I am trying to figure out how to calculate the amount of work done for two people of differing sizes (160lb man which is me and 200lb man) in reference to varying exercises we do in the gym.
All this to see which person is in fact doing more workload per pound. I have ideas, but don't know where to start.
For example, if he and I do a clean and press workout at 50% of body weight and both do the same amount of reps in one minute, did we both do equal work?
Additionally, if we both do box jumps, and I do 25 of them at 20 inches high, and he does 20 of them at 20 inches high, same amount of time, are we doing the same work?
Third, pull-ups. If I do 20 pull ups (160lb man) and he does 16 (200lb man), is that the same amount of work, assuming same time they are done in?
Last of all, running. How in the world can we determine who is doing more work when calculating one mile run times? Any help would be appreciated, as I didn't study this in school. It is very intriguing to us to get the science of this so we can determine who is in fact does more work in each exercise.
Best Answer
"Work" in physics and "effort" are very different things. Work is a very useful notion in fundamental physics, but not at all a useful notion in human motion! The heavier person in all of your examples will be doing more mechanical work, even if they both put the same amount of mental effort in. If they both lifted a 50lb weight, they would do the same amount of mechanical work on the weight, but depending on the biomechanics of it the heavier person would probably still burn more calories! It's complicated and isn't well described by simple mechanics concepts.
Your running example is a good one. Fundamental physics tells us that it is possible to travel a mile, so long as the height doesn't change, while doing 0 (or almost 0) work. Yet the human body burns ~100 food calories (=100 kilocalories) in running a mile! We're limited by the engineering of our body, not by physics, so the physics laws don't really apply.
Another example highlighting the absurdity of some things: say you lift ten 700lb weights, and put them each on shelves six feet in the air. Totally superhuman, but how much work have you done? Fundamental physics tells you that the energy done is 10 * (700 pounds) * (9.81 meters/second^2) * (6 feet). Plugging this in to wolframalpha, we see you've expended about 14 food calories of energy (14 kilocalories). That's about the energy in a potato chip.
These are just the limits imposed by fundamental physics. It tells you that any lifting machine must spend at least 14 kcal of energy to lift those weights. It tells you that you can spend as little energy as you want travelling a mile. How to actually achieve those things is a matter of engineering!