I have an idea that there must be at least a little work [itex]\epsilon[/itex] being done during this process(static).
I assume that, in static system, to push something with a constant force and there was no work done on the object, our body has already lose its energy of [itex]\epsilon[/itex] Joules. This energy can be described as the work deterring the object from its moving. Also, [itex]\epsilon[/itex] is equal to the work deterring us from our moving(3rd Newton's law of motion).
I have
[itex]F = \mu\alpha = \mu\frac{d^{2}}{dt^{2}}\varsigma[/itex] ;
for pretending mass(of arm) [itex]\mu[/itex]
pretending acceleration(of arm) [itex]\alpha[/itex]
and pretending distance(of arm) [itex]\varsigma[/itex]
that is [itex]\varsigma = Ft^{2}/2\mu[/itex]
So I have [itex]\epsilon = \int Fd\varsigma = (Ft)^{2}/2\mu[/itex]
The quantity [itex]\mu[/itex] is what I'm interested.
In the case of lifting object, I see that there must be some relation between the angle of arm and [itex]\mu[/itex]
I don't know, but it must be like [itex]\mu = \mu_{0}/sinθ[/itex]
that is [itex]\epsilon = (Ft)^{2}sin\theta/2\mu_{0}[/itex]
I want to check my assumption with an experiment. Anyway, I decided not to play with ATP or respiration because I have no experience about them(which may cause an error). I'm interested in mechanical device, analogous with our arm. May be, there should be a device that could measure amount of potential energy of spring or some sort of this. but I have no idea.