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Collision Physics: Momentum and Energy Conservation in Collisions

Explore the principles of momentum and energy conservation in collisions, including elastic and inelastic scenarios, with real-life examples and calculations. Understand how objects interact in collisions and the effects of external forces on momentum and energy transfer.

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Collision Physics: Momentum and Energy Conservation in Collisions

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  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 small • Jext = FextDt • 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 balance • No time for external forces m1 m2 v1i v2i Before: v1f v2f After:

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

  5. 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 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. velocity after collision energy lost as heat

  7. 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. If they stick together, how far do they move uphill? Momentum is conserved. The initial momentum is only P = m2v2 The final momentum is P = (m1 + m2) vf = Mvf The final velocity is vf = m2v2 / M = 44 km/h Energy is conserved uphill. Mgh = (1/2) Mvf2 h = vf2 / 2g = 7.8 m Stuck Together v2i h m2 m1

  8. A falling ball has a momentum. After hitting the floor there has been a change in momentum. The change is due to a force from the floor. Bounce pf pi FN

  9. Elasticity • Real collisions lose energy. • Objects are deformed • Objects heat up • Kinetic energy not conserved • If there is some rebound, then there is some elasticity.

  10. 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.

  11. Soft Ball • A ball rebounds to 70% of its initial height. What is the coefficient of restitution? v1f m1 v1i

  12. Two balls fall at the same rate due to gravity, but with different momenta. Ball 1 bounces from the ground. Ball 2 bounces from ball 1. Two Balls pf2 pi2 pf1 pi1

  13. Initially both balls go down together with the same velocity. Double Bounce • The lower ball hits the upper ball and momentum is conserved between the balls. • The lower ball gets a force from the floor and changes momentum. pi2 pf2 pi2 pi1 pf1 pm1

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