It is defined that a constant force is conservative. Does this mean that the work of this force won't change the mechanical energy of the system?
Example: a constant force pulls an object from A to B: its work doesn't depend on on the path so the force is conservative but its work is added to the mechanical energy of the system so the Em is not conserved? Where do I miss something?
Here the force is conservative because of being constant and its work doesnt depend on the path (same Work if moved along the dotted lines) but its work change Em ! ?
Answer
No, a conservative force can definitely change the mechanical energy of an object. And yes, the net work does not depend on the path that is taken. If however, the force acts along a closed loop, the net work which is done equals zero. And yes, it is easy to find a potential for a constant force. Example: $$ \vec{F} = c \cdot (\vec{e}_x + \vec{e}_y + \vec{e}_z)\\ \Phi = -c\cdot (x +y + z) \\ F = -\nabla \Phi $$ So note that the total energy of the system can change and only if you perform a closed loop, the net work done by the conservative force will be zero.
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