How to conserve energy in case of impulsive forces? While solving various problems on impulsive forces, I find it very non-intuitive apply the principle of conservation of energy. When suddenly a force of very short duration is exerted, it is obvious that the work done by the force has to be zero because the force acted for a very short stint of time, hence we can assume that the net displacement produced in the body while the force was being applied is zero. This clearly implies that the body has zero net work done on it but still the momentum of the body has changed, meaning its kinetic energy has changed. I know that the net energy remains conserved (it is one of the supreme laws of physics and just due to my mere ignorance, I can't question its existence), but can you please tell me whether there is a way through which we can apply conservation of energy in case of impulsive forces.
 A: In "collision" type problems the use of the conservation of energy is usually restricted to those collisions which are elastic (kinetic energy conserved) and those where a given amount of energy is inputted to the system e.g. an explosion).
For all other such problems the energy route is very difficult to follow so the problem is usually solved via the conservation of momentum and from that the loss or gain of energy by the system is found.  
Impulsive forces might act for a short time and not move very far but often tend to be relatively large.
For example if the change in momentum (impulse) of a body of mass $1 \rm kg$ is $1\, \rm Ns$ that represents a change in the velocity of $1\,\rm ms^{-1}$.
If the collision took $0.001 \,s$ then the average force acting is $1000\, \rm N$ which in the context of the problem is probably quite large and even if the force move a small distance that would represent a significant amount of work being done by the force.
In an elastic collision that impulsive force does work compressing the material which acts like a spring and the later that stored spring energy is returned as kinetic energy of the colliding bodies.
In an inelastic collision the compression might result in the irreversible breaking of bonds (permanent deformation of the material) and sending vibrations throughout the material which end up raising the temperature of the bodies (heat).
To quantify such changes other than indirectly e.g. momentum considerations, is very,very difficult and apportioning the amounts which go to produce permanent deformation, heat etc even more so.
A: In case of impulsive forces to apply energy conservation we have to write first energy equation before impact
After impact we have to consider momentum changed by it and write second energy equation
