conservation of momentum???

Question

this is a homework problem- I'm telling you so you know I'm not trying to cheat. I need help with it, here goes:

1) Inelastic collisions between varying masses: Consider 2 objects of mass m1 and m2 with m1 moving at velocity V_i
and m2 initially at rest. Assume they collide
completely inelastically in 1D.
a. Write the final velocity of the coalesced mass (V_final, v f ) after the collision in terms of the initial masses and velocities.
b. If m1 >> m2 what velocity does the coalesced mass approach?
c. If m1 << m2 what velocity does the coalesced mass approach?
d. If instead, m2 initially has the opposite velocity to m1 (same magnitude, opposite direction) what is the final velocity in terms of m1’s initial velocity?
e. For what m2 will the final velocity in part (d) equal 0? For what m2 (in terms
of m1) will the final velocity equal ½ the initial velocity of m1?
My idea is to compare my answers with those of others.

Answer 1

a. Applying conservation of momentum
m1 x V_i + m2 x 0 = (m1+m2) x V_f
V_f = (m1 x V_i)/(m1+m2)

b. If m1 >> m2 then m1 + m2 -> m1
Therefore V_f = V_i

c. If m1 << m2 then m1+m2 --> m2
Therfore V_f = (m1/m2) x V_i

d.m1 x V_i - m2 x V_i = (m1+m2) x V_f
=> V_f = ((m1-m2)x(V_i))/(m1+m2)

e. m2 = m1, m2 =(1/3)(m1)

Answer 2

In Inelastic collision momentum is not conserved.
Momentum is a mathematical convienience . Motion is better analysed in terms of energy. In collison Energy is directional.Usually there is no such thing as a perfectly elastic collison . there is always an energy loss.That is why in reality momentum is never conserved. The law of conservation of momentum is only an aproximation assuming that the energy loss in collision is neglible.