Welcome back to Physics 211

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1 Welcome back to Physics 211 The room is very full please move toward the center and help others find a seat. Be patient. The registration database is only updated twice per week. Get to know the people next to you, and work with them on the clicker questions during class. You will enjoy yourself and learn more. If you need to work on your laptop during the lecture, please sit at the back of the room so you don t distract other students. Office Hours

2 Your Comments If you really read this then, do you mind telling us when you close the clicker questions. My previous Physics professor gave us a 5 or 3 second countdown. I talked with some of my peers and they had the same issue. We wouldn't like to be penalized for not being able to think fast enough, at least we could get in an answer that we weren't sure/needed time to check over. For example in the last lecture, I figure out the answer and checked & when I was just about to click the right answer you closed it. Even though my answer was D, I spent time to check it over. Thank you. I would like the to hear a discussion on the two different ship problems in the checkpoint. Figuring out how long something stays in air, which gets hits first, etc Could you please go over the superposition idea the pre-lecture was explaining I feel the later half of the pre-lecture was a little more challenging stuff. I found the average velocity vector question difficult, and it took my a while to understand why you added the vectors going backwards instead of forwards. Parabolic Trajectories please! The lecture guy has a very soothing voice The voice for the slides in the PreLecture is really annoying. The fluidity, and approach through calculus helps tremendously! It must be very hard to teach kids without knowledge of derivatives this material.

3 Lets do a quick recap of calculus concepts from last lecture

4 Differentiating is just finding the Slope x(t) evaluated at t 1 In other words, v(t 1 ) tells us how x(t) is changing at time t 1. t 1 t 28

5 Integrating is just finding the Area v(t) v 0 t i t f t How does this tell you distance? This is easy to see if you start by considering the case of constant velocity v 0. In this case the integral is easy to evaluate: v(t) v 0 = velocity x time t i t f t 42

6 Today's Concepts: a) Vectors b) Projectile motion c) Reference frames Physics 211 Lecture 2

7 Vectors A Think of a vector as an arrow. (An object having both magnitude and direction)

8 Vectors A y A A x 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

9 Vectors q A 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

10 Vector Addition Personally, I found the vector concepts harder to grasp. From what I remembered, my high school teacher didn't go deep into the concept besides basic addition and subtraction.

11 Clicker Question A B Vectors and are shown to the right. Which of the following best describes + A B A B A B C D E

12 Clicker Question A B Vectors and are shown to the right. Which of the following best describes - A B A B A B C D E

13 Another way to think of subtraction A B Vectors and are shown to the right. Which of the following best describes - A B A B 1) Put vectors tail to tail A B B 2) is the vector pointing from the head of to the head of A

14 Vectors in 3D A vector can be defined in 2 or 3 (or even more) dimensions:

15 Kinematics in 3D Three directions are independent but share time

16 Projectile Motion What situations would we use the third dimension(z)in? I am having trouble picturing a problem since I have always used only x and y in 2-D. Also have trouble understanding what the i, j, and k are. Horizontal Vertical Boring

17 Checkpoint A physics demo launches one marble horizontally while at the same instant dropping a second marble straight down. Which one hits the ground first? A) The launched marble hits first. B) The dropped marble hits first. C) They both hit at the same time. I would like you to bring in an apparatus that matches the description of the one used in Checkpoint 1 "Ball Launch". DEMO

18 I wanted to ask something. That bullet thing, that whether it is fired from a gun or allowed to free fall from same height will take same time to reach the ground. Is that really true.? It does't seem true at all in real life. Like, a fired bullet goes straight for who knows how long but the free falling one will, well, fall down almost instantly. Mechanics Lecture 2,

19 Train Demo 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 correct v train car Ball and car start with same x position and x velocity, Since a x = 0 they always have same x position. Demo - train

20 vtrain car

21 Projectile Motion & Frames of Reference Time spent in air depends on vertical motion!

22 Monkey Troubles 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

23 Shooting the Monkey Dart x = v o t 1 y = - gt 2 2 Monkey x = x o 1 y = - gt 2 2

24 Shooting the Monkey Still works even if you shoot upwards! y = y o - 1 / 2 g t 2 x = v ox t y = v oy t - 1 / 2 g t 2 Dart hits the monkey

25 The Ship Problems I find problems without being given hard numbers to be more challenging. I would really like to see some actual problems with numbers being worked out in lecture. I think I understand the concepts, but only by going through problems with numerical solutions will I be able to tell if I firmly grasp the concepts. Mechanics Lecture 2,

26 Checkpoint 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. Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time

27 Checkpoint Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same Destroyer Enemy 1 Enemy 2 A) The distance to Enemy 1 is less than the distance to Enemy 2 B) The projectile for enemy ship two has a smaller initial vertical velocity; therefore, it will be in the air for the shortest time and land first. C) it should be the same because they were shells were fired at the same initial speed.

28 Checkpoint 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 Unless I made a mistake, the last question is missing necessary information (e.g. the two shells hit the same peak altitude) which must be assumed from the drawing, which I have always been told to not trust unless it something is explicitly stated.

29 Checkpoint Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same Destroyer Enemy 1 Enemy 2 A) The x-distance of enemy 1 is less than enemy 2. B) Because the angle is lesser. C) Both shells have the same max height, thus spend the same amount of time in the air.

30 Field Goal Example A field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal? y x 3 m D y-direction v oy = v o sin(30 o ) = 15 m/s y = y o + v oy t + ½ at 2 3 m = 0 m + (15 m/s) t ½ (9.8 m/s 2 ) t 2 t = 2.8 s or t = 0.22 s. x-direction v ox = v o cos(30 o ) = 26 m/s D = x o + v ox t + ½ at 2 = 0 m + (26 m/s)(2.8 s) + 0 m/s 2 (2.8 s ) 2 = 72.8 m Could you go over the equations used in the soccer ball problem in the PreLecture? I'm not sure where they're getting these from.

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