1. 12/05/2013PHY 113 C Fall 2013 -- Lecture 261 PHY 113 C General Physics I 11 AM – 12:15 PM MWF Olin 101 Plan for Lecture 26: 1.Comments on preparing for Final Exam 2.Comprehensive review – Part II 3.Course assessment

2. 12/05/2013 PHY 113 C Fall 2013 -- Lecture 262

3. 12/05/2013PHY 113 C Fall 2013 -- Lecture 263 Final exam schedule for PHY 113 C

4. 12/05/2013PHY 113 C Fall 2013 -- Lecture 264 Comments on Final Exam  It will be comprehensive (covering material from Chapters 1-22)  It is scheduled for 9 AM Dec. 12 th in Olin 101  In class format only; no time pressure  May bring 4 equation sheets  Format will be similar to previous exams; may see problems similar to those on previous exams

5. 12/05/2013PHY 113 C Fall 2013 -- Lecture 265 General advice on how to prepare for Final Exam  Review fundamental concepts and their corresponding equations  Develop equation sheets that help you solve example problems on all of the material. (You can assume that empirical constants and parameters will be given to you; they need not take up space on your equation sheet.)  Practice problem solving techniques.  If you find mysteries, unanswered questions, etc., please contact me.

6. 12/05/2013PHY 113 C Fall 2013 -- Lecture 266 Problem solving steps 1.Visualize problem – labeling variables 2.Determine which basic physical principle(s) apply 3.Write down the appropriate equations using the variables defined in step 1. 4.Check whether you have the correct amount of information to solve the problem (same number of knowns and unknowns). 5.Solve the equations. 6.Check whether your answer makes sense (units, order of magnitude, etc.).

7. 12/05/2013PHY 113 C Fall 2013 -- Lecture 267 Review of some basic concepts Vectors  Keep track of 2 or more components (or magnitude and direction)  Examples  Position vector  Velocity  Acceleration  Force  Momentum Scalars  Single (signed) quantity  Examples  Time  Energy  Kinetic energy  Work  Potential energy  Pressure  Temperature  Mass  Density  Volume

8. 12/05/2013PHY 113 C Fall 2013 -- Lecture 268 Review of some basic concepts Newton’s second law

9. 12/05/2013PHY 113 C Fall 2013 -- Lecture 269 Review of some basic concepts Newton’s second law for angular motion

10. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2610 Review of energy concepts:

11. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2611 Summary of work, potential energy, kinetic energy relationships

12. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2612 Extension of concepts of energy conservation to extended objects

13. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2613 CM

14. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2614 Three round balls, each having a mass M and radius R, start from rest at the top of the incline. After they are released, they roll without slipping down the incline. Which ball will reach the bottom first? A B C

15. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2615 iclicker exercise: In previous example which of the equations on your equation sheet would be most useful?

16. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2616 From your questions -- (question from Exam 2)

17. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2617 Comment on circular motion -- uniform circular motion

18. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2618 r In terms of time period T for one cycle: In terms of the frequency f of complete cycles: Comment on circular motion -- uniform circular motion

19. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2619 Comment on circular motion -- uniform circular motion – effects on gravitationally attractive bodies

20. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2620 Comment on circular motion -- non-uniform circular motion rAt each instant of time Note that if speed v is not constant, then there will also be a tangential component of acceleration: acac aa

21. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2621 From your questions -- (question from Exam 1) a.Neglecting any possible dissipative forces acting on this system, determine the magnitude of the velocity of the ball v f as it is caught by the person at the coordinates (x f,y f ). b.What is the angle  f ? c.Determine the net work of gravity on the ball at it moves from the initial to final positions in its trajectory:.

22. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2622 From your questions -- (question from Exam 1) a.Neglecting any possible dissipative forces acting on this system, determine the magnitude of the velocity of the ball v f as it is caught by the person at the coordinates (x f,y f ). b.What is the angle  f ? c.Determine the net work of gravity on the ball at it moves from the initial to final positions in its trajectory:.

23. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2623 From your questions -- force diagrams m   F1F1 F2F2 mg

24. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2624 mg(-j) r T  F=ma  T- mg cos   mg sin  ma   =I   r mg sin  = mr 2  mra  From your questions -- pendulum

25. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2625 From your questions -- driven Harmonic oscillator

26. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2626 From your questions -- driven Harmonic oscillator

27. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2627 Similar problem from webassign: Damping is negligible for a 0.165-kg object hanging from a light, 6.30-N/m spring. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.600m? (usually neglected)

28. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2628 Examples of two-dimensional collision; balls moving on a frictionless surface

29. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2629 Examples of two-dimensional collision; balls moving on a frictionless surface – energy conservation? Note: In these collision analyses, we are neglecting forces and potential energy iclicker question Why? A.We are cheating physics B.We are applying the laws of physics correctly

30. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2630 Examples of two-dimensional collision; balls moving on a frictionless surface – energy conservation? Assuming that we applying the laws of physics correctly – we can ask the question – Is (kinetic) energy conserved?

31. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2631 From your questions -- conservation of angular momentum mm d1d1 d1d1 mm d2d2 d2d2 I 1 =2md 1 2 I 2 =2md 2 2 I 1  1 =I 2  2   2 =  1 I 1 /I 2 11 22

32. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2632 Example form Webassign #11 X 11 33 22 iclicker exercise When the pivot point is O, which torque is zero? A.  1 ? B.  2 ? C.  3 ?

33. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2633 An example of the application of torque on a rigid object: A horizontal 800 N merry-go-round is a solid disc of radius 1.50 m and is started from rest by a constant horizontal force of 50 N applied tangentially to the cylinder. Find the kinetic energy of solid cylinder after 3 s. K = ½ I  2  i  t =  t In this case I = ½ m R 2 and  = FR R F

34. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2634 Webassign questions on fluids (Assignment #17) A hypodermic syringe contains a medicine with the density of water (see figure below). The barrel of the syringe has a cross- sectional area A = 2.40 10 -5 m 2, and the needle has a cross- sectional area a = 1.00 10 -8 m 2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force of magnitude 2.65 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle's tip.

35. 12/05/2013PHY 113 C Fall 2013 -- Lecture 2635 Send email or come to see me if you have further questions. THANKS!