So I joke that's there's only one mathematical equation that I know. Seem familiar?
Force times distance equals work
work divided by time equals power
I couldn't show it here but the 3 bar equal sign means "equal by definition" so for us power is equal, by definition, to intensity.
Intensity is where the magis happens. Thats why we like it.
So there are a couple of ways I can increase your power output: increase your force (weight) or your distance.
Oftentimes, these two things are are pretty set. I can't change your body weight (today) and I can't change the length of your arms so the work required for you to do a pull-up is pretty much set by you. (Yes, I can add a weight or use a band to "remove" some of your weight, sure. That is one way I can alter your work load)
I can add more weight to your bar or have you move the weight farther (think thruster vs front squat and how far the bar travels.)
I can decrease the time it takes for you to move.
Take a 200 pound man squatting down 12 inches.
200 x 1 = 200 footpounds (FxD=W)
now add a 200# pound bar to him:
200+200 x 1 = 400 footpounds. More work, right?
Duh- of course it's more work to squat 200#.
So say 200 pound man can do 30 airsquats in a minute:
200 footpounds/1 = 200 ftpounds per minute. Thats his power output.
But it takes him 3 minutes to do 30 of the weighted squats:
400 footpounds/3 = 133 ftpounds per minute.
Sure, he CAN do 30 squats with 200 pounds but he SHOULD do 30 squats at body weight because thats where he has higher power output. His intensity is higher during those body weight squats even though they are *easier* than the 200 pound front squats.
CrossFit is about maximizing power output.
Yes, you need to do the 200 pound squats to get stronger. But you HAVE to do the the lighter, quicker, shorter duration training to maximize power output.
The art is in figuring out the correct weight that maximizes your power output. It's a weight that you can move fast. If you slow down , your power is blunted.
Just because there is an "rx'd" weight on the board and even if you CAN move it --- it doesn't mean you should.