ELASTIC & INELASTIC COLLISIONS

In a previous example, calculate the total kinetic energy before and after the collision. Remember that energy is a scalar and directions (negatives) are disregarded. $$EK_{Before} = \frac{1}{2}m_1 u_1^2+ \frac{1}{2} m_2 u_2^2$$ $$EK_{After} = \frac{1}{2}m_1 v_1^2+ \frac{1}{2} m_2 v_2^2$$ '''If a collision is elastic''', the kinetic energy before is equal to the kinetic energy after. $$\frac{1}{2}m_1 u_1^2+ \frac{1}{2} m_2 u_2^2= \frac{1}{2}m_1 v_1^2+ \frac{1}{2}m_2 v_2^2$$ In the kinetic theory of gases, it is assumed that all particles undergo perfectly elastic collisions. In reality this is impossible as some energy will be lost to heat, sound etc... Another way to tell if a collision is elastic is that the relative speed of approach is equal to the relative speed of separation between the objects. The way you can visualise this is imagine you are taking the point of view of one of the particles before and after the collision (the rest frame). $$|u_1 - u_2|= |v_1 - v_2|$$ '''If a collision is inelastic''', the kinetic energy is not the same before and after. Although kinetic energy may not be conserved, momentum and total energy are always conserved.