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Physics 218: Mechanics

Physics 218: Mechanics. Instructor: Dr. Tatiana Erukhimova Lecture 24. Water Slide. Who will come first?. The curve of fastest descent. Cycloid. Inverted cycloid: Brachistochrone. http://curvebank.calstatela.edu/brach/brach.htm. ENERGY DIAGRAMS. Potential Energy Diagrams.

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Physics 218: Mechanics

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  1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 24

  2. Water Slide Who will come first?

  3. The curve of fastest descent Cycloid Inverted cycloid: Brachistochrone http://curvebank.calstatela.edu/brach/brach.htm

  4. ENERGY DIAGRAMS

  5. Potential Energy Diagrams • For Conservative forces can draw energy diagrams • Equilibrium points • Motion will move “around” the equilibrium • If placed there with no energy, will just stay (no force)

  6. Stable vs. Unstable Equilibrium Points The force is zero at both maxima and minima but… • If I put a ball with no velocity there would it stay? • What if it had a little bit of velocity?

  7. A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in the Figure. The particle is released from rest at point A. • What is the direction of the force on the particle when it is at point A? • At point B?

  8. c) At what value of x is the kinetic energy of the particle a maximum? d) What is the force on the particle when it is at point C?

  9. e) What is the largest value of x reached by the particle during its motion? f) What value or values of x correspond to points of stable equilibrium? g) Of unstable equilibrium?

  10. Quiz

  11. Quiz A block of mass m is attached to a vertical spring, spring constant k. The spring is unstretched at y=0. A If the spring is compressed an amount A and the block released from rest, how high will it go?

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