I very well understand that a lot of people have asked the question "where does potential energy come from" on this site, but mine is more of clarification.
If an object was propelled from the ground to a certain height h, it's potential energy at that height (h) is said to be mgh. Since the final K.E and initial K.E is 0, total work done is also 0. Hence why is P.E = mgh and not 0?. I have a possible explanation for it, but I'm not exactly sure. The force required to propel an object on the ground, to a height (h) , has to be greater than it's weight. Let's label this extra force f', therefore;
F= mg+f'. Where F is the propelling force.
Hence the work done by this force is;
W= mgh+f'h
According to the work-energy theorem,
Kf-Ki= Net work done
Net work done = Net force * distance
Net force = weight+ propelling force
.'. Net force= -mg+mg+f'
Hence: Net force= f'
.'. Net work done= f'h
Therefore Kf-Ki= f'h
Since Kf and Ki = 0,
f'h= 0
Recall, Work done= mgh + f'h
Since f'h=0,
Work done = mgh.
Is any of this correct? If not, Where did I go wrong?