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Mechanics: Conservation Laws in Free Fall Motion

Explore the principles of energy conservation in free-fall motion, including frictionless surfaces, gravitational potential energy, and the law of mechanical energy conservation. Learn about Hooke's Law, elastic potential energy, perfect collisions, and momentum conservation.

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Mechanics: Conservation Laws in Free Fall Motion

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  1. Energy Readings: Chapter 10

  2. Free-Fall motion This is the conservation law for free fall motion: the quantity has the same value before and after the motion.

  3. Free-Fall Motion Then Conservation law: the quantity has the same value before and after the motion.

  4. Frictionless surface: acceleration Motion with constant acceleration: Conservation law: the quantity has the same value before and after the motion.

  5. Conservation law: the quantity has the same value at the initial and the final points In all cases the velocity at the final point is the same (FRICTIONLESS MOTION)

  6. Conservation law: or Kinetic Energy – energy of motion Gravitational Potential Energy – energy of position Mechanical Energy Conservation law of mechanical energy (without friction): The units of energy is Joule:

  7. Zero of potential energy Only the change of potential energy has the physical meaning

  8. Restoring Force: Hooke’s Law Hooke’s Law: spring constant

  9. Restoring Force: Hooke’s Law The sign of a restoring force is always opposite to the sign of displacement

  10. Restoring Force: Elastic Potential Energy The elastic potential energy is always positive

  11. Restoring Force: Elastic Potential Energy

  12. Restoring Force: Elastic Potential Energy

  13. Law of Conservation of Mechanical Energy

  14. The law of conservation of momentum

  15. Perfectly Elastic Collisions During the collision the kinetic energy will be transformed into elastic energy and then elastic energy will transformed back into kinetic energy Perfectly Elastic Collision: Mechanical Energy is Conserved (no internal friction) A A B B Perfectly inelastic collision: A collision in which the two objects stick together and move with a common final velocity – NO CONSERVATION OF MECHANICAL ENERGY

  16. Perfectly Elastic Collisions Conservation of Momentum and Conservation of Energy isolated system A A B B Now we have enough equations to find the final velocities.

  17. Example: is always positive, can be positive (if ) or negative (if ) if

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