Message from Prof. Field

Transcription

1 Message from Prof. Field (posted on PHY2053 main web page) PHY 2053 Discussion Section Mistake: I made two errors with the discussion sections: Section 3801 is MW 5 in 1101 NPB and 7835 is WF 5 in 1216 NPB. These sections were goofed up and the TA may not have showed up for the class. I have corrected the schedule at Instructors & TA's. Everything should be okay for next week. I am very sorry for the confusion. Other than that, discussion sections should be meeting 1

2 Introduction Underlying Principles of Physics Significant Figures Units Dimensional Analysis

3 What is Physics? natural science method of collecting and analyzing empirical data about the natural (material) universe organized body of knowledge resulting from application of the scientific method 3

4 Scientific Method observe a repeating pattern / effect construct model / theory of effect extrapolate model - predict new effect outside observed data perform measurement to confirm/disprove predicted effect 4

5 Concept: Measurement physics is based on measurements fundamentally, a measurement is a comparison compare quantity of interest to standardized units [of mass, time..] 5

6 Significant Figures related to measurement uncertainty last digit implies measurement precision 201 cm vs cm practical use in lab, difficult to use here for homeworks and exams, relevant: required precision of match ~3% 6

7 Measurement Units standard units of comparison standards have been evolving over time have usually been culturally tied problems - always at the interface most popular interface: Imperial vs Metric systems 7

8 SI System of Units standardization of units reliability of measurements compatibility of results and devices we will be using the SI system of units in class 8

9 SI in the USA Omnibus Trade and Competitiveness Act of 1988: Industry in the United States is often at a competitive disadvantage when dealing in international markets because of its nonstandard measurement system, designate the metric system of measurement as the preferred system of weights and measures for United States trade and commerce. 9

10 SI Unit of Time 1 second [s] measurement of duration of an effect by comparing to periodic effects pendulum, quartz crystal,... best precision so far: multiple periods of vibration of radiation emitted by an isotope of the Cesium atom ( ) 10

11 SI Fundamental Unit: Length 1 meter [m] originally defined as 1/ distance from north pole to equator for a long time was a physical bar held in vacuum at 0 deg C in Paris nowadays - length traversed by light in vacuum during very short interval 11

12 SI Unit of Mass 1 kilogram [kg] currently still a physical piece of mass (weight) stored at NIST only fund. unit to incorporate power modifier 12

13 Power Modifiers centi (c) 10-2 pico (p) mili (m) 10-3 kilo (k) micro (μ) 10-6 mega (M) nano (n) 10-9 tera (T)

14 Important for Units when using values in formulas, all input values must be in the same units don t forget about power modifiers once a common set of units is established, formulas apply 14

15 Example 1 How far does light travel in one nanosecond (1 ns)? The speed of light is 300, 000 km / s. 15

16 Example 2 How fast is an object moving if it travels one furlong per fortnight? (in cm/s) one furlong = m, one fortnight = 14 days 16

17 Dimensional Analysis every physical quantity has a dimension some dimensions have fundamental units (mass, time, length) cross-check results derive properties (up to a point) 17

18 Approximation rough model will capture the general behavior; specifics can be lost not likely to have to pick models in PHY2053 technique is often used for quick estimates 18

19 Motion Along A Line Distance vs Displacement Velocity - average and instantaneous Velocity vs Speed Acceleration - average and instantaneous 19

20 Position, Displacement and Distance Traveled Reference point: Origin Displacement is the difference between final and initial positions Δx = x2 - x1 = xfinal - xinitial Important: Displacement is a signed quantity! Distance traveled is the sum of absolute values of all displacements, always positive definite Distance traveled = Σi Δxi 20

21 Example 3: A perfect ball is bouncing between two walls. The distance between the two walls is 0.5 m. Initially, the ball is by the left wall. It takes the ball 1 sec to travel the distance between the two walls. Assume the ball starts by the left wall at t = 0s. What is the displacement of the ball and its distance traveled at t = 1s, t = 2s, t = 3s,..., t = N s? (N > 0) 21

22 0.5 m x distance traveled tfinal 0.0 m 0.0 m 0 sec 0.5 m 0.5 m 1 sec 0.0 m 1.0 m 2 sec 0.5 m 1.5 m 3 sec 0.0 m for even values of N 0.5 m for odd values of N N 0.5 m N sec 22

23 End of Lecture 2 in Class 23

24 Average Velocity vs Average Speed Average Velocity is the change in position during a time interval v av,x Δx Δt = x f - x i t f - t i Average Speed is the distance traveled during a time interval (hint: car model ) average speed distance traveled total time 24

25 Example 4: For the perfect ball from Example 3, what is the average velocity and average speed at t = 1 s, t = 2 s, t = 3 s? t = N s? (N > 0) 25

26 Average Velocity, Constant The straight line indicates constant velocity The slope of the line is the value of the average velocity 26

27 Average Velocity, Non Constant The motion is nonconstant velocity The average velocity is the slope of the blue line joining two points 27

28 Instantaneous Velocity The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero v x lim Δx Δt 0 Δt = lim t f t i x f - x i t f - t i The instantaneous velocity indicates what is happening at every point of time Instantaneous speed can be defined by analogy. It is the average speed as the total time becomes infinitesimally short. (= abs. value of instantaneous velocity) 28

29 Instantaneous Velocity Δx Δt 29

30 Instantaneous Velocity Δx Δt 30

31 Instantaneous Velocity Δx Δt 31

32 Instantaneous Velocity Δx Δt 32

33 Average and Instantaneous Acceleration the rate of change of velocity has physical relevance By analogy with velocity, define average acceleration: a av,x Δv x Δt = v x,f - v x,i t f - t i and instantaneous acceleration: a x lim Δv x Δt Δt 0 = lim t f t i v xf - v xi t f - t i 33

34 Example 4: A Mustang GT500 goes from 0 to 60 mph in 4.1 seconds. What is the average acceleration over this period (in m/s 2 )?How many g s is it pulling? 34

35 Next Tuesday: Chapter : Linear Motion, Free Fall 35

36 Supporting Materials 36

37 Demonstrations Standards of Measurement Cart Motion Sensor 37