# Proof of KE loss in inelastic collision

1. Oct 20, 2015

### Xizel

1. The problem statement, all variables and given/known data
Prove that a perfectly inelastic collision loses more kinetic energy than a partially inelastic collision. Given: $$m_1, m_2, v_{1i}, v_{2i}, v_{1f}, v_{2f}$$

2. Relevant equations
$$KE = \frac{1}{2}mv^2$$

3. The attempt at a solution
From conservation of momentum:
$$P_{inelastic} : m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f$$
$$P_{partial} : m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$$

I'm not sure how to progress from this. Thanks.

2. Oct 20, 2015

### Simon Bridge

Compare energy before collision with energy after collision for each case.