What is the 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 total kinetic energy of the system are conserved. The objects rebound without any permanent deformation, and no energy is lost as heat, sound, or internal energy. In contrast, in an inelastic collision, linear momentum is conserved, but total kinetic energy is not. Some kinetic energy is converted into other forms, such as heat, sound, or energy of deformation. The objects may deform permanently or even stick together (perfectly inelastic collision).

Is momentum always conserved in a collision?

Yes, linear momentum is always conserved in any type of collision (elastic, inelastic, or perfectly inelastic), provided the system of colliding objects is isolated, meaning no net external force acts on it. The forces involved in the collision itself are internal forces within the system, and they cancel out in pairs according to Newton's third law, thus not changing the total momentum of the system. This is a fundamental principle derived from Newton's laws of motion.

What is the coefficient of restitution and what does it tell us?

The coefficient of restitution, denoted by 'e', is a dimensionless quantity that quantifies the elasticity of a collision. It is defined as the ratio of the relative speed of separation of the colliding bodies after impact to their relative speed of approach before impact. Mathematically, $e = -\frac{(v_2 - v_1)}{(u_2 - u_1)}$. For a perfectly elastic collision, $e=1$ (relative speeds are equal). For a perfectly inelastic collision (objects stick together), $e=0$ (relative speed of separation is zero). For all other inelastic collisions, $0 < e < 1$. It essentially tells us how much kinetic energy is retained after a collision.

Can kinetic energy increase after a collision?

In standard collision scenarios, where only the kinetic energy of the colliding bodies is considered, kinetic energy generally decreases or remains constant. However, if there's an internal source of energy within the system that gets released during the interaction (like an explosion), the kinetic energy of the system can increase. Such events are sometimes referred to as 'superelastic' or 'explosive' collisions, where the coefficient of restitution can be greater than 1. For typical NEET problems, assume kinetic energy either remains constant (elastic) or decreases (inelastic).

How do I approach a 2D collision problem?

For a 2D collision, the key is to apply the conservation of linear momentum independently along two perpendicular axes (usually x and y). First, draw a clear diagram showing initial and final velocities with their angles. Resolve all initial and final velocity vectors into their x and y components. Then, write separate conservation of momentum equations for the x-components and y-components. If the collision is elastic, you can also use the conservation of kinetic energy equation. This will give you a system of equations to solve for the unknown velocities or angles.

Collisions

Q: Can kinetic energy increase after a collision?

In standard collision scenarios, where only the kinetic energy of the colliding bodies is considered, kinetic energy generally decreases or remains constant. However, if there's an internal source of energy within the system that gets released during the interaction (like an explosion), the kinetic energy of the system can increase. Such events are sometimes referred to as 'superelastic' or 'explosive' collisions, where the coefficient of restitution can be greater than 1. For typical NEET problems, assume kinetic energy either remains constant (elastic) or decreases (inelastic).

Q: How do I approach a 2D collision problem?

For a 2D collision, the key is to apply the conservation of linear momentum independently along two perpendicular axes (usually x and y). First, draw a clear diagram showing initial and final velocities with their angles. Resolve all initial and final velocity vectors into their x and y components. Then, write separate conservation of momentum equations for the x-components and y-components. If the collision is elastic, you can also use the conservation of kinetic energy equation. This will give you a system of equations to solve for the unknown velocities or angles.

Physics

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Version 1Updated 22 Mar 2026

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In physics, a collision is defined as an isolated event in which two or more bodies exert forces on each other for a relatively short period of time, leading to an exchange of momentum and energy. During a collision, the interacting bodies come into direct contact or exert strong forces over a small distance, causing their velocities to change significantly. The fundamental principle governing all…

Quick Summary

Collisions are brief, intense interactions between objects leading to changes in their motion. The most crucial principle is the Conservation of Linear Momentum, which states that for an isolated system, the total momentum before a collision equals the total momentum after.

Momentum is a vector quantity ( $p = mv$ ). Collisions are classified based on what happens to kinetic energy.\n\nElastic collisions conserve both momentum and kinetic energy. The coefficient of restitution ( $e$ ) is 1.

Objects rebound without deformation. \n\nInelastic collisions conserve momentum but *not* kinetic energy; some kinetic energy is lost (converted to heat, sound, deformation). For these, $0 < e < 1$ .

A special case is perfectly inelastic collisions, where objects stick together and move as one, resulting in maximum kinetic energy loss, and $e=0$ .\n\nImpulse ( $J = F_{avg} \Delta t$ ) is the change in momentum ( $\Delta p$ ).

It quantifies the effect of force over time during the collision. For 2D collisions, momentum conservation must be applied component-wise (x and y directions). Understanding these types and principles is fundamental to solving collision problems in NEET.

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Perfectly Inelastic Collision Calculation

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Elastic Collision Velocity Formulas (1D)

For one-dimensional elastic collisions, specific formulas can be derived for the final velocities of the two…

Momentum: —

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

(vector quantity)\n- Impulse:

\vec{J} = \Delta \vec{p} = \vec{F}_{avg} \Delta t

\n- Conservation of Momentum:

m_1\vec{u}_1 + m_2\vec{u}_2 = m_1\vec{v}_1 + m_2\vec{v}_2

(always conserved in isolated system)\n- Elastic Collision: Momentum conserved, Kinetic Energy conserved (

e=1

)\n - 1D Equal Masses: Velocities exchanged (

v_1=u_2, v_2=u_1

)\n - 1D General:

v_1 = \frac{(m_1 - m_2)u_1 + 2m_2u_2}{m_1 + m_2}

v_2 = \frac{(m_2 - m_1)u_2 + 2m_1u_1}{m_1 + m_2}

\n- Inelastic Collision: Momentum conserved, Kinetic Energy NOT conserved (

0 < e < 1

)\n- Perfectly Inelastic Collision: Momentum conserved, Kinetic Energy NOT conserved (max loss), objects stick (

e=0

)\n - 1D:

m_1u_1 + m_2u_2 = (m_1 + m_2)V

\n- Coefficient of Restitution (e):

e = -\frac{(v_2 - v_1)}{(u_2 - u_1)}

e = \frac{\text{relative speed of separation}}{\text{relative speed of approach}}

\n- Bouncing Ball:

e = \sqrt{h_{rebound}/h_{drop}}

MEPI: Momentum Everywhere, Perfectly Inelastic sticks, Elastic Energy too. (Momentum is conserved in Every collision. Perfectly Inelastic collisions mean objects stick together. Elastic collisions conserve Energy, in addition to momentum.)