- #106

etotheipi

A.T. said:More abstract means more general, more widely applicable and thus more useful. The concept of using P = F * v at an interface doesn't just apply to friction:

Instead of surface irregularities that oppose relative motion, you could have many little ants or linear motors propelling the block, which you also don't want to model in detail. Here the sum of the work done by the force pair would be positive. This represents mechanical energy generated at the interface (converted from chemical or electrical).

The whole issue becomes even more fun if an object has two interfaces, with two other object that are in relative motion to each other.

That Blackbird is a pretty crazy machine! The one other thing I got from it is that we can use either real work or centre-of-mass work at the interface, but to compute different quantities. If we choose centre-of-mass work,

##P_{CM, tot} = P_{CM, 12} + P_{CM, 21}## and then also ##P_{CM, tot} + \dot{E}_{int} = 0## if the whole thing is isolated; the total centre-of-mass power equals the negative rate of change of internal energy (which in this case, means everything except translational kinetic) right off the bat.

If we choose to analyse real work, it's a little bit more convoluted.

##P_{RE, tot} = P_{RE, 12} + P_{RE, 21}##

on each body,

##P_{RE, 12} + \dot{Q}_{1} = \dot{E}_{1} = \dot{E}_{int, 1} + \dot{E}_{CM, 1}##

##P_{RE, 21} + \dot{Q}_{2} = \dot{E}_{2} = \dot{E}_{int, 2} + \dot{E}_{CM, 2}##

Of course since the system is isolated, ##P_{RE, tot} = -\dot{Q}_{tot}##. I don't know how to

**derive**it, but I assume it is the case (from the previous discussion) that the total

*real*work done equals negative the change in

**, and not just internal as was the case when we considered COM work. In essence, the total real work done at the interface is the change in mechanical energy, whilst the total COM work done at the interface is the change in translational KE.**

*thermal*energy onlyIn the case of the block and wedge, the centre-of-mass work and real work turn out to be identical, and this is fine since there is only translational KE involved. For the Blackbird, there

*is*rotational KE involved in the turbine, so we need to be a little more careful.

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