Elastic CollisionsMomentum and Kinetic EnergyKinetic Energy at CollisionElastic CollisionDouble ConservationHead-on CollisionRelated VelocitiesEqual MassesStriking a Heavy MassStriking a Light MassElastic CollisionsElastic CollisionsMomentum and Kinetic Momentum and Kinetic EnergyEnergyAn object in motion has a momentum based on its An object in motion has a momentum based on its mass and velocity.mass and velocity.•pp = = mvmvThe object also has kinetic energy.The object also has kinetic energy.•KK = ½ = ½ mvmv22 = = pp22 / 2 / 2mmKinetic Energy at CollisionKinetic Energy at CollisionEnergy is conserved only for Energy is conserved only for conservative forces.conservative forces.Internal forces may be Internal forces may be nonconservative.nonconservative.The force at the collision is The force at the collision is not always conservative.not always conservative.energy lost to heat2222121121iiivmvmK Before:m1v1iv2im22222121121fffvmvmK After:v2fv1fElastic CollisionElastic CollisionFor conservative forces the For conservative forces the energy is conserved.energy is conserved.After the collision of contact After the collision of contact the potential energy is zero.the potential energy is zero.The total kinetic energy is The total kinetic energy is conserved – equal before conserved – equal before and after the collision.and after the collision.This an elastic collision.This an elastic collision.fiPP fiKK ElasticDouble ConservationDouble ConservationElastic collisions conserve Elastic collisions conserve both momentum and kinetic both momentum and kinetic energy.energy.Two equations govern all Two equations govern all elastic collisions.elastic collisions.2222121121222212112122112211ffiiffiivmvmvmvmvmvmvmvmm1m2v1iv2ibeforem1m2v1fv2fafterHead-on CollisionHead-on CollisionAn elastic head-on collision An elastic head-on collision takes place in one takes place in one dimension.dimension.If the collision is not head-If the collision is not head-on, the force pair is in a on, the force pair is in a different direction.different direction.m1m2v1iv2im1m2v1iv2iforce and velocity in a line force and velocity on different linesRelated VelocitiesRelated Velocities)()(22211122221111iffiiffivvmvvmvmvmvmvm))(())(()()(2222211111222222121122221221212112121121ififfifiiffiiffivvvvmvvvvmvvmvvmvmvmvmvmm1m2v1iv2imomentum in a linekinetic energy conservationsolve for velocitiesffiiiffivvvvvvvv12212211Equal MassesEqual MassesA 150 g ball moves at 1.4 m/s.A 150 g ball moves at 1.4 m/s.•The momentum is 0.21 kg m/sThe momentum is 0.21 kg m/sIt strikes an equal mass ball at It strikes an equal mass ball at rest.rest.•vv11ii = 1.4 m/s = 1.4 m/s•vv22ii = 0 = 0•Therefore, Therefore, vv11ff = 0 = 0•and and vv22ff = = vv11iiffiiffiivvvvvvvv12211221m1m2v1im1m2v2fmomentum:kinetic energy:Striking a Heavy MassStriking a Heavy MassLet Let mm11 << << mm22, when a golf ball , when a golf ball bounces off the floor.bounces off the floor.The floor is at rest.The floor is at rest.•vv22ii = 0 = 0The final velocity is equal The final velocity is equal and opposite the initial and opposite the initial velocityvelocity021121211121112211fiifffiffivvvmmmmvvvvvmvmvmmomentum:kinetic energy:combined:m1v1iv1fStriking a Light MassStriking a Light MassLet Let mm11 >> >> mm22, when a car , when a car strikes a ball.strikes a ball.The ball is at rest.The ball is at rest.•vv22ii = 0 = 0For a very heavy For a very heavy mm11 , the , the final velocity of final velocity of mm22 is twice is twice the initial velocity of the initial velocity of mm11 . .ifiifffiffivvvvmmmmvvvvvmvmvm1211212111211122112momentum:kinetic
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