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Welcome back to Physics 211

Welcome back to Physics 211. Today’s agenda: Velocity and acceleration in two-dimensional motion Motion under gravity -- projectile motion Acceleration on curved path. Current homework assignments. WHW2: In blue Tutorials in Physics homework book

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Welcome back to Physics 211

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  1. Welcome back to Physics 211 Today’s agenda: Velocity and acceleration in two-dimensional motion Motion under gravity -- projectile motion Acceleration on curved path

  2. Current homework assignments • WHW2: • In blue Tutorials in Physics homework book • Second assignment – HW-13 #2, HW-14 #4, HW-17 #7, HW-20 #2 (not HW-19 #1) • due Wednesday Sept 12th in recitation • Can check clicker registration outside Room 111 (after tomorrow)

  3. Exam 1: next Thursday (9/20/07) • Seating arrangement will be posted outside Stolkin • Material covered: • Textbook chapters 1, 2, and 3 • Lectures up to 9/18 (slides online) • Tutorials on Velocity, Acceleration in one dimension, and Motion in two dimensions • Problem Solving Activities 1, 2, and 3 (on Graphs,Vectors, and Problems on motion in two dimensions) • Homework assignments

  4. Preparing for exam • Review homework problems and worksheets from recitation workshops • Work through practice exam problems (posted on website) • Work on more practice exam problems next Wednesday in recitation workshop • Try extra end-of-chapter problems in textbook • Solve problems on Mastering Physics website (not required!) -- use course ID = MPPLOURDE0001

  5. 2D Motion in components Note: component of position vector along x-direction is the x-coordinate! y Q yQ s – vector position  s = xQi + yQj j x xQ i

  6. Displacement in 2D Motion y Ds sI sF s – vector position Displacement s = sF - sI, also a vector! O x

  7. Describing motion with vectors • Positions and displacements s,Ds = sF - sI • Velocities and changes in velocity: vav= ––––,vinst= lim ––– Dv = vF - vI • Acceleration: aav= ––––,ainst= lim –––– Dt0 Dt0

  8. 2D Motion in components • x and y motions decouple • vx = dx/dt vy = dy/dt • ax = dvx/dt ay = dvy/dt • If acceleration is only non-zero in 1 direction, can choose coordinates so that 1 component of acceleration is zero • e.g., motion under gravity

  9. Simplest case • 2D motion with constant acceleration • Describes motion of ball under gravity (close to surface of Earth) • i.e., x and y components of position vector satisfy constant acceleration equations …

  10. Motion under gravity ax = 0 vx = v0x x= x0 + v0xt ay = -g vy = v0y - gt y= y0 + v0yt - (1/2)gt2 y v0y = v0sin(q) v0x = v0cos(q) v0 q x Projectile motion...

  11. Projectile question • A ball is thrown at 45o to vertical with a speed of 7 m/s. Assuming g=10 m/s2, how far away does the ball land?

  12. Ball A is released from rest. Another identical ball (ball B) is thrown horizontally at the same time and from the same height. Which ball will reach the ground first? 1. Ball A 2. Ball B 3. Both balls reach the ground at the same time. 4. The answer depends on the initial speed of ball B.

  13. A ball is ejected vertically upward from a cart at rest. The ball goes up, reaches its highest point and returns to the cart. In a second experiment, the cart is moving at constant velocity and the ball is ejected in the same way, where will the ball land? 1. In front of the cart. 2. Behind the cart. 3. Inside the cart. 4. The outcome depends on the speed of the cart.

  14. DEMO: shooting the bear … • Bear released at same time ball projected from end of tube • What happens to the bear and the ball? • Does outcome depend on angle relative to floor?

  15. Projectile motion y x R : when is y=0 ? t[vy1-(1/2)gt] = 0 i.e., T = (2v)sinq/g  R (x-eqn.)  hmax (y-eqn.)

  16. A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship will be hit first? 1. A 2. Both at the same time 3. B 4. need more information

  17. Maximum height and range

  18. Motion on a curved pathat constant speed Is the acceleration of the object equal to zero?

  19. Velocity is tangent to path Ds sI sF O v = Ds/Dt lies along dotted line. As Dt  0 direction of v is tangent to path

  20. Motion on a curved pathat constant speed

  21. Subtracting vectors Recall that vF+ (-vI) = Dv Dv vF vI same as -vI vF Dv

  22. For an object moving at constant speed along a curved path, the acceleration is not zero.

  23. For which of the following motions of a car does the change in velocity vector have the greatest magnitude? (All motions occur at the same constant speed.) 1. A 90° right turn at constant speed 2. A U-turn at constant speed 3. A 270° turn on a highway on-ramp 4. The change in velocity is zero for all three motions.

  24. A car moves along the path shown. Velocity vectors at two different points are sketched. Which of the arrows below most closely represents the direction of the average acceleration? 1. 2. 3. 4.

  25. A child is riding a bicycle on a level street. The velocity and acceleration vectors of the child at a given time are shown. Which of the following velocity vectors may represent the velocity at a later time? a 1. 2. 3. 4.

  26. Reading assignment • Motion in 2D • 3.3 - 3.4 in textbook

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