Presentation Transcript

1. Announcements First 2 homework sets (1D, 2D kinematics) are due on Tuesday @ 11:59 PM (smartPhysics) First quiz is next Friday (January 17) You must know the TA of the discussion section you attend: we will hand back quizzes in discussion sessions Quiz is at the beginning of class (first 10-15 minutes). BE ON TIME!!!

2. Classical Mechanics Lecture 2: Vectors and 2-D Kinematics

   Today's Concepts: a) Vectors b) Projectile motion c) Reference frames
3. Problem of the day (from Exam #1, Spring 2012) Lionel Messi kicks a soccer ball across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance.) What is the height, H, of the ball at the peak of its trajectory?
4. Projectile Motion In this class, a “projectile” is an object that moves only under the influence of uniform gravity (e.g., neglect air resistance; variations in gravity, etc.) Projectiles follow parabolic paths. The velocity of a projectile changes constantly during flight: it is ALWAYSaccelerating.
5. ACT! Lionel Messi kicks a soccer ball across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance.) Which of the following statements is correct? The ball’s horizontal speed remains constant during its flight. The ball’s horizontal acceleration remains constant during its flight. The ball’s vertical acceleration remains constant during its flight. A and C A, B, and C (Back of card)
6. Projectile Motion & Frames of Reference Thief Cop We talked about both of these cases in Unit 1: Constant v Constant a
7. Superposition vtrain car Since gravity acts downward only, motion along x and y are independent: Total motion is the “superposition” of motion along x and y – solve each part separately!
8. ACT A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land? A) Forward of the center of the car B) At the center of the car C) Backward of the center of the car vtrain car Since ax= 0, the ball and the center of car have the same x position and x velocity throughout the motion!!!

9. Spring loaded cart with tunnel demo

10. Kinematics in 3D with Constant Acceleration For projectile motion: Can arrange coordinate system to eliminate “z” Can align y-axis with gravity (vertical: up is “+”) ax = 0 ay = -g = -9.81 m/s2
11. ACT! Lionel Messi kicks a soccer ball across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance.) The ball’s peak height, H, is determined by: its initial horizontal speed, v0x . its initial vertical speed,v0y. both its initial horizontal and vertical speed. its time of flight (3 s). the horizontal distance traveled (60 m).
12. H depends ONLY on v0y : But: What is the value of H? 5 meters 7 meters 9 meters 11 meters 13 meters So:
13. Projectile motionand vectors During its flight, a projectile’s velocity vector will change continuously: it undergoes constant (uniform) acceleration At any point in time, the velocity vector will point in its direction of motion The velocity vector can be broken into two independent components: horizontal and vertical We need to review a little about vectors…
14. Vectors Ay Ax Think of a vector as an arrow.(An object having both magnitude and direction)
15. Computing the magnitude of a vector To find the magnitude of a vector, use the quadratic formula: The magnitude of the velocity vector is called “speed”. (We don’t have a special name for the magnitude of acceleration or position/displacement)
16. ACT! Lionel Messi kicks a soccer ball across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance.) What is the initial speed of the ball just after being kicked? v0 = 20.0 m/s v0 = 14.7 m/s v0 = 24.8 m/s v0 = 34.7 m/s Hints:
17. Vectors θ Think of a vector as an arrow.(An object having both magnitude and direction) The object is the same no matter how we chose to describe it
18. ACT! Lionel Messi kicks a soccer ball across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance.) What is the initial launch angle of the ball with respect to the ground? 27.6° 36.3° 43.8° 53.7° Hints:
19. Vector Addition
20. 2 of 250 32 ACT: Vector Addition Vectors and are shown to the right. Which of the following best describes + ? Add vectors tip to tail: A BCDE
21. ACT: Vector Subtraction 2 of 250 32 Vectors and are shown to the right. Which of the following best describes - ? Add vectors tip to tail: A BCDE
22. 2 of 250 32 ACT: Vector Addition, part II Vectors and are shown to the right. Which of the following best describes + ? Add vectors tip to tail: A BCDE
23. You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting? A) Right at the monkey B) Below the monkey C) Above the monkey ACT: Monkey Troubles
24. Shoot the Ball demo (horizontal) Two blocks demo (one drops, one shoots horizontal)- After Shoot the Ball demo while Adam is setting up shoot the cougar (upward angle)
25. Hitting the Ball… Bullet x=vot Ball x = xo
26. Shooting the Cougar… Cougar Still works even if you shoot upwards! Bullet Bullet hits Cougar!!
27. You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting? A) Right at the monkey B) Below the monkey C) Above the monkey ACT: Monkey Troubles
28. A destroyer simultaneously fires two shells with the same initial speed at two different enemy ships. The shells follow the trajectories shown. Which ship gets hit first. Checkpoint: Three Ships (part 1) Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time
29. …Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same Revote: Three Ships (part 1) Destroyer Enemy 1 Enemy 1 Enemy 2 Enemy 2 A) The horizontal and vertical components are independent. Therefore, since the shells are shot at the same speed, the ship that gets hit first is the one that is closer, since it lies closer to the destroyer. B) since both are shot with same initial speed, the shell shot at enemy 1 has a greater initial velocity in the y direction and therefore takes longer to hit the ship C) the shells were both fired at the same time with the same speed and from the same place. The vertical starting position is the same for both so they will land at the same time
30. Travel Time What determines the peak height? 0 What is vy at peak height? Substitute tup to find peak height Time up/down depends only on initial vertical velocity!
31. …Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same Revote: Three Ships (part 1) Destroyer Enemy 1 Enemy 1 Enemy 2 Enemy 2 Time up and down only depends on the initial vertical velocity!!! Since the initial (total) velocity of both shells is the same, then shell 1 (with a larger angle) must have larger initial vertical velocity, so it stays up longer Think of a “Hail Mary” pass vs. a “bullet” pass of the same horiz. distance
32. Checkpoint: Three Ships (part 2) A destroyer fires two shells with different initial speeds at two different enemy ships. The shells follow the trajectories shown. Which enemy ship gets hit first? Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time
33. …Which enemy ship gets hit first? A) Enemy 1 B)Enemy 2 C)Same Revote: Three Ships (part 2) Destroyer Enemy 1 Enemy 2 A) since the magnitude of velocity is bigger for enemy ship one, it will get hit first B) From the picture one can deduce that shell 2 has the greater vi, as it travels the greatest distance. As such it will arrive at it target first. C) Same y component, so both shots will reach the same height and objects dropped from the same height will land at the same time.
34. …Which enemy ship gets hit first? A) Enemy 1 B)Enemy 2 C)Same Revote: Three Ships (part 2) Destroyer Enemy 1 Enemy 2 Time up/down will be the same for objects traveling the same vertical distance!!!