The definition of work=force x distance. And force=mass x acceleration. So any time you are doing exercise you are doing a certain amount of work, namely, (accelerating your mass) through a distance. Your mass never changes during the exercise, and the distance changes slightly only if you engage in certain modifications on certain exercises. So the same amount of work is being done. What makes the difference on modified exercises is simply that you are recruiting more muscles to help out until the muscles the exercise is designed to target are really strong enough to do it on their own.
Obviously there is more subtlety to the physics than this, but the point is, your muscles are still doing the same amount of work, but certain variables have been adjusted to enable them to push through the full ROM with success as well as challenge.
Calling them fake pushups is just as bad, IMO, because it invalidates the work being done which, for that person, may be their max effort given their fitness level.
Sorry, I'm an engineer
Work = Force * Distance
Force = Mass * Acceleration
In the case of a knee push up, you mass may not change, but the force required to lift your body does. Think of a see-saw or one of the dip machines with weights to assist lifting you. Your legs from the knee down are no longer being lifted the same, the now act to counteract the weight of the rest of your body. Also, there are things called moments which are a force acting a distance from a point that cause rotations. The pushing in your arms is actually counter acting the moment created by your weight. If you are on your knees The length of your body decreases, causing the ratio between the distance of your knees feet to your center of gravity and to your arms to to increase making it so less force required to lift your body.
I'm not saying the work is invalid or less important that the work done by a regular push-up. I think it is part of a progression towards greater strength.
I just felt the need to go more in depth with the physics because I'm a nerd like that. I'll draw it up when I get a chance to make it less than utterly confusing. Who knew physics with just words was difficult.
