Elastic collision is a collision in which momentum and kinetic energy are conserved
<aside> 📌 Conservation of kinetic energy is the total kinetic energy of two objects before a collision is equal to the total kinetic energy of the two objects after the collision
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An inelastic collision is a collision in which momentum is conserved, but some kinetic energy is lost
<aside> 💡 Perfectly elastic collision is an ideal collision in which external forces are minimized (or negligible) to the point where momentum and kinetic energy are perfectly conserved $\frac{1}{2}m_1v_{i_1}^2 + \frac{1}{2}m_2v_{i_2}^2 = \frac{1}{2}m_1v_{f_1}^2 + \frac{1}{2}m_2v_{f_2}^2$
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Perfectly inelastic collision is an ideal collision in which two objects stick together perfectly so they have the same final velocity; in this situation, momentum is perfectly conserved, but kinetic energy is not
In a system that cannot exchange any matter or energy with its surroundings (isolated), the total momentum of the system is conserved for all elastic, inelastic, perfectly elastic, and perfectly inelastic collisions
$m_1\overrightarrow v_{i1} + m_2 \overrightarrow v_{i2} = m_1\overrightarrow v_{f1} + m_2 \overrightarrow v_{f2}$