What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day

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Q. What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day to day life for inelastic collision.

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Concept understanding — Perfectly Inelastic Collision

Perfectly Inelastic Collision

Imagine two lumps of wet clay flying toward each other. When they hit, they don't bounce apart — they squash together into one bigger lump and keep moving as a single object. That's the core picture: the colliding bodies stick together and move with a common velocity after the collision.

This is the defining feature of a perfectly inelastic collision. It's the most extreme case of inelasticity — the bodies lose their separate identities and become one.

Why "Perfectly Inelastic"?

The word "inelastic" means kinetic energy is not conserved. In any real collision, some kinetic energy transforms into heat, sound, or deformation. A perfectly inelastic collision takes this to the maximum: the bodies deform so much that they lock together, and the kinetic energy loss is as large as it can possibly be — while still obeying the law of conservation of momentum.

Watch out

Do not confuse "perfectly inelastic" with "total energy loss." Momentum is always conserved in any collision (in the absence of external forces). Kinetic energy is not — and in this case, it's reduced to the minimum possible value.

The Precise Statement

For two masses $m_1$ and $m_2$ moving with initial velocities $u_1$ and $u_2$ along a straight line, after a perfectly inelastic collision they move together with a common velocity $v$ .

Conservation of momentum gives:

m_1 u_1 + m_2 u_2 = (m_1 + m_2) v

So the common velocity is:

v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2}

This is simply the velocity of the centre of mass of the system — which remains unchanged throughout the collision.

The Kinetic Energy Loss

Before collision, the total kinetic energy is:

K_i = \frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2

After collision, with both masses moving together:

K_f = \frac{1}{2} (m_1 + m_2) v^2

The loss in kinetic energy is:

\Delta K = K_i - K_f

You can show (by substituting $v$ and simplifying) that:

\Delta K = \frac{1}{2} \frac{m_1 m_2}{m_1 + m_2} (u_1 - u_2)^2

This is the maximum possible kinetic energy loss for a given pair of masses and initial velocities, consistent with momentum conservation. Notice it depends only on the relative speed $(u_1 - u_2)$ and the reduced mass $\frac{m_1 m_2}{m_1 + m_2}$ .

Tip

If one body is initially at rest ( $u_2 = 0$ ), the loss simplifies to $\frac{1}{2} \frac{m_1 m_2}{m_1 + m_2} u_1^2$ . The larger the mass of the stationary body, the more energy is lost.

A Quick Check: The Coefficient of Restitution

The coefficient of restitution $e$ is defined as: …

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Step 1. Definition. An inelastic collision is one in which the total kinetic energy of the colliding bodies before the collision is not equal to the total kinetic energy after it -- some of it, $\Delta Q$ , is converted into heat, sound, light, or permanent deformation during the impact.

Step 2. Difference from elastic collision. Both elastic and inelastic collisions always conserve total linear momentum (a direct consequence of Newton's third law, independent of collision type). The difference lies entirely in kinetic energy: an elastic collision conserves it exactly, while an inelastic collision does not. Correspondingly, the forces active during an elastic collision are conservative (fully recoverable), while those in an inelastic collision are non-conservative (energy is genuinely lost from the mechanical system, as heat etc.).

Step 3. The most extreme inelastic case is the perfectly (completely) inelastic collision, where the bodies stick together and move with one common velocity $v=(m_1u_1+m_2u_2)/(m_1+m_2)$ -- this loses the maximum kinetic energy possible for the given initial momenta. …

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Q.What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day to day life for inelastic collision.

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