I. Collisions are an example of momentum conservation since the sum of the external forces is either zero or very small. The total initial momentum is therefore equal to the total final momentum.
II. Inelastic Collision
A. Momentum is conserved and total Kinetic Energy is not conserved
B. Most common example in physics courses- objects collide and move off together after the collision. For this COMPLETELY INELASTIC collision only momentum is conserved.
Pinitial = Pfinal
m1v1i + m2v2i = (m1 + m2)vf
III. Elastic Collisions
A. Both momentum and total Kinetic Energy are conserved
B. Conservation Equations
m1v1i + m2v2i = m1v1f + m2v2f
(1/2)m1v1i2 + (1/2)m2v2i2 = (1/2)m1v1f2+ (1/2)m2v2f2