John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw

1. Physics 114A - MechanicsLecture 6 (Walker: 3.4-5)The r, v, and a VectorsJanuary 14, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

2. Announcements • Homework Assignments #1-3 are now available on WebAssign. Assignment #1 is due at 11:59 PM on Thursday, January 16. Be sure to do the “A” homework (not “B”). So far 215/219 students have registered for 114A on WebAssign. Everyone MUST register on WebAssign before Exam 1. • Obtain a H-iTT clicker from the University Bookstore. RF Clickers should be set to Channel 01. Register your clicker using the “Clicker” link on the Physics 114A Syllabus page. So far 195/219 students have registered their clickers. • CLUE (Center for Learning & Undergraduate Enrichment) is offering free tutoring and exam prep. See CLUE for details. • The 117 labs started yesterday. By 8:00 AM on the day of your lab, you must complete the Pre-Lab exam on WebAssign. Physics 114A - Lecture 6

3. Lecture Schedule (Part 1) We are here. Physics 114A - Lecture 6

4. Unit vectors are dimensionless vectors of unit length. For example, the vector has magnitude (with units) Ax and points along the +x axis. A Unit Vectors Physics 114A - Lecture 6

5. 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. Physics 114A - Lecture 6

6. Unit Vectors Example: Physics 114A - Lecture 6

7. The displacement vectorΔr points from the original position to the final position. Position, Displacement, Velocity, & Acceleration Vectors The position vector r points from the origin to the location in question. Physics 114A - Lecture 6

8. The Displacement Vector Physics 114A - Lecture 6

9. The Average Velocity Vector Average velocity vector: (3-3) So vav is in the same direction as Δr. Physics 114A - Lecture 6

10. The Average & Instantaneous Velocity Vectors Instantaneous velocity vector is tangent to the path: Physics 114A - Lecture 6

11. Velocity Vectors Physics 114A - Lecture 6

12. 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? Example: A Dragonfly Physics 114A - Lecture 6

13. A sailboat has coordinates (130 m, 205 m) at t1=0.0 s. Two minutes later its position is (110 m, 218 m). (a) Find ; (b) Find ; Example: Velocity of a Sailboat Physics 114A - Lecture 6

14. Velocity & Acceleration Vectors The average acceleration vector a is in the direction of the change in velocity Dv: Physics 114A - Lecture 6

15. 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. Physics 114A - Lecture 6

16. N (y) E(x) Example: Car Acceleratingon 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? Physics 114A - Lecture 6

17. Acceleration Vectors Physics 114A - Lecture 6

18. Position, Displacement, Velocity, & Acceleration Vectors The velocity vector v always points in the direction of motion. The acceleration vector a can point anywhere. Physics 114A - Lecture 6

19. 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; Physics 114A - Lecture 6

20. 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. Example: A Thrown Baseball Physics 114A - Lecture 6

21. 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. Physics 114A - Lecture 6

22. Direction of theAcceleration Vector Bungee Jumper’sDecent and Ascent Bungee Jumper Physics 114A - Lecture 6

23. Example: Human Cannonball You are asked to substitute for an illperformer in a circus that is sponsoredby your school. The job, should youchoose to accept it, is to be shotout of a cannon. Never afraidto accept a challenge, youaccept. The barrel of the cannon is inclined at an angle of 600 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 usingthe relation: 3. Draw the acceleration from: Physics 114A - Lecture 6

24. Before Thursday, read WalkerChapter 3.6 • Homework Assignment #1 should be submitted using the WebAssign system by11:59 PM on Thursday, January 16 (day after tomorrow!). Homework Assignment #2 should be submitted using the WebAssign system by 11:59 PM on Thursday, January 23. End of Lecture 6