Q: Is momentum conserved in an inelastic collision?

Yes. On a frictionless track there is no external force, so total linear momentum is conserved in every collision regardless of e — even when e = 0 and the bodies stick together. What changes with e is the kinetic energy: only e = 1 conserves KE; for any e < 1 some KE is converted to heat, sound, and deformation.

Q: What happens when two equal masses collide elastically in 1D?

They exchange velocities. If one is moving and the other is stationary, the moving one stops dead and the stationary one moves off with the original velocity. This velocity-swap is the most-tested NEET/JEE result for 1D elastic collisions.

Q: Why does kinetic energy decrease but momentum stay the same in a collision?

Momentum is a vector tied to Newton's third law — the equal-and-opposite impulses cancel, so the system total never changes. Kinetic energy is a scalar that can be converted into other forms (heat, sound, permanent deformation) during the collision. The fraction lost is fixed by e: ½·(m₁m₂/M)·(1 − e²)·v_rel².

Q: What is the final common velocity in a perfectly inelastic collision?

Both bodies move together at the velocity of the centre of mass, v_cm = (m₁u₁ + m₂u₂)/(m₁ + m₂). This is the case of maximum possible kinetic-energy loss for a given pair of initial momenta.

Question 1

What is the coefficient of restitution?

Accepted Answer

It is the ratio of the relative speed of separation after a collision to the relative speed of approach before it: e = (v₂ − v₁)/(u₁ − u₂). e = 1 is a perfectly elastic collision (kinetic energy conserved), e = 0 is perfectly inelastic (the bodies move together), and 0 < e < 1 is partially elastic.

Question 2

Is momentum conserved in an inelastic collision?

Accepted Answer

Yes. On a frictionless track there is no external force, so total linear momentum is conserved in every collision regardless of e — even when e = 0 and the bodies stick together. What changes with e is the kinetic energy: only e = 1 conserves KE; for any e < 1 some KE is converted to heat, sound, and deformation.

Question 3

What happens when two equal masses collide elastically in 1D?

Accepted Answer

They exchange velocities. If one is moving and the other is stationary, the moving one stops dead and the stationary one moves off with the original velocity. This velocity-swap is the most-tested NEET/JEE result for 1D elastic collisions.

Question 4

Why does kinetic energy decrease but momentum stay the same in a collision?

Accepted Answer

Momentum is a vector tied to Newton's third law — the equal-and-opposite impulses cancel, so the system total never changes. Kinetic energy is a scalar that can be converted into other forms (heat, sound, permanent deformation) during the collision. The fraction lost is fixed by e: ½·(m₁m₂/M)·(1 − e²)·v_rel².

Question 5

What is the final common velocity in a perfectly inelastic collision?

Accepted Answer

Both bodies move together at the velocity of the centre of mass, v_cm = (m₁u₁ + m₂u₂)/(m₁ + m₂). This is the case of maximum possible kinetic-energy loss for a given pair of initial momenta.

1D Collision — Momentum & Restitution

Learned it? Now prove it under the clock.