total energy of a system?
if we consider the total energy of system its mechanical energy (E=K+U ;K is kinetic, U is potential)
then how can we determine each of the two in a multi-body system; for example :
► a body sliding on a slope and dragging a rope on a pulley (the body+ the pulley)
► three bodies interacting gravitationally (a planet + some of its satellites)
Comments
Ah, but you missed one of the tricks of the trade. You define both bodies, e.g., planet and satellites, as one system. Hey, we do call it the solar "system."
We define a system so that it is closed when we can. That simplifies a lot of calculations. Even if there is some input/output with the outside, if it's negligible, we will define the system as closed.
In which case, total energy TE = pe + ke + qe is the general case for that system where pe is stored energy, ke is kinetic, and qe is other, like friction heat or sonic energy.
Note, pe does not have to be mechanical. In fact, pe = e = mc^2 is a prime example of stored energy that is not mechanical; this is energy stored as rest mass. In fact we can show the total energy of a particle with rest mass m is TE = sqrt((mc^2)^2 + ke^2).
Anyway...pick and define your system wisely. It can save a lot of grief come problem solving time.