Collisions: (c) perfectly elastic collision and inelastic collision.

The idea

In a perfectly elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not; some is transferred to thermal energy, sound or deformation. A special case is a perfectly inelastic collision, where bodies stick together and move with a common velocity, giving maximum kinetic energy loss. For example, two identical trolleys approaching at equal speeds and sticking together have zero total momentum and stop, converting all kinetic energy. To test elasticity, calculate total ½mv² before and after; equal values indicate a perfectly elastic collision, while a decrease indicates an inelastic one.

What earns the marks

• A perfectly elastic collision conserves both momentum and kinetic energy.
• An inelastic collision conserves momentum but not kinetic energy.
• In a perfectly inelastic collision the bodies coalesce and share a common final velocity.
• Kinetic energy may be transferred to thermal energy, sound or deformation in an inelastic collision.

Common mistakes and how to put them right

• Assuming kinetic energy is always conserved in collisions.

  Put it right: The correct test is to compare total kinetic energy before and after, since only perfectly elastic collisions conserve it.

• Believing momentum is lost in an inelastic collision.

  Put it right: The correct principle is that momentum is conserved whenever no resultant external force acts.

• Treating a collision as perfectly elastic because the bodies bounce apart.

  Put it right: The correct criterion is numerical conservation of kinetic energy, not the appearance of bouncing.

Exam tips

• Calculate total kinetic energy before and after to classify a collision as elastic or inelastic.
• Use conservation of momentum first to find unknown velocities, then test kinetic energy.
• State clearly which quantity is conserved and which is not when explaining a collision.