Classical Mechanics Lecture 2

Transcription

1 Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b) Projec@le mo@on c) Reference frames Mechanics Lecture 2, Slide 1

2 Unit 6 Activity Guide Today

3 Not everyone is doing the pre-lecture This is a bad strategy you are losing easy points Mechanics Lecture 2, Slide 2

4 Your Comments I had no difficul@es with anything What did the mountain climber name his son?! Cliff.

5 Your Comments

6 Vectors A y A x Think of a vector as an arrow. (An object having both magnitude and direc@on) The object is the same no ma/er how we chose to describe it Mechanics Lecture 2, Slide 6

7 Vectors A θ Think of a vector as an arrow. (An object having both magnitude and direc@on) The object is the same no ma/er how we chose to describe it Mechanics Lecture 2, Slide 7

8 Vector Addition Mechanics Lecture 2, Slide 8

9 Clicker Question Vectors and are shown to the right. Which of the following best describes + A B C D E Mechanics Lecture 2, Slide 9

10 Clicker Question Vectors and are shown to the right. Which of the following best describes A B C D E Mechanics Lecture 2, Slide 10

11 Clicker Question Vectors and are shown to the right. Which of the following best describes + A B C D E Mechanics Lecture 2, Slide 11

12 Vectors in 3D A vector can be defined in 2 or 3 (or even more) dimensions: Mechanics Lecture 2, Slide 12

13 Clicker Question In the graph shown to the right,v1 is the velocity vector for a particle in two-dimensional motion at time t = 0, while v2 is the velocity vector for that particle at time t = 1 s. Which of the following graphs represent aavg, the average acceleration vector of the particle over the time interval from t = 0 to t = 1 s? y ~v 1 Δv ~v 2 ~v 1 x

14 Kinematics in 3D Mechanics Lecture 2, Slide 13

15 Checkpoint 1 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 Mechanics Lecture 2, Slide 14

16 Projectile Motion Horizontal Vertical Boring Mechanics Lecture 2, Slide 15

17 v train car Time spend in the air depends on the maximum height Maximum height depends on the velocity Mechanics Lecture 2, Slide 17

18 Projectile Motion & Frames of Reference Mechanics Lecture 2, Slide 21

19 Checkpoint 2 A destroyer simultaneously fires two shells with the same ini@al 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 65% of you got this one right let s try again Mechanics Lecture 2, Slide 22

20 Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same Checkpoint 2 Destroyer Enemy 1 Enemy 2 A) they are traveling at the same speed, but the enemy one trajectory is shorter B) Both shots were accelera@ng towards the ground at the same rate, but the shot fired at Enemy 2 did not go as high and therefore took to fall back to the ground. C) we are given that two shells are fired at same speed. therefore, both ships should get hit at the Mechanics Lecture 2, Slide 23

21 Checkpoint 3 A destroyer fires two shells with different ini@al 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 62% of you got this one right let s try again Mechanics Lecture 2, Slide 24

22 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 Video of 70-yard Field Goal = 79.6 yards Mechanics Lecture 2, Slide 26

23 1) If you toss a ball up into the air, which of the following tables would accurately describe its velocity and accelera@on. A) Going up At the top Going down Velocity + 0 Accelera@on B) C) Going up At the top Going down Velocity + 0 Accelera@on + 0 Going up At the top Going down Velocity + 0 Accelera@on 0 +

24 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 shoo@ng? A) Right at the monkey B) Below the monkey C) Above the monkey Mechanics Lecture 2, Slide 18

25 See ya Wednesday!

26 Today

27 Sharing and Transfering Videos Use sfuvault.sfu.ca to share videos from your camera

28 Shooting the Monkey Dart x = v o t Monkey x = x o Mechanics Lecture 2, Slide 19

29 Shooting the Monkey y = y o 1 / 2 g t 2 y = v oy t 1 / 2 g t 2 Dart hits the monkey DEMO Mechanics Lecture 2, Slide 20

30 Train Demo Clicker Question 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. Neglec@ng 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 posi@on and x velocity, Since a = 0 they always have same x posi@on. Demo - train Mechanics Lecture 2, Slide 16

31 Bungee A bungee jumper jumps. At which point is her accelera-on the maximum upward. A) While standing at the jump-off point B) Just aner jumping and falling C) When the bungee just starts to stretch D) Midway down while slowing E) At his lowest point A B C D E

32 Inertial Mass

33 Today: Omit Activity 5-9: The Motion of a Freely Rolling Ball Activity 5-10: 1D Tapping of a Ball Starting from Rest Activity 5-11: 1D Tapping of a Ball with Initial Motion Activity 5-12: Finding Equations to Describe x vs. t Session two will not be graded, but we ve posted old data so you can look at it.

34 Session Two Session Two will not be graded BUT Make sure you understand Activity 5-16: Vector Magnitude and Direction x = y = r = Text

35 Session Two Session Two will not be graded BUT Make sure you understand Activity 5-16: Vector Magnitude and Direction x = 2.5 cm y = 4.0 cm Text θ = arctan(y/x) =