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Physics 114A - Mechanics Lecture 8 (Walker: 4.1&2) 2D Motion Basics January 17, 2014

Physics 114A - Mechanics Lecture 8 (Walker: 4.1&2) 2D Motion Basics January 17, 2014. John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu. Announcements.

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Physics 114A - Mechanics Lecture 8 (Walker: 4.1&2) 2D Motion Basics January 17, 2014

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  1. Physics 114A - MechanicsLecture 8 (Walker: 4.1&2)2D Motion BasicsJanuary 17, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

  2. Announcements • Homework Assignments #2 is due on WebAssign (220/220) at 11:59 PM on Thursday, January 23. Assignments #3 is due on Thursday, Jan. 30. • Clicker registrations are converging: (206/220) • On Friday, January 24, we will have Exam 1. It will have a 75 point multiple-choice part and a 25 point free-response part. It will have assigned seating, specified by seating charts posted before the exam on the entry doors. Today is your last chance to request a left-handed seat, a right-handed aisle seat, or a front row seat (L, A, F). • My office hours are in the hour before class on Tuesdays and in the hour after class on Thursdays, both in the “114” area of the Physics Study Center on the Mezzanine floor of PAB A. Physics 114A - Lecture 8

  3. Lecture Schedule (Part 1) We are here. Physics 114A - Lecture 8

  4. Two-Dimensional Kinematics Physics 114A - Lecture 8

  5. Constant Velocity If velocity is constant, motion is along a straight line: A turtle walks from the origin at a speed of v0=0.26 m/s and an angle of 250. In a time t, the turtle moves through a straight line distance of d = v0t, with horizontal displacement x = d cos q and a vertical displacement y = d sin q. Equivalently, the turtle’s horizontal and vertical velocity components arevx = v0cos q and vy = v0sin q. Physics 114A - Lecture 8

  6. Example: The Eagle Descends An eagle perchedon a tree limb 19.5 mabove the water spotsa fish swimming nearthe surface. He pushesoff the limb anddescends toward thewater, maintaining aconstant speed of 3.10m/s at 20° below horizontal. • How long does it take for the eagle to reach the water? • How far has the eagle traveled horizontally when it reaches the water? Physics 114A - Lecture 8

  7. Constant Acceleration in 2D Physics 114A - Lecture 8

  8. Motion in Two Dimensions Motion in the x- and y-directions should be solved separately: Physics 114A - Lecture 8

  9. Example:A Hummer Accelerates A hummingbird is flying in such a way that it is initially moving vertically with a speed of 4.6 m/s and accelerating horizontally at a constant rate of 11 m/s2. Find the horizontal and vertical distance through which it moves in 0.55 s. Physics 114A - Lecture 8

  10. Projectile Motion:Basic Equations • Assumptions: • Ignore air resistance • Use g = 9.81 m/s2, downward • Ignore the Earth’s rotation • If the x-axis is horizontal and the y-axis points upward, the acceleration in the x-direction is zero and the acceleration in the y-direction is -9.81 m/s2 Physics 114A - Lecture 8

  11. Constant Acceleration withax = 0 and ay = -g Physics 114A - Lecture 8

  12. Projectile Motion:Basic Equations The acceleration is independent of the direction of the velocity: Physics 114A - Lecture 8

  13. Independence of Vertical and Horizontal Motion When you drop a ball while walking, running, or skating with constant velocity, it appears to you to drop straight down from thew point where you released it. To a person at rest, the ball follows a curved path that combines horizontal and vertical motions. Physics 114A - Lecture 8

  14. Clicker Question 1 Two divers run horizontally off the edge of a vertical cliff. Diver 2 runs with twice the speed of Diver 1. When they reach the surface of the water below, how are the horizontal distances xi that each diver covers related? • x1 = x2 • 2x1 = x2 • x1 = 2x2 • 4x1 = x2 • x1 = 4x2 Physics 114A - Lecture 8

  15. Projectile Motionin Vector Form Physics 114A - Lecture 8

  16. Graphs of x-y and v-t Physics 114A - Lecture 8

  17. Example:Canoeing on the Lake Two canoeists start paddling at the same time and head toward a small island 1 km north in a lake. Canoeist 1 paddles at 1.35 m/s at an angle of 450 north of east and Canoeist 2 starts on the opposite shore, a distance of 1.5 km from Canoeist 1. (a) At what angle q2 relative to north must Canoeist 2 paddle to reach the island? (b) At what speed must Canoeist 2 have, if the canoes are to reach the island at the same time? Physics 114A - Lecture 8

  18. Example: Cliff Diving • Two boys, George and Sam, divefrom a high overhanging cliff intoa lake below. • George (1) drops straight down. • Sam (2) runs horizontally anddives outward. • If they leave the cliff at the same time,which boy reaches the water first? • (b) Which boy hits the water with the greater speed? Since the vertical motion determines the time required to reach the water, both boys reach the water at the same. George reaches the water with only a vertical velocity, but Sam reaches the water with both horizontal and vertical velocity components. The vertical velocities are the same for both, so Sam’s speed on entering the water is greater than that of George. Physics 114A - Lecture 8

  19. Example: Electron in Motion An electron in a cathode ray tube is traveling with a horizontal speed of 2.10 x 109 cm/s when it enters the gap between deflection plates that give it an upward acceleration of 5.30 x 1017 cm/s2. (a) How long does it take for the electron to cover a distance of 6.20 cm? (b) What is the vertical displacement during this time? Physics 114A - Lecture 8

  20. Example: Jumping a Crevasse A mountain climber encounters a crevasse in an ice field. The opposite side of the crevasse is 2.75 m lower, and the horizontal gap is 4.10 m. To cross the crevasse, the climber gets a running start and jumps horizontally. (a) What is the minimum speed v0 needed for the climber to cross the crevasse? (b) Suppose the climber jumps at 6.0 m/s, where does he land? (c) What is his speed on landing? Physics 114A - Lecture 8

  21. Before the next lecture on Tuesday, read Walker, Chapter 4.3-5. We will have Exam 1 on Friday. Request L, A, or F seating, if desired. • Homework Assignment #2 is due at 11:59 PM on Thursday, January 23. Homework Assignment #3 is due at 11:59 PM on Thursday, January 30. • Monday is the Martin Luthur King Holiday. We will have Lecture 9 on Tuesday; pre-exam review on Thursday. Bring questions. End of Lecture 8

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