1. Physics 218, Lecture IX1 Physics 218 Lecture 9 Dr. David Toback

2. Physics 218, Lecture IX2 Overview Today’s lecture is about problem solving for Chapters 4 & 5 Learn how to use everything we’ve learned so far to solve problems with: –Rope –Friction –Friction and Uniform Circular Motion

3. Physics 218, Lecture IX3

4. 4 Rope Problems A PHYS218 rope is a perfect rope. It is massless and it doesn’t stretch. This means: The acceleration of any part of a rope is the same as any other part The magnitude of the acceleration of the two things it attaches are equal The tension (Force) exerted by each end is the same

5. Physics 218, Lecture IX5 Two Boxes and a Pulley You hold two boxes, m  and m , connected by a rope running over a pulley at rest. The coefficient of kinetic friction between the table and box I is . You then let go and the mass m  is so large that the system accelerates Q: What is the magnitude of the acceleration of the system? Ignore the mass of the pulley and rope and any friction associated with the pulley

6. Physics 218, Lecture IX6 Banking Angle You are a driver on the NASCAR circuit. Your car has m and is traveling with a speed V around a curve with Radius R What angle, , should the road be banked so that no friction is required?

7. Physics 218, Lecture IX7  Skiing You are the ski designer for the Olympic ski team. Your best skier has mass m. She plans to go down a mountain of angle  and needs an acceleration a in order to win the race What coefficient of friction, , do her skis need to have ?

8. Physics 218, Lecture IX8 Skidding on a Curve A car of mass m rounds a curve on a flat road of radius R at a speed V. What coefficient of friction is required so there is no skidding? Kinetic or static friction?

9. Physics 218, Lecture IX9 2 boxes connected with a string Two boxes with masses m 1 and m 2 are placed on a frictionless horizontal surface and pulled with a Force F P. Assume the string between doesn’t stretch and is massless. a)What is the acceleration of the boxes? b)What is the tension of the strings between the boxes? M2M2 M1M1

10. Physics 218, Lecture IX10 An Incline, a Pulley and two Boxes In the diagram given, m 1 and m 2 remain at rest and the angle  is known. The coefficient of static friction is  and m 1 is known. What is the mass m 2 ?  m2m2 m1m1 Ignore the mass of the pulley and cord and any friction associated with the pulley

11. Physics 218, Lecture IX11 Is it better to push or pull a sled? You can pull or push a sled with the same force magnitude, F P, but different angles , as shown in the figures. Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, , which is better? FPFP

12. Physics 218, Lecture IX12 Next Week HW4 Due Monday Labs & Recitation as usual: Chapter 5 problems For Lecture next Tuesday –Reading Chapter 6 Chapter 7, Section 1 & 2 –Reading Questions Q7.1 and Q7.2

13. Physics 218, Lecture IX13

14. Physics 218, Lecture IX14 Before we begin… Exam this Thursday –I will give you a formula sheet A copy is already on web –Here at 8:00AM –Only on topics through Chapter 3 on Syllabus –3 multi-part problems: Some short answer, dominated by chapter 3 topics and full length problems using only variables Today’s lecture not on the exam

15. Physics 218, Lecture IX15 Yet more before we begin HW1, HW2, HW3 (+ associated quizzes) and math quizzes are now past due –If you need an extension, I need an email Mini-practice exam becomes available when you have gotten perfect scores on all of the above 5 Bonus points on the exam if you get a perfect score on the Mini-Practice BEFORE the exam on Thursday

16. Physics 218, Lecture IX16 Next time Thursday –I will give you a formula sheet A copy is already on web –Here at 8:00AM –Only on topics through Chapter 3 on Syllabus –3 multi-part problems: Some short answer, dominated by chapter 3 topics and full length problems using only variables Today’s lecture not on the exam

17. Physics 218, Lecture IX17 Thursday and Next Week Thursday: Exam –I will give you a formula sheet (new version on the web) –Here at 8:00AM –Only on topics through Chapter 3 on Syllabus –Make sure you know your section number and your UIN HW4 Due Monday Labs & Rec as usual, work on Chapter 5 For Lecture next Tuesday –Chapter 6 –Chapter 7, Section 1 & 2 –Reading Questions Q7.1 and Q7.2

18. Physics 218, Lecture IX18 Exam 1 Results from Last Semester Overall: Mean=52/75 or ~70% Green: People who took the mini-practice exam: Mean = 56(+5)/75 Red: People who didn’t: Mean = 38/75 My advice is to study for the exam by finishing all the HW and testing whether you really understand by turning them all in and getting a 100 on the mini-practice exam by yourself in as few tries as possible Extra problems at the end of my lecture notes

19. Physics 218, Lecture IX19 Need help? Supplemental Instruction is free and meets 3 times a week. Helpdesk has hours everyday and is free. –Hours are posted on my website Private tutoring available by appointment For more information about all of these see: http://physics218.physics.tamu.edu/help/

20. Physics 218, Lecture IX20 Exam 1 Overall: Mean=52/75 or ~70% Green: People who took the mini-practice exam. Mean = 58(+5)/75 (not shown) Red: People who didn’t. Mean = 44/75 Bonus points will be added later. Students

21. Physics 218, Lecture IX21 The Skier in slush A skier is going down a mountain which is at an angle . She has mass m but the snow is so slushy that she has constant velocity. What is the coefficient of friction  ? 

22. Physics 218, Lecture IX22 Conical Pendulum A small ball of mass m is suspended by a cord of length L and revolves in a circle with a radius given by r = Lsin . 1.What is the velocity of the ball? 2.Calculate the period of the ball.

23. Physics 218, Lecture IX23 Circular Motion Example A ball of mass m is at the end of a string and is revolving uniformly in a horizontal circle (ignore gravity) of radius R. The ball makes N revolutions in a time t. a)What is the centripetal acceleration? b)What is the centripetal force?