Is linear momentum always conserved in a collision?

Yes, linear momentum is always conserved in any type of collision, provided the system of colliding objects is isolated, meaning no net external force acts on it during the collision. This is a direct consequence of Newton's third law and the impulse-momentum theorem. While the momentum of individual objects may change drastically, the vector sum of their momenta before the collision will be equal to the vector sum of their momenta after the collision. This fundamental principle holds true for elastic, inelastic, and perfectly inelastic collisions alike.

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. This means the total kinetic energy of the system before and after the collision remains the same. In contrast, in an inelastic collision, linear momentum is conserved, but kinetic energy is *not* conserved. Some amount of kinetic energy is lost, typically converted into other forms of energy such as heat, sound, or energy used for deformation of the colliding bodies. Most real-world collisions are inelastic.

What is the coefficient of restitution and what do its values signify?

The coefficient of restitution (e) is a dimensionless quantity that describes the 'bounciness' of a collision. It is defined as the ratio of the relative speed of separation of the objects after collision to their relative speed of approach before collision. Its value ranges from 0 to 1. If e=1, the collision is perfectly elastic, meaning relative speed of separation equals relative speed of approach. If e=0, the collision is perfectly inelastic, meaning the objects stick together and have zero relative speed of separation. For inelastic collisions where objects don't stick, $0 < e < 1$.

Can kinetic energy ever increase in a collision?

In a standard collision where only mechanical forces are at play, the total kinetic energy of the system cannot increase. It can either be conserved (elastic collision) or decrease (inelastic collision, where energy is converted to heat, sound, deformation). However, if there are internal energy sources within the system that are released during the collision (e.g., an explosion), then the kinetic energy of the system *can* increase. But for typical collision problems in NEET, assume kinetic energy either stays the same or decreases.

How does impulse relate to collisions?

Impulse is a measure of the change in momentum of an object. During a collision, objects exert large forces on each other over a very short time interval. The product of the average force and this time interval is the impulse. According to the impulse-momentum theorem, the impulse acting on an object is equal to the change in its linear momentum ($vec{J} = \Delta\vec{p}$). This concept is crucial for understanding how forces during a collision affect the motion of objects, even when the exact force-time profile is unknown.

Collisions

Q: Can kinetic energy ever increase in a collision?

In a standard collision where only mechanical forces are at play, the total kinetic energy of the system cannot increase. It can either be conserved (elastic collision) or decrease (inelastic collision, where energy is converted to heat, sound, deformation). However, if there are internal energy sources within the system that are released during the collision (e.g., an explosion), then the kinetic energy of the system *can* increase. But for typical collision problems in NEET, assume kinetic energy either stays the same or decreases.

Q: How does impulse relate to collisions?

Impulse is a measure of the change in momentum of an object. During a collision, objects exert large forces on each other over a very short time interval. The product of the average force and this time interval is the impulse. According to the impulse-momentum theorem, the impulse acting on an object is equal to the change in its linear momentum ($vec{J} = \Delta\vec{p}$). This concept is crucial for understanding how forces during a collision affect the motion of objects, even when the exact force-time profile is unknown.

Physics

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Version 1Updated 22 Mar 2026

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In physics, a collision is defined as a strong interaction between two or more bodies that occurs over a relatively short period, during which the interacting bodies exert forces on each other that are significantly larger than any other external forces present. This intense interaction leads to an abrupt change in the momentum and kinetic energy of the colliding bodies. Crucially, during a collis…

Quick Summary

Collisions are brief, intense interactions between objects leading to changes in their motion. The fundamental principle governing all collisions, provided no net external force acts on the system, is the conservation of linear momentum.

This means the total momentum before the collision equals the total momentum after. Collisions are categorized based on the conservation of kinetic energy. In an elastic collision, both linear momentum and kinetic energy are conserved.

These are idealized and often involve hard, non-deforming objects. In an inelastic collision, linear momentum is conserved, but kinetic energy is not; some kinetic energy is transformed into other forms like heat or sound.

A special case is a perfectly inelastic collision, where objects stick together after impact, resulting in the maximum possible loss of kinetic energy. The coefficient of restitution (e) quantifies the 'bounciness' of a collision: $e=1$ for elastic, $e=0$ for perfectly inelastic, and $0 < e < 1$ for general inelastic collisions.

Understanding these types and applying the conservation laws, along with the concept of impulse, is key to solving collision problems.

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Linear Momentum: —

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

(vector quantity)

Impulse: —

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

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)

Kinetic Energy: —

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

Elastic Collision: — Momentum conserved, KE conserved,

e=1

- 1D: $u_1 - u_2 = -(v_1 - v_2)$ (Relative speed of approach = Relative speed of separation)

Inelastic Collision: — Momentum conserved, KE *not* conserved,

0 \le e < 1

Perfectly Inelastic Collision: — Objects stick together,

e=0

. Max KE loss.

- 1D: $m_1u_1 + m_2u_2 = (m_1 + m_2)V$

Coefficient of Restitution (e): —

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

(Ratio of relative speed of separation to approach)

Rebound Height: —

h = e^2H

(for a ball dropped from H)

MICE KEPT: Momentum Is Conserved for Every collision. Kinetic Energy Preserves Totally (only for Elastic).