Elastic Collision (1D)
Both KE and momentum conserved — live v₁', v₂' from standard formulas.
Key Notes
Elastic collision: BOTH momentum AND kinetic energy are conserved.
1D two-body: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (momentum) AND ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂² (KE).
Solving these gives final velocities in terms of initial — exact formulas exist (see Formulas section).
Equal masses (m₁ = m₂): velocities are EXCHANGED — incoming particle stops, target moves with original speed.
Massive target (m₂ ≫ m₁): incoming particle bounces back with nearly same speed; target barely moves.
Light target (m₂ ≪ m₁): incoming particle continues nearly unchanged; target shoots off at 2u₁.
Real-world approximations: hard steel balls, atomic collisions (in some regimes), Newton's cradle.
Macroscopically, perfectly elastic collisions don't exist — some energy always lost to heat, sound, deformation.
Formulas
Conservation laws
Both p and K conserved.
Final velocity v_1
Useful formula — derivation in textbooks.
Final velocity v_2
Symmetric to v_1.
Equal masses, target at rest
Special case — clean velocity exchange.
Important Points
Elastic = KE conserved. Inelastic = KE lost (not conserved).
Equal-mass head-on elastic collision: velocities swap. Famous example: Newton's cradle.
Heavy target (e.g., car vs wall): light projectile bounces back at nearly original speed.
Light target (e.g., car vs ping-pong ball): heavy projectile barely slows; target rockets off.
In the COM frame, both particles reverse direction; in the lab frame the picture is more complex.
Relative velocity reverses: v_2 − v_1 = −(u_2 − u_1) — useful shortcut.
Elastic Collision (1D) notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.