Concept understanding — Conservation of Momentum in Collisions
Conservation of Momentum in Collisions
When two objects collide — two billiard balls, two train carriages coupling together, a bat striking a ball — each one exerts a force on the other for the brief instant they are in contact. This concept looks specifically at what those internal, mutual forces do to the total momentum of the colliding pair.
Setting Up the Idea
Consider two bodies of masses m1 and m2, moving with velocities u1 and u2 just before they collide, and velocities v1 and v2 just after. During the collision, body 1 pushes on body 2 with some force F, and by Newton's third law, body 2 pushes back on body 1 with force −F — equal in size, opposite in direction, acting for exactly the same contact time Δt.
Since impulse equals change in momentum (FΔt=Δp):
Change in momentum of body 1: −FΔt
Change in momentum of body 2: +FΔt
Add the two changes together and they cancel to zero. Whatever momentum one body loses, the other gains — the total is untouched.
Important
For any collision where no external force acts on the pair (an isolated system), the total linear momentum just before the collision equals the total linear momentum just after:
m1u1+m2u2=m1v1+m2v2
Why "Internal" Forces Don't Change the Total
The collision force between the two bodies is an internal force of the two-body system — it acts between the objects, not from outside. Internal forces always come in Newton's-third-law pairs, and any equal-and-opposite pair produces zero net impulse on the system as a whole. External forces — gravity, friction from the floor, air resistance — are usually negligible during a collision because contact lasts only a fraction of a second, far too short for a small external force to produce a noticeable impulse.
Watch out
Momentum conservation applies to the system's total, not to each object individually. One ball can slow down drastically and the other speed up — their individual momenta change freely; only the sum stays fixed.
Worked Example
A 2 kg ball moving at 3 m/s (rightward) strikes a stationary 1 kg ball. After the collision the 2 kg ball moves at 1 m/s in the same direction. Find the velocity of the 1 kg ball.
'Constant temperature' during the collision signals that no energy is lost as heat, i.e. the collision is elastic — in an elastic collision both momentum and kinetic energy are conserved, but the quantity this extra condition specifically guarantees is kinetic energy (momentum is conserved in ANY collision regardless of temperature). …
No temperature rise means no energy lost as heat — the collision is elastic, so kinetic energy is conserved.
Momentum is always conserved in any collision (elastic or inelastic) as long as no external force acts — so mentioning temperature would be unnecessary if momentum were the intended answer. Temperature rising is the signature of kinetic energy being converted into heat in an inelastic collision. Since the te …
Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.
CBSE 2024Set ANNUAL1 markMCQ
Q.Two balls collide at constant temperature. Conserved physical quantity is
(A) temperature
(B) velocity
(C) kinetic energy
(D) momentum
›Reveal solutionSolution
No temperature rise means no energy lost as heat — the collision is elastic, so kinetic energy is conserved.
Momentum is always conserved in any collision (elastic or inelastic) as long as no external force acts — so mentioning temperature would be unnecessary if momentum were the intended answer. Temperature rising is the signature of kinetic energy being converted into heat in an inelastic collision. Since the te …
Q.Read the following passage and answer questions no. 4 and 5:
In all type of collision, the linear momentum is conserved but the kinetic energy is not conserved in inelastic collision. When a body suspended from weightless string is struck by another body moving with high speed and both the bodies stick to each other and move as one body, the collision between them is known as perfectly inelastic collision.
Which quantity is conserved during all types of collision?
(a) Linear momentum
(b) Kinetic energy
(c) Both Linear momentum and Kinetic energy
(d) None of these
›Reveal solutionSolution
Linear momentum is always conserved in a collision (as long as no external force acts), while kinetic energy is conserved only for elastic collisions.
During a collision, the two colliding bodies exert equal and opposite forces on each other (Newton's third law) for the same short duration of contact. By Newton's second law, this means they receive equal and opposite impulses, so the total momentum of the system just before and just after collision is the same -- this holds true regardless of whether the collision is elastic, inelastic, or perfectly inelastic, as long as no external force acts on the system during the collision.