Here is a question which stumped me when teaching high school students.
The Work-Energy equation can be written as:
$$
W_{ext} + W_{non-conservative} = \Delta{U} + \Delta{K}
$$
Here, $\Delta{U}$ refers to the difference in potential energy of the system in consideration. Potential Energy is nothing but the negative of work done by conservative forces.
I would like to talk about one special potential energy, and that is Gravitational Potential Energy.
Now, let's say I have a block of mass $m$. We write the gravitational potential energy for this block as $mgh$. When doing so, we say that this potential energy is the potential energy of the block-earth system. So, we mean that Earth is a part of our system.
Now, if earth is a part of our system, everything on earth is a part of the system. It means if I am standing near this block and apply some force on it, that force will not be external and hence its work done would not be counted in the $W_{ext}$!! This doesn't make any sense.
As a student, I never looked at gravitational potential energy this way. But now, when I look at it, it is mind-boggling to think the whole earth is part of the system.
Please clarify where my logic/reasoning is going wrong.
Best Answer
The usual approach is to treat the block as the 'system' and Earth as the 'environment.' Then gravity is an external force acting on the system, or stated alternatively: An interaction between the system and Earth. In the energy balance, one may either put gravity in the tally of external work (done on the system), xor introduce a gravitational potential energy to account for it.