Shoud the total energy of a particle increase when work is done on that particle? Shoud the total energy of a particle$($kinetic energy $+$ potential energy$)$ increase when positive work is done on that particle?
If the answer is yes, then why the total energy does not increase when work is done on a falling object by gravitational force?
 A: Positive work done on a particle by a non-conservative force does increase the total energy of the particle & work done by it depends on the path followed by the particle. On the other hand, gravitational force is a conservative force work done by which doesn't depend on the path followed by the particle & doesn't increase total energy ($KE+PE$) of particle.   
A: I love this question. This is the gist: gravity is a conservative force. What it means is gravity trades one form of "energy" for another. When an object is falling, gravity trades the initial potential energy of the object(due to it's elevation) for speed(kinetic energy). Hence, the same energy takes on different forms and the sum stays the same. With a non-conservative force like a pull from you, the kinetic energy of the body increases in the direction of the applied force. The object that is pulled doesn't convert it's own energy to another form like the ball that is falling from an elevation. Rather, energy is added to the object as positive work is done on it. With gravity however, work is still done on the object as it falls except gravity uses the potential of the object to speed up the same object. Gravity cheats the object into believing it is adding to it's energy when in actual sense it is just using up it's initial energy (potential) to speed it up(kinetic energy). So it doesn't add or remove to the energy of the object. And this is why the total mechanical energy of the body stays the same.
