What is the primary difference between an elastic and an inelastic collision?

The primary difference lies in the conservation of kinetic energy. In an elastic collision, both linear momentum and kinetic energy are conserved. The objects rebound perfectly without any loss of kinetic energy. In contrast, in an inelastic collision, while linear momentum is conserved, kinetic energy is *not* conserved. A portion of the initial kinetic energy is transformed into other forms of energy, such as heat, sound, or deformation energy, leading to a net loss of kinetic energy from the system.

Is linear momentum always conserved in an inelastic collision?

Yes, absolutely. The principle of conservation of linear momentum states that if no net external force acts on a system of particles, the total linear momentum of the system remains constant. This principle holds true for *all* types of collisions, whether elastic, inelastic, or perfectly inelastic. The internal forces between colliding bodies, though large, are internal to the system and do not change the total momentum of the system.

What is a 'perfectly inelastic collision' and how is it different from a general inelastic collision?

A perfectly inelastic collision is a special type of inelastic collision where the colliding objects stick together after impact and move as a single, combined mass with a common final velocity. This results in the maximum possible loss of kinetic energy consistent with the conservation of momentum. A general inelastic collision, on the other hand, involves kinetic energy loss, but the objects do not necessarily stick together; they might separate, but with a reduced relative velocity compared to their approach. The coefficient of restitution is zero for perfectly inelastic collisions and between 0 and 1 for general inelastic collisions.

How do we calculate the kinetic energy lost in an inelastic collision?

The kinetic energy lost in an inelastic collision is simply the difference between the total kinetic energy of the system before the collision and the total kinetic energy after the collision. That is, $\Delta KE = KE_{initial} - KE_{final}$. For a one-dimensional collision, a general formula for kinetic energy loss is $\Delta KE = \frac{1}{2}\frac{m_1m_2}{m_1+m_2}(u_1-u_2)^2(1-e^2)$, where 'e' is the coefficient of restitution. For a perfectly inelastic collision ($e=0$), the loss is maximum and given by $\Delta KE_{max} = \frac{1}{2}\frac{m_1m_2}{m_1+m_2}(u_1-u_2)^2$.

What is the significance of the coefficient of restitution (e) in inelastic collisions?

The coefficient of restitution (e) is a crucial parameter that quantifies the degree of elasticity or inelasticity of a collision. It is defined as the ratio of the relative speed of separation to the relative speed of approach of the colliding bodies. For inelastic collisions, 'e' lies in the range $0 \le e < 1$. A value of $e=0$ signifies a perfectly inelastic collision where objects stick together, indicating maximum kinetic energy loss. Values closer to 1 (but less than 1) indicate less kinetic energy loss, meaning the collision is 'less inelastic' or 'more elastic'.

Can an inelastic collision occur in two or three dimensions?

Yes, inelastic collisions can certainly occur in two or three dimensions. The principles remain the same: linear momentum is conserved as a vector quantity, meaning its components along each axis (x, y, z) are conserved independently. However, kinetic energy is still not conserved. Analyzing 2D or 3D inelastic collisions involves resolving velocities into components and applying momentum conservation along each perpendicular axis. For example, a billiard ball hitting another at an angle, where some energy is lost due to friction or deformation, would be a 2D inelastic collision.

Inelastic Collisions

Q: Can an inelastic collision occur in two or three dimensions?

Yes, inelastic collisions can certainly occur in two or three dimensions. The principles remain the same: linear momentum is conserved as a vector quantity, meaning its components along each axis (x, y, z) are conserved independently. However, kinetic energy is still not conserved. Analyzing 2D or 3D inelastic collisions involves resolving velocities into components and applying momentum conservation along each perpendicular axis. For example, a billiard ball hitting another at an angle, where some energy is lost due to friction or deformation, would be a 2D inelastic collision.

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Version 1Updated 22 Mar 2026

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An inelastic collision is a type of collision in which the total kinetic energy of the system is not conserved, although the total linear momentum of the system remains conserved. During such a collision, some part of the initial kinetic energy is transformed into other forms of energy, such as heat, sound, or internal energy causing deformation of the colliding bodies. This energy transformation …

Quick Summary

Inelastic collisions are fundamental interactions where objects collide, and while their total linear momentum is always conserved, their total kinetic energy is not. A portion of the initial kinetic energy is transformed into other forms like heat, sound, or deformation energy.

This energy transformation means the system's mechanical energy decreases. The degree of inelasticity is quantified by the coefficient of restitution, 'e', which ranges from $0 \le e < 1$ . A perfectly inelastic collision is a special case where objects stick together after impact, moving as a single unit, and experiencing the maximum possible kinetic energy loss.

Understanding the conservation of momentum and the non-conservation of kinetic energy, along with the concept of 'e', is crucial for solving problems related to inelastic collisions, especially common scenarios like bullet-block systems in NEET.

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Key Concepts

Conservation of Momentum in Inelastic Collisions

Even though kinetic energy is lost, the total linear momentum of the system remains constant in an inelastic…

Perfectly Inelastic Collisions and Energy Loss

In a perfectly inelastic collision, objects stick together and move as a single unit. This is characterized…

Coefficient of Restitution (e) and its Range

The coefficient of restitution, $e$ , is a measure of the elasticity of a collision. It is defined as $e =…

Linear Momentum (p): —

\vec{p} = m\vec{v}

. Conserved in all collisions (isolated system). \n- Kinetic Energy (KE):

KE = \frac{1}{2}mv^2

. NOT conserved in inelastic collisions. \n- Inelastic Collision: Momentum conserved, KE NOT conserved.

0 \le e < 1

. \n- Perfectly Inelastic Collision: Objects stick together.

e=0

. Maximum KE loss. \n- Conservation of Momentum (1D):

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

. \n- Coefficient of Restitution (e):

e = \frac{|v_2 - v_1|}{|u_1 - u_2|}

. \n- Common Final Velocity (Perfectly Inelastic):

V = \frac{m_1u_1 + m_2u_2}{m_1 + m_2}

. \n- Kinetic Energy Loss (General):

\Delta KE = KE_{initial} - KE_{final}

. \n- Max KE Loss (Perfectly Inelastic):

\Delta KE_{max} = \frac{1}{2}\frac{m_1m_2}{m_1+m_2}(u_1-u_2)^2

In Momentum Conserved, Kinetic Energy Lost (IMCKEL) for Inelastic Collisions. \nEquals Zero Sticks Together (EZST) for Perfectly Inelastic.