Elastic and Inelastic Collisions - AP Physics C: Mechanics

Momentum. Always conserved when no external forces act.

Initial relative velocity = - Final relative velocity. Speed of approach equals speed of separation.

Internal forces are equal and opposite. Newton's third law applies during collision.

Perfectly inelastic collision. Objects stick together, no separation occurs.

External forces are negligible. Collision duration is typically very short.

Coefficient = 0. Zero elasticity means maximum energy loss.

Collision where kinetic energy is not conserved. Momentum conserved but kinetic energy is lost to other forms.

Causes additional energy loss. Reduces kinetic energy through work done.

Partially lost to other forms. Energy converts to heat, sound, and deformation.

Initial KE = Final KE. Total kinetic energy remains constant throughout.

Objects combine, single shared velocity. Objects stick together with common final velocity.

Elastic collision. No kinetic energy is lost to other forms.

Maximum kinetic energy is lost. Objects stick together, energy lost to deformation.

Converted to heat, sound, and deformation. Energy transforms from kinetic to other forms.

Measures elasticity of collisions. Ratio of separation to approach velocities.

Objects do not rebound after collision. Objects remain together after collision impact.

Equal to initial velocity of approach. Coefficient of restitution equals one for elastic.

Center of mass velocity is unchanged. No external forces change system momentum.

External forces are negligible. Collision duration is typically very short.

Perfectly inelastic collision. Objects stick together, no separation occurs.

Internal forces are equal and opposite. Newton's third law applies during collision.

Change in momentum, $F \times t$. Force applied over time changes momentum.

$\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2$. Total kinetic energy before collision.

$m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'$. Vector form of momentum conservation law.

Total kinetic energy is conserved. No kinetic energy is lost during collision.

Perfectly inelastic collision. Objects stick together after collision occurs.

$KE = \frac{1}{2}mv^2$. Energy of motion depends on mass and velocity squared.

No external forces on the system. Net external force must be zero for conservation.

Coefficient = 1. Maximum elasticity means no energy loss.