I Doubts on Work-Energy theorem for a system

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1. Apr 4, 2016

Soren4

While studying energy conservation on Morin I found this explanation about the work-energy theorem for a system.
Using Koenig theorem $$\Delta K_\textrm{system}=\Delta K +\Delta K_\textrm{internal}$$ so we have

I've got two main question on that:

1. Why are only external forces considered for the work?
2. How is the formula above related to the following? $$W_{conservative}=-\Delta V$$
Here are my consideration/doubts:
1. Considering a system of $n$ material points the following holds.
$$\sum W=\Delta K_\textrm{system}$$
But here $$\sum W=\sum W_{i}=\sum \left(W_{i}^{(\textrm{ext})}+W_{i}^{(\textrm{int})}\right)$$
The amount of work considered is the sum of the work done on each point (both from external and internal forces).
And in general we do not have that $$\sum W_{i}^{(\textrm{int})}=0$$
Counterexample: two masses attracting each other gravitationally.

2. If we use the formula reported above we have $$W_{external}+W_{conservative}=\Delta K$$
But does this make sense?

2. Apr 4, 2016

drvrm

as the external forces are doing work -its being considered.