Is there any meaningful (physical) way to compare the energy expended in the exercise of doing $x$ pushups in $t_1$ seconds, vs the exercise of doing the plank for $t_2$ seconds?
I'm confused about the concepts of energy, work, and power, in the case where no distance is traversed.
For instance, take a push-up. I can approximate the work I've done by using the change in potential energy $\Delta U = mgh$, ie. $$W = mg \Delta h$$ $$= m [kg] * 9.8 [m/s^2] * h[m]$$ where $m$ is some proportion of my body mass, and $h$ is a bit less that the length of my arm.
The result has the units of $Newton-meters$, or $kg m^2/s^2$, aka $Joules$. I can also measure the average power of my push-up using $\Delta W/\Delta t$, which has the units of $J / s$, or $kg m^2/s^3$, aka $Watts$.
Fine so far -- but now take a plank (holding the push-up position for some time). Obviously when you do a plank, you are expending some energy, even though you are not doing any work (since there is no change in potential energy). What are you doing then? You are counteracting the force of gravity on your body mass (that is, $9.8 [m/s^2] * mass [kg]$) for a fixed time. This would produce units of $kg m/s^3$ -- these units are not named, that I can recall.
So my question is twofold:
- Is there an actual unit that describes the energy I've expended in doing a plank, beyond $(mass * g * time) kg m/s^3$
- Is there any meaningful way to compare the energy I've expended by doing a plank, with the energy I would expend in doing $x$ pushups? (Beyond work or power, since those values are always zero for the plank, which is not helpful.)