without tension, the energy input will be equal (and then greater) than the energy output of the force of the impact. For a few reasons, first you have a negative mechanical advantage (lever is closer to folcrum). And a chain is only as good as it's weakest link, you have to match the force with your own body at the lever of impact in order to feel the force of the actual full impact. Otherwise you cannot bounce. Your arm just flops and the table takes the momentum. And there is no bounce just as when you slap your hand on a table. Now if you were to 'follow' through with the flop you would "press" away from the table and lift your hand or your self.
I can't believe you still don't believe me about the 4x the energy. This is like the first thing you learn in conceptual physics. You have to change double the momentum, and then you have half the time to do it (cause it's going faster). It results in quadruple the energy.
You cannot simply redirect momentum a complete 180 degrees from it's direction, without some sort of energy input. Redirecting momentum at all takes energy input. Redirecting in complete 180 degrees requires the most energy, which is what you are doing. And I wouldn't even consider this a redirection as you pass through the origin of the vector when doing this. Once again your true colors of "arm-chair physicist" is coming through. No one I know in their right mind would consider a complete 180 degree turn of a force or velocity a "redirection" That vector is in complete opposition of the "original."
Just to clear this ridiculous nonsense up once and for all, when you throw a ball upwards to be released at 10 m/s per second and let it come down again, let's (very conservatively) say it reaches at least 5 m/s before returning to the height where it set off from. Based on your theory for how calculations are to be made, the ball changed velocity by 15m/s or more, before returning to the starter height. So are you going to feed that figure into the equation? Where is all this kinetic energy being created between start and finish? Based on your theory for how to perform calculations, by the time the ball reached the height it started at, we'd have created a whole bunch of magical free energy. I can scarcely believe that I'm having to argue on such a simple (not to mention pianistically irrelevant) matter.
hahahaha. This is pathetic.
A ball thrown up at a velocity of 10 m/s will have the same velocity on the way down (-10m/s) when it reaches throwing height. Minus wind resistance and air friction. If the ball came down at 5 m/s that is one *very* windy day. Windy in a upwards fashion none the less. lol.
And then you have the "brilliance" to say this is a conservative estimate...
Face.
Palm.
And this example you're giving me is not an impact, but a constant acceleration of gravity. A completely different problem. In this case only one of the "v^2"'s is actually changing and that is the momentum. The other velocity, of the change in momentum, is unchanging. In simpler terms the change in momentum is happening at the same velocity in both the up and the down swing, which tells us that the acceleration of gravity is constant (9.8m/s/s). That's good, I like the gravity to be constant.
If this change of "15 m/s" were to happen in the same time frame as a 7.5 m/s change, impossible in terms of gravity, then yes the energy required would be quadruple. Not in this poorly constructed problem of yours though.
Do you really treat discussion of science like a defence lawyer treats a court case- purely with a view to hoping to "win" at all costs? Or can you honestly not see what transparently bogus use of the equation you made? Are you going to file a patent on your energy creation scheme- or are you going to admit that you completely misused the equation?
You have made absolutely no argument against my "equation" you have only stated that it is wrong. I'm very happy that "science" as your calling it, doesn't work on statements alone. If it were it wouldnt be very useful, and hardly scientific.
It is your equation with the gaping hole in it, and you still haven't addressed the paddle ball issue. Which by the way is a much fairer comparison to your theory, than your "issue" was in comparison to mine. Mine has the same actions only in different places, yours is a completely different situation.