Question regarding systems in work & energy

[Aghle Sorkh]

My professor (for some weird reasons) makes us write "system [body(ies)]" whenever we are asked to solve a physics problem for work and energy. Systems make me completely confused because sometimes if we have two or more systems, then the net work becomes zero. My question is this: How do I know when the net work becomes zero? Please give me examples of writing "system _" when solving a question.

If the above doesn't make sense, here is an example:

Suppose there is a mass on the air with 0 initial velocity. Find the final velocity (assuming force of gravity is the only force acting on it). The way our professor asked us to solve it is by writing "system mass & earth"... in which case the work due to gravity apparently becomes zero (??). Please explain situations where net work becomes zero and where net work is not zero when I include Earth on my system... Sorry for the confusion!

 

[Simon Bridge]

Welcome to PF;

An example where net work is zero:
The net work about any closed path in a conservative force field is zero.
Gravity is an example of a conservative force.

However, you profs example is odd since the path is not closed. But then, you have not fully described it.
I think you need to take us through the example more carefully.

What I suspect is happening is "conservation of energy": in a closed system the total change in energy is zero.
Since work is change in energy...