Questions: Elastic and Inelastic Collisions

Question 1

Two rubber balls collide and bounce back vigorously. A student says 'That must be elastic — look how hard they bounced!' A lab partner says 'We can't tell without measuring kinetic energy before and after.' Who is right?

• A. The first student — a hard bounce is the definition of an elastic collision
• B. The lab partner — elastic means kinetic energy is conserved, which cannot be determined from appearance alone
• C. Both — a vigorous bounce necessarily implies kinetic energy conservation
• D. Neither — elasticity is determined by the coefficient of restitution, which requires measuring deformation

Answer: (B)

Elastic is a precise technical term: a collision is elastic if and only if kinetic energy is conserved — the objects emerge with the same total KE they had before impact. How vigorous or dramatic the bounce appears is irrelevant. Real rubber balls are actually inelastic; they deform, generate heat, and lose kinetic energy even in a 'hard' bounce. The only way to classify a collision as elastic is to measure KE before and after (or measure e = 1 using relative speeds). The visual appearance of the collision tells you nothing definitive about energy conservation.

Question 2

Two clay balls collide and stick together, moving as one mass after the impact. Which quantities are conserved in this collision?

• A. Both momentum and kinetic energy
• B. Kinetic energy only
• C. Momentum only
• D. Neither — the sticking together means energy is destroyed and momentum redistributed

Answer: (C)

This is a perfectly inelastic collision (e = 0). Momentum is always conserved in a collision with no net external force — including perfectly inelastic ones. Kinetic energy is NOT conserved: the objects deform permanently, generating heat and sound, and the combined mass moves slower than either original object was moving (in center-of-mass frame, all kinetic energy in that frame is lost). Note that option D is wrong in a subtle way: total energy IS still conserved globally — kinetic energy converts to internal energy (heat, deformation), it is not destroyed. Only kinetic energy decreases.

Question 3

In any collision between two objects with no net external force, total momentum of the system is conserved regardless of whether the collision is elastic, inelastic, or perfectly inelastic.

• T. True
• F. False

Answer: True

Momentum conservation is a consequence of Newton's third law and the absence of net external forces — it does not depend on what happens to kinetic energy. During a collision, the internal forces between the colliding objects are equal and opposite, so they cancel in the momentum sum. This holds whether the collision converts some kinetic energy to heat (inelastic) or none at all (elastic). Momentum conservation is universal across collision types; kinetic energy conservation is the special additional condition that defines elasticity.

Question 4

In an inelastic collision, total energy is not conserved — some energy is permanently destroyed during the impact.

• T. True
• F. False

Answer: False

Total energy is always conserved — this is one of the most fundamental principles in physics. What changes in an inelastic collision is the form of energy: kinetic energy converts to internal energy (heat, sound, permanent deformation of the objects). The total energy budget is unchanged; it is redistributed. Saying energy is 'lost' is sloppy shorthand for 'lost from the kinetic budget.' The distinction matters because it determines what tools you can use: for inelastic collisions you cannot apply KE conservation, but total energy conservation still holds and connects kinetic energy loss to thermal energy gain.

Question 5

Why can you apply two conservation laws (momentum AND kinetic energy) when solving an elastic collision, but only one (momentum) for a perfectly inelastic collision? What determines this?

Model answer: In an elastic collision, the internal forces between the objects are perfectly conservative — no energy leaves the kinetic budget. Both momentum and KE are unchanged after the collision, giving two independent equations to solve for the two unknown final velocities. In a perfectly inelastic collision, kinetic energy is converted to internal energy (heat, deformation). The amount converted is unknown without additional information about the materials, so KE conservation cannot be written as a constraint on final velocities. Momentum conservation still holds (external forces are absent), giving one equation for one unknown (the shared final velocity of the combined mass). The collision type determines how many usable conservation laws you have.

This is the practical core of the topic. The coefficient of restitution e encodes which case you're in: e = 1 allows both laws, e = 0 (perfectly inelastic) allows only momentum conservation. For intermediate e, you use the restitution condition (v₂' - v₁' = -e(v₂ - v₁)) as your second equation instead of KE conservation, which avoids needing to know the details of energy dissipation.