This example illustrates the conservation of momentum (or linear momentum) in a system of two interacting masses. According to the principles of classical mechanics, the total linear momentum is conserved in any collision, so that:
$$ p_{\text{total, before}} = p_{\text{total, after}} $$
where momentum is defined as \( p = m \cdot v \), with \( m \) being the mass and \( v \) the object's velocity.
In an elastic collision, in addition to the conservation of momentum, kinetic energy is also conserved. This implies that:
$$ m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}, \quad \frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 = \frac{1}{2} m_1 v_{1f}^2 + \frac{1}{2} m_2 v_{2f}^2. $$
On the other hand, in an inelastic collision, kinetic energy is not conserved (it is lost in the form of heat or deformations, for example), but the conservation of linear momentum still holds. In a perfectly inelastic collision, the objects stick together after impact and move with the same final velocity \( v_f \), given by:
$$ v_f = \frac{m_1 v_{1i} + m_2 v_{2i}}{m_1 + m_2} $$
Results
| Mass 1 (kg) | Velocity 1 (m/s) | Mass 2 (kg) | Velocity 2 (m/s) | Total Momentum (kg·m/s) | Total Kinetic Energy (J) | |
|---|---|---|---|---|---|---|
| Before Collision | ||||||
| After Collision |