Slide 1Water SlideSlide 3Slide 4Slide 5Potential Energy DiagramsStable vs. Unstable Equilibrium PointsSlide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 24Water SlideWho will come first?http://curvebank.calstatela.edu/brach/brach.htmThe curve of fastest descentCycloidInverted cycloid:BrachistochroneENERGY DIAGRAMSPotential 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)0dxdUxFStable vs. Unstable Equilibrium PointsThe 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?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.a)What is the direction of the force on the particle when it is at point A?b) At point B?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?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?QuizQuizA block of mass m is attached to a vertical spring, spring constant k. The spring is unstretched at y=0. AIf the spring is compressed an amount A and the block released from rest, how high will it
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