For Spencer,
The point I want to make clear to you is that using the notion of "power" as the simple math you learn from elementary school physics is really inappropriate and mostly useless or misleading when talking about training. Of course it's nice that it's simple, the problem is that it's the wrong math to use here, for so many reasons.
Chris should have explained why the example he gave should not be interpreted this way as I am sure he was just using it as an example to make a very different point (just that it takes more force and effort to move a heavy weight faster and that this -could- be used in training too, emphasis on the could rather than -must-).
To explain this further: For one, your definition and the example Chris used use work as displacement times force, which gives you a value of zero if you don't move, like in holding an iron cross, yet you should know very well that you still obviously use a ton of energy, stimulate muscle strength increases and muscle growth. You are producing forces often against non-ideal leverage angles, to fight gravity. It's like taking a large truck with a powerful engine revved up, set in drive gear and with your foot on the gas pedal, but the truck is connected with a cable to something so massive and heavy that it won't bulge, leaving your simplified definition with zero work and zero power. But it should be now obvious to you that it's not (it's however much horsepower the engine is producing despite the lack of motion of truck+cargo, if it made it easier for you to think, it's the same power you would compute looking at the car moving without cargo).
As I already mentioned, while you -can- use things like plyometrics to develop strength with lighter loads, you can also develop strength without ANY effective motion at all, for example isometric holds at different fixed positions of a specific motion (just to get the benefit of full range anyways).
Power would be interesting only if you wanted to know how much damage you would do to your face if you accidentally hit yourself in the face with the barbell you are lifting, obviously more if it picked up velocity. And even there you should realize that displacement and velocity builds up over time from a constant force (think of a train accelerating after a stop), so actually again you could even use 100% of your power against a weight for such a small time that the object would move very little and still slowly, while using less strength but for longer contraction would allow the weight to pick up more velocity, a situation where the opposite would happen.
And more importantly, we are talking about multiple muscle fibers here, mostly independently contractable. Each muscle fiber will feel a fraction of the total weight based on how many you can recruit simultaneously (which also changes with fatigue, adaptation, etc), which is another important reason why it's really bad to talk about total power etc as if it was a fixed quantity, because even when it is, the actual final output is not what we care about during training.
During training what we care about is how each fiber feels the training stimulus, and how other parts of the body like neural pathways and hormonal and metabolic changes also respond and adapt, creating increases in our ability to generate strength, power etc.
In fact even eating different food, taking steroids, or even doing training that doesn't even involve muscle contraction exercises can increase your strength, because again it's a physiological adaptation based on many factors, not some kind of magical replication of the exact movements you did in training. Specificity of training exercises can be very useful in most circumstances, but you don't want to invoke a good rule-of-thumb thing to actually make wrong predictions like that nothing else can ever produce strength and would actually reduce it.
For Jonsmith,
With your odd guarantee you are making the same wrong assumption (in the opposite direction) that started this thread, the main point is again that there is no magical difference between weighted or body-weight exercises, they can both be good exercises, and your muscle fibers don't even know if they are contracting because you are lifting a particular weight from the ground or because you are at an odd angle and lifting an equivalent fraction of your bodyweight in the same motion. There are 'practical' tradeoffs in each (generally easier or harder to add exact extra weight, to involve multiple muscles and support muscles together, train balance and other aspects simultaneously etc), but those are not fundamental differences related to bodyweight or weights themselves but more with the way people generally tend to use them differently.
