Work done over a closed loop Is it true that the work done in the motion of a body over a closed loop is zero for every force in nature?
 A: No, there are the so-called conservative forces, for which it is of course true (like the gravitational field). However there are such forces in newtonian mechanics such as friction, for which it is not true. Bet I still think you ment the gravitational or for ex. electrostatic force.
A: Yes, every fundamental force of nature is a conservative force, which means that it can be expressed as the gradient of a potential energy, and that it does no work over a closed loop. Every fundamental force respects the principle of conservation of energy.
Some emergent forces, such as surface friction and fluid drag, do not seem to be conservative at first glance. However, these forces are actually just very complicated interactions of the fundamental forces (such as electromagnetism) acting on a very large number of particles. The forces are still conservative on the micro-scale; it's just that, on the macro-scale, you can almost never actually construct a closed loop motion of any of the bodies. So if you put a paddle into water and spin it clockwise and then counter-clockwise, the reverse motion doesn't recover the energy expended in the forward motion because it's not actually re-tracing the same path back through configuration space that it initially followed. If you somehow could achieve that perfect reversal, you'd find that by precisely reversing the collisions between all of those water molecules and the paddle, you'd end up returning all the energy back to the paddle, and undoing the work that was done on the water.
For engineering and computational simulation purposes, it's useful to think of forces like friction as being dissipative forces distinct from others and damping closed-loop motion, because it lets us predict accurate results without having to keep track of the huge numbers of particles that real material objects are made of. But from a theoretical physics point of view, all the forces are actually conservative.
A: Actually, there is a non-conversative force which does work along a closed loop. It is produced by an electric field which on its part is generated by a time-varying magnetic field (Faraday's law). The general definition of the electric field looks like this in cgs-system: 
$$\mathbf{E} = - \frac{1}{c}\frac{\partial \mathbf{A}}{\partial t} -\nabla \phi$$
It is often forgotten that the electric field generated by a non-zero time-varying vector potential is non-conservative. In order to make even more clear it is useful to write down Faraday's law:
$$\oint \mathbf{E}d\mathbf{r} = -\frac{1}{c} \int_S \frac{\partial \mathbf{B}}{\partial t} d\mathbf{F}$$ 
The amazing fact is that there is a physics device which uses this effect: the betatron.
Between two poles of an electromagnet an electron beam is circulating in a loop. There is no radio frequency device providing the electrons with energy. The ramping of the magnetic field in time changes $\mathbf{A}$ respectively $\mathbf{B}$ which on its part creates the electrical field which has closed loop field lines. The electrons following the closed electrical field lines get more and more energy on each revolution. So non-zero work is carried out by this non-conservative (electric) field.
