In one line: JEE/NEET Physics · Work, Energy & Power series · Part 6 of 8 · All parts →✪ Key points — the 30-second versionMomentum (mass × velocity) survives EVERY.
JEE/NEET Physics · Work, Energy & Power series · Part 6 of 8 · All parts →
- Momentum (mass × velocity) survives EVERY collision; energy often doesn’t
- Elastic: both momentum and KE survive (ideal, bouncy)
- Inelastic: momentum survives, KE partially dies (most real crashes)
- Perfectly inelastic: bodies stick together — maximum KE loss
- Explosions run the same rule in reverse
In every crash — a car wreck, a cricket ball on a bat, two ice pucks — one quantity ALWAYS survives the impact untouched, while another usually dies. Knowing which is which solves every collision question in one line each. Part 6 of the Work, Energy & Power series.
- The survivor: momentum
- The casualty: kinetic energy
- The three types of collision
- Equal masses in elastic hits: the neat swap
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
The Survivor: Momentum
Why so unbreakable: it’s Newton’s third law bookkeeping. During the crash, the two bodies push each other with equal, opposite forces for the same time — the changes cancel exactly. Whatever happens inside the crash (denting, heat, sound), the total motion-quantity is locked.
The Casualty: Kinetic Energy
Unlike momentum, KE is a one-direction street: the crash can convert it into heat, dents, and sound — never back. So the sorting is simple:
| Type | Momentum | Kinetic energy | Example |
|---|---|---|---|
| Elastic | survives | survives TOO (ideal) | steel balls, gas molecules, billiards (near) |
| Inelastic | survives | partially dies | most real hits — cricket ball, cars |
| Perfectly inelastic | survives | maximum loss — bodies STICK | coupled train wagons, ball in mud |
Equal Masses in Elastic Hits: The Neat Swap
Beautiful shortcut: equal masses colliding elastically simply exchange velocities. The moving one stops; the stopped one moves off with the first one’s speed. Newton’s cradle shows it in slow, clicking elegance.
Solved Examples
Momentum survivor: (2×6) + 0 = (2+4)v → 12 = 6v.
v = 2 m/s. ✔
Answer: 2 m/s
Before: ½(2)(36) = 36 J. After: ½(6)(4) = 12 J.
24 J died → heat and dent (67% of the energy!).
The pattern: momentum bookkeeping gave the speed; energy bookkeeping gives the loss — always two separate questions. ✔
Answer: 24 J lost (to heat/deformation)
Momentum: 1(4) = v₁ + 3v₂.
Elastic adds KE: 8 = ½v₁² + (3/2)v₂².
Solve the pair: v₁ = 4−3v₂ → substitute → v₂ = 2 m/s, v₁ = −2 m/s.
Read it: the light ball BOUNCES BACK (−2), the heavy one crawls forward (2). Light things bounce off heavy things — cricket ball vs bat, you vs a truck. ✔
Answer: 1 kg ball: −2 m/s (rebounds); 3 kg ball: +2 m/s
- Conserving KE in a sticking collision. The classic error. Sticking = max energy death. Only momentum survives.
- Signs. All velocities must carry direction (+/−). ‘Both move at v’ with one actually reversing flips every answer.
- Adding speeds instead of momenta. Mass × velocity, each with its sign — never velocities alone.
- Forgetting equal-mass elastic swap. It’s a free shortcut: equal masses exchange velocities — no algebra needed.
This Physics in Your Daily Life
- Car crumple zones are deliberate KE-killers: bending metal absorbs your crash energy over distance so your body doesn’t — momentum physics you hope never to use.
- Newton’s cradle desk toy: the equal-mass elastic swap, clicked in metal, forever.
- Cricket and tennis: ‘sweet spot’ hits are the most elastic (least energy lost to vibration) — the ball leaves fastest; off-center hits waste energy in sting.
- Railway coupling is the perfectly-inelastic lab: wagons locking together at hump yards, sharing one speed after contact.
- Airbags and helmets extend collision TIME — same momentum change, gentler force (impulse idea) — safety engineering living inside this card.
Practice set (answers hidden — try first)
(NEET-level) 3 kg at 4 m/s sticks to a stationary 3 kg. Common speed:
(JEE Main-level) That collision’s KE loss:
(Concept) Two identical steel balls, one moving, one at rest, elastic collision. After:
(JEE Main-level) A light ball hits a heavy wall elastically head-on. The ball’s speed:
(Concept) Which quantity NEVER survives an explosion-then-reassembly? / Which always survives a collision?
- 🧠 Chant: ‘momentum always lives, energy often dies’.
- 🧠 Sticking = maximum death of KE — compute speed by momentum, loss by energy.
- 🧠 The swap: equal masses, elastic — they just trade velocities.
- 🏠 Daily: crumple zones are engineered energy death — protecting you by dying.
- 🏠 Daily: Newton’s cradle on a desk = this card as office jewellery.
- 🔁 momentum conservation: always
- 🔁 elastic: momentum + KE conserved
- 🔁 perfectly inelastic: stick together, max KE loss
- momentum survives EVERY collision — no exceptions
- elastic: KE survives too (ideal bounces)
- sticking collision: maximum KE death
- equal masses + elastic = velocity swap
- light body hitting heavy body bounces back
Quick revision
- Momentum (mass × velocity) survives EVERY collision; energy often doesn’t
- Elastic: both momentum and KE survive (ideal, bouncy)
- Inelastic: momentum survives, KE partially dies (most real crashes)
- Perfectly inelastic: bodies stick together — maximum KE loss
- Explosions run the same rule in reverse
- The casualty: kinetic energy
- 1Work Done: When a Force Actually Achieves Something
- 2Kinetic Energy and the Work-Energy Theorem: The Great Shortcut
- 3Potential Energy: Stored Work, Ready to Strike
- 4Conservation of Energy: The Universe’s Perfect Bookkeeping
- 5Power and Efficiency: How FAST You Can Do the Work
- 6Collisions: The Great Sorting — What Survives, What Dies
- 7Springs and Vertical Circles: Energy in Two Classic Stages
- 8The Finale: Energy in the Real World, and the Complete Formula Card
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