What is PHYSICS ?

1. What is PHYSICS?

2. What is PHYSICS study of matter and energy (physical world) delusionary attempt to find order in dirt and cosmos quintessential reductionist paradigm (= most basic science) different kinds of sciences (different from engineering in objectives)

3. Need some numbers to work on. Let’s go measure something! What is to be measured? How to measure it? Problems & limitations Ways to circumvent Measurement standards

5. Many units to match the dimension of an item or quantity being measured. Time: second, minute, hour, day, year, century, millenium Length: centimeter, meter, kilometer inch, foot, yard, rod, mile Matter: gram, kilogram, metric ton ounce, pound, slug Force (derived unit): Newton, pound (lb)

6. How well can these measurements be made? In principle, any arbitrary precision. In practice, limited by instrument and method. Express precision by significant figures and scientific notation. Look at the statistical basis of measurement data.

7. Measure the diameter 13.7 cm

8. Scientific Notation useful for expressing large dynamic range (keeps track of the decimal point) and significant figures m.mmm 10eee ( m.mmmEeee on a calculator ) where 1.0  m.mmm < 10.0 and eee can be + or 

9. Workshop Physics is a new method of teaching introductory physics without formal lectures. • Instead students learn collaboratively through activities and observations. Observations are enhanced with computer tools for the collection, graphical display, analysis and modeling of real data. • Typical Workshop Physics classes meet for two 3.5-hour long sessions each week and students use an Activity Guide.

11. In developing Workshop Physics it is assumed that the acquisition of transferable skills of scientific inquiry are more important than either problem solving or the comprehensive transmission of descriptive knowledge about the enterprise of physics. • There were two major reasons for the emphasis on inquiry skills based on real experience.

12. First, the majority of students enrolled in introductory physics at both the high school and college level do not have sufficient concrete experience with everyday phenomena to comprehend the mathematical representations of them traditionally presented in these courses.

13. The processes of observing phenomena, analyzing data, and developing verbal and mathematical models to explain observations, afford students an opportunity to relate concrete experience to scientific explanation.

14. A second equally important reason for emphasizing the development of transferable skills is that, when confronted with the task of acquiring an overwhelming body of knowledge, the only viable strategy is to learn some things thoroughly and acquire methods for independent investigation to be implemented as needed.

15. Although lectures and demonstrations are useful alternatives to reading for transmitting information and teaching specific skills, they are unproved as vehicles for helping students learn how to think, conduct scientific inquiry, or acquire real experience with natural phenomena.

16. The time now spent by students passively listening to lectures is better spent in direct inquiry and discussion with peers. • Many educators believe that peers are often more helpful than instructors in facilitating original thinking and problem solving on the part of students.

17. Statistical Measures • Systematic errors: consistent influence on measurements which can increase or decrease all values in the same direction. Examples? • Ruler too long or short, or bent. • Uncertainty is a fact of measurement. • How do you know if systematic error is present?

18. Random errors: inconsistent influence on individual measurements which can usually be eliminated. Why can we say this? • If we perform the measurement a significant number of times, the high and the low uncertainties will cancel out each other. The bell curve. • Examples? • Statistics deals with random errors

19. Weigh some breakfast cereals

20. Consider the average Tasteeo Under Excel, highlight the B8 cell and insert the AVERAGE function AVERAGE(B2:B7) Next, highlight the B9 cell and insert the STDEV function STDEV(B2:B7)

21. Consider the average Tasteeo With the TI-83, enter the column of data using the STAT editor. Return to STAT, select 1-Var Stats. This will be returned to the main screen, so now 1-Var Stats L1

22. And obtain: • 1-Var Stats • x = 41.81666667 • x=250.9 • x2=10496.45 • Sx=.9641922353 • σx=.8801830618 • n=6 Where is the average? Where is the std dev? Beware of σx (what is it?) Are all digits significant?

23. Mathematical Preliminaries • Data is often repeated measurements of the same quantity. • A “reliable” central measure of the data is the mean (average). • The first moment of the distribution, the standard deviation, is related to the probability that each measurement is close to the mean.

24. Standard deviation tells us how close anadditional measurement would come to the center distribution of an infinite number of measurements. • We assume that our finite average comes close to the infinite mean.

25. 68% of the measurements fall within 1 standard deviation from the mean

26. 95 % would fall within 2 STDEV’S from the mean

27. Some data appears to form a normal (gaussian) distribution on a histogram. Even if it doesn’t, it is convenient to model the data as gaussian to calculate the Std Dev. • Another reliable measure for the data is the standard deviation of the mean (SDM). This expresses the probability that the mean can vary. The SDM is gaussian for large sample sizes. • There are higher moments of the distribution which are informative in some situations (e.g., skew, kurtosis).

28. Behold the Histogram! A histogram representing the variation in a set of measurements. The height of each bar is proportional to the number of measurements in each small range of values.

29. Consider the definition of the mean and the std dev (standard deviation).

30. A test of significance is if any new data is beyond the 95% (“2σ” or two standard deviations) level. A smooth Gaussian distribution curve showing the 95% confidence interval.

31. Generally one arrives at a best estimate of a measurement of interest by making a series of measurements and averaging the results. The standard deviation is a measure of the level of uncertainty in the data.

32. Standard Deviation of the Mean

35. Estimating Volume

36. Estimating Speed According to a rule-of-thumb, every five seconds between a lightning flash and the following thunder gives the distance of the storm in miles. Assuming that the flash of light arrives in essentially no time at all, estimate the speed of sound in m/s from this rule.

37. Kinematics in One Dimension MECHANICS comes in two parts: kinematics: motion (displacement, time, velocity) x, t, v, a dynamics: motion and forces x, t, v, a, p, F

38. Kinematics in One Dimension

39. Velocities Average velocity - over the trip, or distance, or time Instantaneous velocity - right now speed

41. Acceleration How to express a change in velocity? Again, two kinds of acceleration:

42. Kinematics defined by - x, t, v, a x displacement t  time v  velocity a acceleration

43. An automobile is moving along a straight highway, and the driver puts on the brakes. If the initial velocity is v1 = 15.0 m/s and it takes 5.0 s to slow to v2 = 5.0 m/s, what is the car’s average acceleration?

44. From the definition for average acceleration:

45. Motion at Constant Acceleration kinematics - x, t, v, a How are these related? For simplicity, assume that the acceleration is constant: a = const

46. Consider some acceleration: The resulting velocity:

47. For a constant acceleration: Realize a displacement:

48. How about an equation of motion without time?

49. Equations of Motion