1. Physics 218, Lecture XXIII1 Physics 218 Lecture 23 Dr. David Toback

2. Physics 218, Lecture XXIII2 Schedule for the Rest of the Semester Today: Chapter 13, Part 2 Next Tuesday: Final Exam Review –I’ll give you a handout at the end of class No lectures next Thursday, Reading day Final exam is Monday December 11 th We will skip Chapter 15

3. Physics 218, Lecture XXIII3 Next Semester Some of you continue to ask about next semester: I am NOT teaching 208 However I am planning on teaching a new course: “Big Bang, Black Holes, No Math” –Cosmology Without The Math –Based on “A Brief History of Time” by Stephen Hawking –If you can’t take it, you might pass this info along to friends

4. Physics 218, Lecture XXIII4 Chap 13 Overview: Oscillations Last time: –Oscillations and vibrations –Equations of motion –Our spherical cow: Mass on a spring –Simple Harmonic Motion This time: –Energy –Uniform Circular Motion –Pendulums

5. Physics 218, Lecture XXIII5

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7. 7 Review: Simple Harmonic Motion Mass on a Spring Amplitude: Max distance Period: Time it takes to get back to here

8. Physics 218, Lecture XXIII8 Questions Simple Harmonic Motion x = A sin(  t +  ) Can you answer the following: What is the amplitude? What is the phase? What is the angular frequency? What is the velocity at the end points? What is the velocity at the middle?

9. Physics 218, Lecture XXIII9 Energy in SHO’s Potential Energy for a spring U = ½kx 2 Kinetic Energy for a block KE = ½mv 2 Total Energy E = U+KE = ½kx 2 +½mv 2

10. Physics 218, Lecture XXIII10 Energy Example A box of mass m is attached to a spring of constant k, stretched to a distance X o, held in place and then and released. Ignore gravity and friction. As a function of time: 1.What is the position? 2.What is the velocity? 3.What is the kinetic energy? 4.What is the potential energy? 5.What is the total energy of the system?

11. Physics 218, Lecture XXIII11 Uniform Circular Motion It turns out Uniform Circular Motion is really Simple Harmonic Motion but in two dimensions

12. Physics 218, Lecture XXIII12 Uniform Circular Motion in 2D A ball is moving anti-clockwise in uniform circular motion with a radius R and speed V. At t=0 we set  0 =0. 1.What is the equation of motion for  ? 2.What is the equation of motion in the x direction? 3.What is the displacement at all times? 4.What is the velocity at all times? 5.What is the speed at all times?

13. Physics 218, Lecture XXIII13 Mass on a spring with gravity h Initial Final Take an un-stretched spring. Gently add a mass and let go. The total stretch from equilibrium is a distance h before it starts to rise again. It then oscillates What is the angular velocity, , of motion?

14. Physics 218, Lecture XXIII14 Pendulums Pendulums can be a pretty good Simple Harmonic Oscillator The amount of swing has to be small

15. Physics 218, Lecture XXIII15 Example: Pendulum For small swing (  small) show that the motion of a ball on a pendulum is simple harmonic

16. Physics 218, Lecture XXIII16 Period of a Pendulum Show that the period of a pendulum doesn’t depend on the mass.

17. Physics 218, Lecture XXIII17 Challenge Exam 2nd Announcement of this semester’s 218 Challenge Exam: Monday December 4 th at 6:00PM –Not required (just for fun) –Does not (will not!!!) count as part of your final grade Test your skills against the best Aggies from all the Physics 218 sections (not just this lecture) on Physics 218 material Students who perform well will be recognized as Mechanics Scholars, and honored at a banquet in their honor. Other prizes, including cash. Handout information on the web now If you have a 95% exam average or above, I believe you have an Excellent chance of winning!

18. Physics 218, Lecture XXIII18 Coming up… Tuesday: Last class meeting –Review for the final, we’ll skip Chapter 15 –Do all the problems on the handout before class –Be prepared to vote for which type of problem you want to review most Monday December 11 th Final Exam, 1PM. Here –The material in Chapters 12 and 13 will be on the final –I guarantee there will be at least one problem from each chapter on the final Homework 13 and FCI II are due Wednesday A 100% on all homework is required in order to pass the class

19. Physics 218, Lecture XXIII19

20. Physics 218, Lecture XXIII20 Next Lecture Notes on the final: –Chapter 14 will be on the final. –Nothing from Chapter 15 on the final. –I guarantee there will be at least one problem from these last two weeks on the final –Final is Monday Dec 15 th, 1:00PM-3:00PM, here Next time –Review –Come prepared with questions

21. Physics 218, Lecture XXIII21 Draw position as a function of Time? Spring and Mass Paper which tells us what happens as a function of time

22. Physics 218, Lecture XXIII22 Ballistic Pendulum A bullet plows into a block of wood which is part of a pendulum. We know m, M and v. How high, h, does the block of wood go? What is the equation of motion after the collision?

23. Physics 218, Lecture XXIII23 Some Useful Relations and Weird Results

24. Physics 218, Lecture XXIII24 Doing a mass on a spring with g Take an un-stretched spring with constant k. Add a mass, m. Slowly stretch to -x 0, and bring to rest and let go. What is the equation of motion? Add a mass Stretch