Irodov Problem 1.168

In an perfectly elastic collision and there are no external forces on the system of particles, both energy and momentum are conserved. So we have have (please refer to the figure beside),




From (1) , (2) and (3) we have,




The fraction of energy lost by mass m1 is give by,





b)





In case of a head on collision the two masses will continue to move along the same line. Since the collision is elastic both momentum and energy of the system will be conserved.





From (1) and (2) we have,









The fraction of energy lost by mass m1 is give by,

Irodov Problem 1.167

At with problem 1.166, the final velocity v of the fused masses is given by . The loss in kinetic energy is given by,

Irodov Problem 1.166

In a perfectly inelastic collision the two masses will fuse and start to move together. Since there are no external forces acting on the system of particles the momentum of the system must be conserved. Let the masses be m1 and m2 and their corrosponding velocities prior to collision be v1 and v2. Let v be the final velocity of the particle. Then we have,
m1v1 + m2v2 = (m1+m2) v.

So in this problem the final velocity will be [3i -2j + 2(4j -6k) ]/(2+1) = i + 2j - 4k