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4.4 Elastic and Inelastic Collisions

Syllabus
2024
Topic
4.4
Level
—

Learning objectives

4.4A—Describe whether an interaction between objects is elastic or inelasticDescribe whether an interaction between objects is elastic or inelastic.• An elastic collision between objects is one in which the initial kinetic energy of the system is equal to the final kinetic energy of the system.• In an elastic collision, the final kinetic energies of each of the objects within the system may be different from their initial kinetic energies.• An inelastic collision between objects is one in which the total kinetic energy of the system decreases.• In an inelastic collision, some of the initial kinetic energy is not restored to kinetic energy but is transformed by nonconservative forces into other forms of energy.• In a perfectly inelastic collision, the objects stick together and move with the same velocity after the collision. TOPIC 5.1 Rotational Kinematics

Classify collisions using system kinetic energy

Choose the system-level test

Use the total kinetic energy of the colliding system immediately before and immediately after the collision. Momentum conservation alone cannot distinguish elastic from inelastic collisions.

Ksys=∑i12mivi2K_{\text{sys}}=\sum_i\frac{1}{2}m_i v_i^2

Compare collision classes

Collision type System kinetic-energy test What happens after?
Elastic Kf=KiK_f=K_i Objects separate; each object's kinetic energy may still change
Inelastic Kf<KiK_f<K_i Some kinetic energy is transformed into other forms
Perfectly inelastic Kf<KiK_f<K_i Objects stick and share one final velocity

Classify from energy data

Classification example: the colliding objects have Ki=18 JK_i=18\,\text{J} before and Kf=12 JK_f=12\,\text{J} after.

ΔKsys=Kf−Ki=12 J−18 J=−6 J\Delta K_{\text{sys}}=K_f-K_i=12\,\text{J}-18\,\text{J}=-6\,\text{J}.

Because system kinetic energy decreases, the collision is inelastic. The missing 6 J6\,\text{J} of kinetic energy is transformed into other forms. If the objects also stick, it is perfectly inelastic.

Keep totals and transformations clear

Elastic does not mean every object keeps its own kinetic energy; only the system total is unchanged. Inelastic does not mean energy disappears. It means some initial kinetic energy is not restored as kinetic energy after the interaction.