Collision Component Relations Smooth — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Collision Component Relations (Smooth) Applies to two-dimensional collisions between objects where the collision surface is smooth (no friction) and the initial and final velocities can be resolved into normal and tangential components. Resolve the initial and final velocities into tangential (t) and normal (n) components relative to the collision surface. For a smooth collision, no tangential force acts, leading to the conservation of tangential momentum and thus v 1t = u 1t and v 2t = u 2t . The normal component relation is defined by the coefficient of restitution, e , which relates relative separation velocity to relative approach velocity. The definition yields e = v 2n - v 1n u 1n - u 2n . Rearranging this gives the final relation for the normal components: v 2n - v 1n = e(u 1n - u 2n ) . e 0 Tangential components are conserved: v 1t = u 1t and v 2t = u 2t . Forgetting that tangential components are always conserved, even if the collision is highly inelastic. Confusing the definition of e : it relates relative separation velocity to relative approach velocity. Applying the normal component relation to the total velocity instead of just the normal component.