Well, this will really make you ponder where the force production and power is coming from, with kettlebell snatches...
My guess is that 30-40% of the power comes from the upper body and the rest from the lower body. Why? I can 1 hand swing 40kg to about shoulder height without involvement of the upper body (using the arm as a rope, basically). This is very hard, and I doubt I could swing a heavier weight to horizontal. However, I can snatch 40kg, that is, if I use the upper body, the kettlebell can go overhead. There is no way I could "overhead swing", or "american swing" 40kg. So, the lower body gets the kettlebell from arm pointing down to arm horizontal. The rest of the energy needed to overcome gravity must come from the different mechanics, and involve the upper body. Why not 50%? Because when you hinge, your arm will get lower than if you keep your knees straight, so a bit more energy is needed for the "lower half" of the swing"snatch" than the "upper half".
Of course, this is not an exact calculation, and the mechanics of the two movements differs, but I think this is in the right ballpark. In fact, if you don't snatch for a while and get back into it, your upper body will let you know on the next day...
It's neat how much force you can produce without actually moving much at all.
Indeed. Makes me think of Bruce Lee's one-inch punch, and many other martial art techniques.
I also use this to surprise opponents with my punch volleys in tennis. A punch volley is, as its name implies, a volley in which you hit the ball head on, with the goal of hitting hard. Kind of a "low smash". However, you usually don't have time when you volley to take a long swing. What I do, is I tense my whole body and do a very small but quick movement when I hit the ball that can send the ball flying.