Collisions bring objects together; explosions push them apart. Both happen along a single line here, and both always conserve momentum. What changes is kinetic energy — and whether it’s conserved is exactly what separates an elastic collision from an inelastic one.
📘 What you need to know
A collision: two moving objects interact briefly. An explosion: one stationary object splits and the parts move apart.
Momentum is always conserved in collisions and explosions — kinetic energy is not always conserved.
Elastic collision: kinetic energy is conserved. Inelastic collision: kinetic energy is not conserved.
Totally inelastic: the objects stick together and move as one — the maximum possible KE is lost.
Kinetic energy: Ek = ½mv² — always positive, since v² removes the sign.
In an explosion, KE is never conserved — everything starts at rest with zero KE.
Collisions vs explosions
In a 1D collision, two objects moving along the same line meet and interact, then move apart (or together) along that same line. In a 1D explosion, a single object starts at rest and splits into pieces that fly off in opposite directions along the line.
A collision: objects come together and separate again. An explosion: a single object starts at rest and splits apart.
Elastic vs inelastic collisions
Both types conserve momentum, but they differ in kinetic energy:
Elastic: kinetic energy is conserved — total KE before equals total KE after. A truly perfectly elastic collision is an idealisation (it’s common at the particle level, but real macroscopic collisions always lose a little energy).
Inelastic: kinetic energy is not conserved — some is transferred away as heat, sound, or deformation.
Totally inelastic: the objects stick together after impact and move with one common velocity. This loses the maximum possible amount of kinetic energy.
Elastic collisions bounce apart with KE conserved; totally inelastic collisions stick together, losing the maximum possible KE.
Checking which type it is
To classify a collision, compare the total kinetic energy before and after:
Kinetic energyEk = ½mv²
KE before = KE after → elastic.
KE before > KE after → inelastic (energy was lost).
An explosion always starts with everything at rest, so the initial KE is always zero — meaning kinetic energy is never conserved in an explosion (KE after is always greater than zero).
Quick reference: momentum conserved always • elastic = KE conserved • inelastic = KE lost • totally inelastic = stick together, max KE lost • explosions never conserve KE.
Worked examples
WE 1
A symmetric head-on elastic collision
Two identical spheres, each of mass m, move towards each other at the same speed v and collide elastically head-on. Find the total kinetic energy after the impact.
Elastic → KE after = KE beforeKE before = ½mv² + ½mv²total KE after = mv²
WE 2
Trolleys that stick together (inelastic)
Trolley A (0.80 kg) moving at 3.0 m s⁻¹ collides head-on with a stationary trolley B (1.60 kg). They stick together and move off at 1.0 m s⁻¹. Show this collision is inelastic.
KE before = ½(0.80)(3.0)² + 0= ½ × 0.80 × 9.0 = 3.6 JKE after = ½(0.80 + 1.60)(1.0)²= ½ × 2.40 × 1.0 = 1.2 JKE after < KE beforeinelastic — 2.4 J was lost
WE 3
An explosion (recoil)
A 2.0 kg object at rest splits into two pieces. One piece (0.50 kg) flies off at 8.0 m s⁻¹. Find the velocity of the other piece (1.5 kg), and explain why kinetic energy isn’t conserved here.
Momentum before = 0 (everything at rest)Momentum after: 0.50 × 8.0 + 1.5 × v = 0v = −(0.50 × 8.0) ÷ 1.5v ≈ −2.7 m s⁻¹ (opposite direction)KE before = 0, but KE after > 0, so KE is never conserved in an explosion
💡 Top tips
Momentum first, always. It’s conserved in every collision and explosion — start there.
Then compare KE to decide elastic vs inelastic; you can’t tell from momentum alone.
“Stick together” is a strong clue for totally inelastic — combine the masses into one moving object.
KE is always positive. Squaring velocity removes the sign, so never write a negative KE.
For an explosion, momentum before is zero — use that to relate the velocities of the pieces.
⚠ Common mistakes
Assuming momentum and KE are conserved together. Momentum always is; KE often isn’t.
Plugging signed velocity into the KE formula and getting confused by negative numbers — square it first.
Treating real-world collisions as perfectly elastic by default — at this level, assume inelastic unless told otherwise.
Forgetting an explosion has zero KE before, so it can never be “elastic”.
A useful habit: always calculate momentum before doing anything else — it’s never wrong. Only then check kinetic energy to classify the event. Up next, we leave linear motion behind and turn to Angular Velocity, the start of circular motion.
Need help with SL Forces & Momentum?
Get 1-on-1 help from an IB examiner who knows exactly what Paper 1 & 2 are looking for.
