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 the collision is exactly equal to the total kinetic energy after the collision. In contrast, in an inelastic collision, while linear momentum is still conserved (assuming no external forces), kinetic energy is *not* conserved. Some kinetic energy is converted into other forms, such as heat, sound, or permanent deformation of the colliding objects.

Are perfectly elastic collisions possible in the real world?

Perfectly elastic collisions are an idealization and are very rare in the macroscopic world. In reality, some amount of kinetic energy is always lost to heat, sound, or permanent deformation during any collision between macroscopic objects. However, at the atomic and subatomic levels, collisions between particles like electrons, protons, or gas molecules can be very close to perfectly elastic, making the model highly useful in fields like nuclear physics and kinetic theory of gases.

What is the role of the coefficient of restitution in elastic collisions?

The coefficient of restitution ($e$) quantifies the 'bounciness' of a collision. It is defined as the ratio of the relative speed of separation after the collision to the relative speed of approach before the collision. For a perfectly elastic collision, the relative speed of separation is equal to the relative speed of approach, meaning $e=1$. This value of 1 signifies that there is no net loss of kinetic energy during the collision, and the objects rebound with maximum possible relative speed.

Is momentum always conserved in an elastic collision?

Yes, linear momentum is always conserved in an elastic collision, provided the system of colliding bodies is isolated, meaning no external forces act on it. In fact, the conservation of linear momentum is a fundamental principle that applies to *all* types of collisions (elastic, inelastic, and perfectly inelastic) under isolated conditions. The conservation of kinetic energy is the additional condition that specifically defines an elastic collision.

What happens if a light body collides elastically with a much heavier body at rest?

If a light body ($m_1$) collides elastically with a much heavier body ($m_2$) that is initially at rest ($u_2=0$), the light body will bounce back with nearly the same speed it had initially, but in the opposite direction ($v_1 approx -u_1$). The heavy body will remain almost at rest ($v_2 approx 0$). Think of a tennis ball hitting a massive wall; the wall barely moves, and the ball rebounds with almost its original speed.

Elastic Collisions

Physics

NEET UG

Version 1Updated 22 Mar 2026

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An elastic collision is a type of collision in which the total kinetic energy of the system of colliding bodies is conserved, in addition to the conservation of total linear momentum. This implies that there is no net loss of kinetic energy in the form of heat, sound, or permanent deformation during the collision process. While kinetic energy may temporarily convert into potential energy of deform…

Quick Summary

Elastic collisions are fundamental interactions where two key quantities are conserved: total linear momentum and total kinetic energy. This means that the 'push' and the 'energy of motion' of the system remain unchanged before and after the collision.

While momentum conservation applies to all collisions (elastic or inelastic), kinetic energy conservation is the defining characteristic of an elastic collision. In such collisions, objects deform temporarily during contact but fully regain their original shape, ensuring no permanent energy loss to heat, sound, or deformation.

The coefficient of restitution, a measure of 'bounciness', is exactly 1 for elastic collisions. Key scenarios include one-dimensional head-on collisions, where specific formulas predict final velocities based on masses and initial velocities.

Special cases, like equal masses exchanging velocities or a light object bouncing off a heavy one, are particularly important for NEET. Though idealizations in the macroscopic world, elastic collisions are crucial models in microscopic physics.

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Key Concepts

Conservation Laws in 1D Elastic Collisions

In a one-dimensional elastic collision between two bodies, say $m_1$ and $m_2$ , with initial velocities $u_1$ …

Special Case: Equal Masses and One at Rest

When two bodies of equal mass ( $m_1 = m_2 = m$ ) undergo a 1D elastic collision, and one of them is initially…

Special Case: Light Body Colliding with Massive Body at Rest

Consider a very light body ( $m_1$ ) colliding elastically with a much heavier body ( $m_2$ ) that is initially…

Definition: — Total linear momentum and total kinetic energy are conserved.

Coefficient of Restitution: —

e=1

1D Momentum Conservation: —

m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2

1D Kinetic Energy Conservation: —

rac{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

Relative Velocity Relation: —

u_1 - u_2 = v_2 - v_1

(relative speed of approach = relative speed of separation)

Final Velocities (General 1D):

- $v_1 = left(\frac{m_1 - m_2}{m_1 + m_2}\right)u_1 + left(\frac{2m_2}{m_1 + m_2}\right)u_2$ - $v_2 = left(\frac{2m_1}{m_1 + m_2}\right)u_1 + left(\frac{m_2 - m_1}{m_1 + m_2}\right)u_2$

Special Case ($m_1=m_2, u_2=0$): —