CollisionsPoint of ContactMomentum at CollisionEnergy LossInelastic CollisionCompletely InelasticStuck TogetherElasticityCoefficient of RestitutionSoft BallCollisionsCollisionsPoint of ContactPoint of ContactWhen two objects collide there is a point of contact.When two objects collide there is a point of contact.The moment of contact is short.The moment of contact is short.•Impulse due to external forces is smallImpulse due to external forces is small•JJextext = = FFextext ttThe objects in collision at the time of collision can be The objects in collision at the time of collision can be viewed as an isolated system.viewed as an isolated system.Momentum at CollisionMomentum at CollisionFor an isolated system For an isolated system momentum is conserved.momentum is conserved.Always true in collisions.Always true in collisions.•Reaction forces balanceReaction forces balance•No time for external forcesNo time for external forcesiiivmvmP2211Before:m1v1iv2im2v1fv2fAfter:fffvmvmP2211fiPP Energy LossEnergy LossFriction can cause a loss of energy at contact.Friction can cause a loss of energy at contact.•Real springs are not perfectly elasticReal springs are not perfectly elastic•Materials heat upMaterials heat upThe energy lost at the collision is lost for kinetic The energy lost at the collision is lost for kinetic energy. energy. InelasticInelastic collisions always have a loss of kinetic collisions always have a loss of kinetic energy.energy.Inelastic CollisionInelastic CollisionFor non-conservative forces For non-conservative forces some energy is lost.some energy is lost.After the collision there is After the collision there is less energy available.less energy available.The total kinetic energy is The total kinetic energy is not conserved – less after not conserved – less after the collision.the collision.This is an inelastic collision.This is an inelastic collision.fiPP fiKK InelasticCompletely InelasticCompletely InelasticCollisions that end with the two objects together are Collisions that end with the two objects together are completely (or perfectly) inelastic.completely (or perfectly) inelastic.The energy lost in the completely inelastic collision is The energy lost in the completely inelastic collision is usually turned into heat. usually turned into heat. energy lost as heatvelocity after collisionStuck TogetherStuck TogetherA 950 kg car sits at the A 950 kg car sits at the bottom of an icy hill.bottom of an icy hill.•It is struck by a 7600 kg It is struck by a 7600 kg truck moving at 50 km/h.truck moving at 50 km/h.•If they stick together, how If they stick together, how far do they move uphill?far do they move uphill?Momentum is conserved.Momentum is conserved.•The initial momentum is The initial momentum is only only PP = = mm22 vv22•The final momentum is The final momentum is P = (P = (mm11 + + mm22) ) vvff = = MM vvff•The final velocity is The final velocity is vvff = = mm22 vv22 / / MM = 44 km/h = 44 km/hEnergy is conserved uphill.Energy is conserved uphill.•MghMgh = (1/2) = (1/2) MM vvff22•hh = = vvff22 / 2 / 2gg = 7.8 m = 7.8 mm2m1v2ihElasticityElasticityReal collisions lose energy.Real collisions lose energy.•Objects are deformedObjects are deformed•Objects heat upObjects heat up•Kinetic energy not conservedKinetic energy not conservedIf there is some rebound, then there is some If there is some rebound, then there is some elasticity.elasticity.Coefficient of RestitutionCoefficient of RestitutionIf there is no energy loss a rebound would have equal If there is no energy loss a rebound would have equal and opposite velocity.and opposite velocity.For an inelastic collision the coefficient of restitution For an inelastic collision the coefficient of restitution measures the relative amount of energy loss by measures the relative amount of energy loss by comparing the rebound velocity.comparing the rebound velocity.ffiivvvv1221iiffvvvve1212Soft BallSoft BallA ball rebounds to 70% of its A ball rebounds to 70% of its initial height. What is the initial height. What is the coefficient of restitution?coefficient of
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