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I Doubts on Work-Energy theorem for a system

  1. Apr 4, 2016 #1
    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 [itex]n[/itex] 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. jcsd
  3. Apr 4, 2016 #2
    as the external forces are doing work -its being considered.
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