Perfectly Elastic Collision

Perfectly Elastic Collision

### Conditions

Momentum conservation:

$$m_1u_1+m_2u_2=m_1v_1+m_2v_2$$

Kinetic energy conservation:

$$\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2$$

### Final Velocities

$$v_1=\frac{m_1-m_2}{m_1+m_2}u_1+\frac{2m_2}{m_1+m_2}u_2$$

$$v_2=\frac{2m_1}{m_1+m_2}u_1+\frac{m_2-m_1}{m_1+m_2}u_2$$

### Usage

- Used in ideal collision problems.