Physics 111. Thursday, September 2, Ch 2: motion diagrams - position - displacement - average velocity graphing - position vs time graphs

Transcription

1 ics Thursday, ember 2, 2004 Ch 2: motion diagrams - position - displacement - average velocity graphing - position vs time graphs

2 Announcements Lab manuals are available in the bookstore for $10 each. Make sure to get a copy BEFORE coming to lab. There will be a short quiz at the beginning of lab, so be on time!

3 An event Using the center of the ball to define its location x = +0.5 cm clock = 0.3 sec The combination of the location of an object at the corresponding clock reading. x = 0 x = 1 cm x = 2 cm

4 Summary To locate a moving object, we describe the instantaneous position of the object at a particular instant in time. Can we use the information on position (x) and the clock reading to help us determine how fast the ball was moving?

5 Tennis Ball Watch the tennis ball. +y Which of the following best describes the y- components of velocity and acceleration at the top of the motion? 1) v y > 0; a y > 0 2) v y = 0; a y < 0 3) v y < 0; a y < 0 4) v y = 0; a y = 0 5) v y > 0; a y < 0 6) v y = 0; a y > 0 7) v y < 0; a y > 0 8) None of these

6 Positions x = -0.5 cm clock = 0.1 sec x = +0.5 cm clock = 0.3 sec x = +1.5 cm clock = 0.5 sec x = +2.5 cm clock = 0.7 sec x = 0 x = 1 cm x = 2 cm Motion diagrams summarize the motion. Start with a multiple exposure photo of the rolling ball.

7 x = -0.5 cm clock = 0.1 sec x = +0.5 cm clock = 0.3 sec x = +1.5 cm clock = 0.5 sec x = +2.5 cm clock = 0.7 sec x = 0 x = 1 cm x = 2 cm Always use the same time interval (Δt) within a given motion diagram.

8 Student Demo Need a student volunteer - walker. Need a 5 more volunteers - artists. Need a 1 more volunteer - official time keeper. Motion Diagrams, student demo

9 Student Demo Time keeper starts the motion, calls out each second. Walker walks at constant velocity. Artists draw on board a picture at location of the walker each second. Motion Diagrams, student demo

10 Student Demo 2 Need a student volunteer - walker. This time, start slowly and increase speed as you go across the room. Everyone else - sketch a motion diagram! Worksheet Problem #1 Q1: Motion Diagrams, student

11 Student Demo 2 x 1 x = 0 t 1 t 2 t 3 t 4 t 5 Δx x 2,1 2 Δx 3,2 x 3 x4 x 5 Δ x 2,1 = x 2 x 1 displacement Δ x 4,3 Δ x 5,4 Motion Diagrams, student demo

12 Ball Motion Diagrams - Displacement page 11 1) F, E, D, A, C, B 2) A, B, C, D, E, F 3) E, B, A=C, D=F 4) F, D=E, A, B, C 5) F=D, A=E, B=C 6) F=D, E, A, B, C 7) None of the Above

13 Given the following motion diagram Worksheet Problem #2 is the object 1) Moving left to right 2) Moving right to left 3) Can t tell x = 0

14 velocity The displacement vectors you drew earlier are directly proportional to the velocity vectors. v j,i = Δ x j,i Δt = x j x i t j t i t 0 v 1,0 t 1 t 2 t 3 t 4 t 5 v 2,1 v 3,2 v 4,3 v 5,4 x = 0 So, let s label these adjoining arrows as velocity vectors.

15 Ball Motion Diagrams - Velocity I page 1 1) A, D, F, E, B, C 2) A, E, D, B, F, C 3) A=D=F, E, B, C 4) A=D=F, B=E, C 5) E, B, A, D, C, F 6) A, C, D, B=E, F 7) None of the Above

16 Average Velocity v = Δ x j,i j,i Δt = x x j i t j t i Which means the average velocity over the time interval [t j, t i ]. Note that this is a vector quantity, although in 1-D kinematics, direction will be + or -.

17 x = -0.5 cm clock = 0.1 sec x = +0.5 cm clock = 0.3 sec x = +1.5 cm clock = 0.5 sec x = +2.5 cm clock = 0.7 sec v x = 0 initial Δx x = = Δt t f f x t i i x = +1 cm x = +2 cm final cm cm cm = ( 05. ) = + 3 = s 01. s 0. 6s cm s

18 x = +0.5 cm clock = 0.1 sec x = -0.5 cm clock = 0.3 sec x = -1.5 cm clock = 0.5 sec x = -2.5 cm clock = 0.7 sec v x = 0 initial Δx x = = Δt t f f x t i i x = -1 cm x = -2 cm final cm cm cm = 2. 5 ( ) = 3 = s 01. s 0. 6s cm s

19 So for the same motion, we got two different answers! v Δx = = Δt x t f f x t i i cm cm cm = ( 0. 5 ) = + 3 = s 01. s 0. 6s cm s v Δx = = Δt x t f f x t i i cm cm cm = 2. 5 ( ) = 3 = s 01. s 0. 6s cm s One answer > 0; one answer < 0. Which one is correct??? BOTH!

20 How can they both be correct??? Our Choice of coordinate systems was completely arbitrary! I could just as easily put the origin 10 m to the left of where it was in the preceding plots! As with position, the velocity must be related to a well-defined coordinate system. The magnitude is NOT enough to describe the motion!!

21 Ball Motion Diagrams - Velocity II page 3 1) A=D, C, B=E, F 2) A, E, D, B, F, C 3) A=D=F, E, B, C 4) A=D=F, B=E, C 5) E, B, A, D, C, F 6) F, B=E, C, A=D 7) None of the Above

22 Worksheet Problem #3 graphing 1 Sketch on your worksheet a plot of position versus clock reading for the red and blue balls. Discuss your graph with your neighbor. position clock reading edge of page x = 0 x = 1 cm x = 2 cm

23 position edge of page clock reading Just from looking at the plot, can you tell which ball is moving faster, red or blue? If I were to add a yellow ball, which is the fastest? The slowest? How do you know?

24 How does velocity relate to this graph? position clock reading edge of page Ahhhh the velocity is related to the slope of the line!!! Steeper lines mean greater velocity magnitudes (speed). Be careful: negative slopes mean negative velocities!

25 Worksheet Problem #4 graphing 2 What type of motion does this graph represent? Try to mimic this motion by moving your finger across your desktop. position NONSENSE! clock reading Discuss with your neighbor!

26 Worksheet Problem #5

27 Worksheet Problem #5 A person initially at point P in the illustration stays there a moment and then moves along the axis to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls slowly back to P, where she stays to end the problem. Which of the position vs. time graphs at right correctly represents this motion? PI, Mazur (1997)

28 Ball Motion Diagrams - Average Speed page 10 1) A, E, C, F, D, B 2) E, F, C, D, A=B 3) E, C, D, A=B=F 4) E, C, D, A=B, F 5) C, D, A=B, F, E 6) C, D, A=B=F, E 7) None of the Above