1. Collisions

2. Point of Contact  When two objects collide there is a point of contact.  The moment of contact is short. Impulse due to external forces is smallImpulse due to external forces is small J ext = F ext  tJ ext = F ext  t  The objects in collision at the time of collision can be viewed as an isolated system.

3. Momentum at Collision  For an isolated system momentum is conserved.  Always true in collisions. Reaction forces balanceReaction forces balance No time for external forcesNo time for external forces Before: m1m1 v1iv1i v2iv2i m2m2 v1fv1f v2fv2f After:

4. 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 lost at the collision is lost for kinetic energy.  Inelastic collisions always have a loss of kinetic energy.

5. Inelastic Collision  For non-conservative forces some energy is lost.  After the collision there is less energy available.  The total kinetic energy is not conserved – less after the collision.  This is an inelastic collision. Inelastic

6. 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

7. 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

8. Elasticity  Real collisions lose energy. 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 some elasticity.

9. Coefficient of Restitution  If there is no energy loss a rebound would have equal and opposite velocity.  For an inelastic collision the coefficient of restitution measures the relative amount of energy loss by comparing the rebound velocity.

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