# Momentum and collisions

1. Aug 25, 2011

### Hanga

This is not dircectly a coursework question, rather I need someone to tell me what is correct and what is not correct in my assumption of Momentum and collisions, esp conservation of linear momentum.

For some reason I stand to belive there are two diffirent equations for conservation of linear momentum Pbefore=Pafter. In one case we have

m1u1+m2u2 = m1v1m1v2

In the other we have
1/2m1u1^2 + 1/2m2u2^2 = 1/2m1v1^2 + 1/2m2v2^2

For some reson I stand to belive that they are for Perfectly inelastic collisions and Elastic collisions respectivly. Is this the case? Is there some "key word" in a work question that I can look for to say "Ah! I'm going to have use equation x"?

2. Aug 25, 2011

### Pi-Bond

Conservation of momentum is only the first equation you wrote. The second one is the conservation of energy (the expression assumes the potential energy remains constant). Kinetic energy is conserved along with momentum in an elastic collision.

3. Aug 25, 2011

### Staff: Mentor

Perfectly elastic collisions (Momentum and kinetic energy are both conserved):
$m_1 u_1 + m_2 u_2= m_1 v_1 + m_2 v_2$ and $\frac{1}{2}m_1 u_1^2 + \frac{1}{2}m_2 u_2^2 = \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2$

Perfectly inelastic collisions (Only momentum is conserved):
$m_1 u_1 + m_2 u_2 = (m_1 + m_2) v^2$