Elastic and Inelastic Collisions

In every collision, momentum is conserved (provided no external forces act). But what about kinetic energy? This is where the distinction between elastic and inelastic collisions becomes crucial.

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Kinetic Energy in Collisions

Momentum is always conserved in a collision. Energy is also always conserved — but kinetic energy might not be. During a collision, kinetic energy can be transformed into other forms: heat, sound, deformation of materials, and internal energy.

The amount of kinetic energy retained after a collision determines its classification:

Type	Kinetic Energy	Example
Perfectly elastic	Fully conserved	Collisions between gas molecules, some atomic collisions
Inelastic	Partially lost	Most real-world collisions (car crashes, ball bouncing)
Perfectly inelastic	Maximum loss (objects stick together)	Bullet embedding in a block, cars locking together

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Perfectly Elastic Collisions

In a perfectly elastic collision, both momentum and kinetic energy are conserved:

$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$m1​u1​+m2​u2​=m1​v1​+m2​v2​ $\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$21​m1​u12​+21​m2​u22​=21​m1​v12​+21​m2​v22​