1. Physics 114A - Mechanics Lecture 6 (Walker: 3.4-5) The r, v, and a Vectors January 12, 2012 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

2. January 12, 2012Physics 114A - Lecture 62/24 Announcements Because of recent problems with WebAssign, I have moved the due date for Assignment #1 to 11:59 PM on Tuesday, January 17. Now all 215 registered students have WebAssign Accounts. Good! Assignment #2 is still due at 11:59 PM on Thursday, January 19. Register your clicker using the “Clicker” link on the Physics 114A Syllabus page. So far 188/215 students have registered their clickers. You may talk to your neighbors during a clicker session. If your clicker ID is not appearing, reset it to Channel 01 and/or if necessary, get closer to the pickup antenna. We will have Exam 1 on Friday, January 20. It will be about 75% multiple choice and 25% free response. The questions will be based on Walker “2-dot” end-of-chapter questions. There will be assigned seating. If you wish a left-handed seat, a right-handed aisle seat, or a front row seat, send your request to me by E-mail.

3. January 3, 2012Physics 114A - Lecture 13/21 Physics 114A - Introduction to Mechanics - Winter-2012 Lecture: Professor John G. Cramer Textbook: Physics, (Edition: UW Vol. 1 or Complete 4th), James S. Walker WeekDateL#Lecture TopicPagesSlidesReadingHW DueLab 1 2-Jan-12H1 New Year Holiday No Lab 1st week 3-Jan-121Introduction to Physics1221Chapter 1 5-Jan-122Position & Velocity8222-1 to 2-3No HW 6-Jan-123Velocity & Acceleration10252-4 to 2-5 2 9-Jan-124Equations of Motion9202-6 to 2-7 1-D Kinematics 10-Jan-125Vectors8243-1 to 3-3 12-Jan-126r, v & a Vectors5243-4 to 3-5HW1 13-Jan-127Relative Motion3183-6 3 16-Jan-12H2 MLK Birthhday Holiday Free Fall & Projectiles 17-Jan-1282D Motion Basics5194-1 to 4-2 19-Jan-1292D Examples13224-3 to 4-5HW2 20-Jan-12E1 EXAM 1 - Chapters 1-4 Lecture Schedule (Part 1) We are here.

4. January 12, 2012Physics 114A - Lecture 64/24 Unit Vectors Unit vectors are dimensionless vectors of unit length. For example, the vector has magnitude (with units) A x and points along the +x axis. A

5. January 12, 2012Physics 114A - Lecture 65/24 Scalar-Vector Multiplication Multiplying vectors by scalars: the scalar multiplier changes the vector length, and the scalar sign can reverse the direction. This property allows vectors to be factored into a unit vector and a multiplier. The unit vector specifies only the direction, while the multiplier provides the magnitude and units of the vector.

6. January 12, 2012Physics 114A - Lecture 66/24 Unit Vectors Example:

7. January 12, 2012Physics 114A - Lecture 67/24 Position, Displacement, Velocity, & Acceleration Vectors The position vector r points from the origin to the location in question. The displacement vector Δr points from the original position to the final position.

8. January 12, 2012Physics 114A - Lecture 68/24 The Displacement Vector

9. January 12, 2012Physics 114A - Lecture 69/24 The Average Velocity Vector Average velocity vector: (3-3) So v av is in the same direction as Δr.

10. January 12, 2012Physics 114A - Lecture 610/24 The Average & Instantaneous Velocity Vectors Instantaneous velocity vector is tangent to the path:

11. January 12, 2012Physics 114A - Lecture 611/24 Velocity Vectors

12. January 12, 2012Physics 114A - Lecture 612/24 Example: A Dragonfly A dragonfly is observed initially at position: Three seconds later, it is observed at position: What was the dragonfly’s average velocity during this time?

13. January 12, 2012Physics 114A - Lecture 613/24 Example: Velocity of a Sailboat A sailboat has coordinates (130 m, 205 m) at t 1 =0.0 s. Two minutes later its position is (110 m, 218 m). (a) Find ; (b) Find ;

14. January 12, 2012Physics 114A - Lecture 614/24 Velocity & Acceleration Vectors The average acceleration vector a is in the direction of the change in velocity  v :

15. January 12, 2012Physics 114A - Lecture 615/24 Acceleration on a Curve Typically, for a vehicle moving on a curve at a uniform speed, the acceleration is perpendicular to the velocity and the magnitude of the velocity stays the same, while the velocity’s direction changes. For example, consider a car that has an initial velocity of 12 m/s east, and 10 seconds later its velocity is 12 m/s south.

16. January 12, 2012Physics 114A - Lecture 616/24 Example: Car Accelerating on a Curve A car is traveling northwest at 9.00 m/s. Eight seconds later it has rounded a corner and is now headed north at 15.0 m/s/ (a) What is the magnitude and direction of the acceleration during those 8.0 s? N (y) E(x)

17. January 12, 2012Physics 114A - Lecture 617/24 Acceleration Vectors

18. January 12, 2012Physics 114A - Lecture 618/24 Position, Displacement, Velocity, & Acceleration Vectors The velocity vector v always points in the direction of motion. The acceleration vector a can point anywhere.

19. January 12, 2012Physics 114A - Lecture 619/24 Clicker Question 1 A particle moves to the right in the x-y plane along the blue path. Identify each vector in the figure as a position (P), velocity (V), or acceleration (A) vector. (1) 1=V, 2=A, 3=P, 4=V; (2) 1=A, 2=P, 3=V, 4=P; (3) 1=P, 2=V, 3=V, 4=A; (4) 1=P, 2=A, 3=A, 4=V;

20. January 12, 2012Physics 114A - Lecture 620/24 Example: A Thrown Baseball The position of a thrown baseball is given by: (a) Find the velocity as a function of time. (b) Find the acceleration as a function of time.

21. January 12, 2012Physics 114A - Lecture 621/24 Example: Rounding a Curve A car is traveling east at 60 km/h. It rounds a curve, and 5.0 s later it is traveling north at 60 km/h. (a) Find the average acceleration of the car.

22. January 12, 2012Physics 114A - Lecture 622/24 Direction of the Acceleration Vector Bungee Jumper’s Decent and Ascent Bungee Jumper

23. January 12, 2012Physics 114A - Lecture 623/24 You are asked to substitute for an ill performer in a circus that is sponsored by your school. The job, should you choose to accept it, is to be shot out of a cannon. Never afraid to accept a challenge, you accept. The barrel of the cannon is inclined at an angle of 60 0 above the horizontal. Your physics teacher offers you extra credit if you successfully use a motion diagram to estimate your acceleration during the ascending portion of your flight. 1. Make a motion diagram with velocities. 2. Draw a vector addition diagram using the relation: 3. Draw the acceleration from: Example: Human Cannonball

24. Before the next lecture, read Walker Chapter 3.6 Homework Assignment #1 should be submitted using the WebAssign system by 11:59 PM on Thursday, January 12 (Tonight!). Homework Assignment #2 should be submitted using the WebAssign system by 11:59 PM on Thursday, January 19. End of Lecture 6