Inelastic Collisions

Energy Loss  Friction can cause a loss of energy at contact. Real springs are not perfectly elasticReal springs are not perfectly elastic Materials heat upMaterials heat up  The energy not lost at the collision is available for kinetic energy.  Inelastic collisions always have a loss of kinetic energy.

Stuck Together  A 950 kg car sits at the bottom of an icy hill. It is struck by a 7600 kg truck moving at 50 km/h.It is struck by a 7600 kg truck moving at 50 km/h. If they stick together, how far do they move uphill?If they stick together, how far do they move uphill?  Momentum is conserved. The initial momentum is only P = m 2 v 2 The final momentum is P = (m 1 + m 2 ) v f = M v f The final velocity is v f = m 2 v 2 / M = 44 km/h  Energy is conserved uphill. Mgh = (1/2) M v f 2 h = v f 2 / 2g = 7.8 m m2m2 m1m1 v2iv2i h

Completely Inelastic  Collisions that end with the two objects together are completely (or perfectly) inelastic.  The energy lost in the completely inelastic collision is usually turned into heat. energy lost as heat velocity after collision

Elasticity  Real collisions are generally not elastic. Objects are deformedObjects are deformed Objects heat upObjects heat up Kinetic energy not conservedKinetic energy not conserved  If there is some rebound, then there is elasticity. Imperfect springImperfect spring

Coefficient of Restitution  In an elastic collision the initial and final velocities were exactly related.  For an inelastic collision the coefficient of restitution measures the relative amount of energy loss.

Soft Ball  A ball rebounds to 70% of its initial height. What is the coefficient of restitution? next m1m1 v1iv1i v1fv1f