1. College Physics
Chapter 1
Introduction

2. Theories and Experiments
The goal of physics is to develop theories based on experiments
A theory is a “guess,” expressed mathematically, about how a system works
The theory makes predictions about how a system should work
Experiments check the theories’ predictions
Every theory is a work in progress

3. Fundamental Quantities and Their Dimension
Length [L] meters
Mass [M] kilograms
Time [T] seconds
other physical quantities can be constructed from these three
These are called derived units with examples of velocity, m/s, force;kg-m/s2

4. Units
To communicate the result of a measurement for a quantity, a unit must be defined
What is a gram? How long is a meter?
Defining units allows everyone to relate to the same fundamental amount
How is a second defined?

5. Systems of Measurement
Standardized systems
agreed upon by some authority, usually a governmental body
SI -- Systéme International
agreed to in 1960 by an international committee
main system used in this text
also called mks (meter, kilogram, second) for the first letters in the units of the fundamental quantities

6. Systems of Measurements, cont
cgs – Gaussian system
named for the first letters of the units it uses for fundamental quantities
Centimeter, gram, second
US Customary
everyday units
often uses weight, in pounds, instead of mass as a fundamental quantity

7. Length Units SI – meter, m cgs – centimeter, cm
US Customary – foot, ft
Defined in terms of a meter – the distance traveled by light in a vacuum during a given time of 1/ second. This establishes the speed of light at m/sec or its accepted value of 3.00 x 108 m/s.

8. Mass Units SI – kilogram, kg cgs – gram, g USC – slug, slug
Defined in terms of kilogram, based on a specific cylinder of platinum and iridium alloy kept at the International Bureau of Weights and Measures located in Sevres, France.

9. Standard Kilogram

10. Time
Units
seconds, s in all three systems
times the period of oscillation of radiation from a cesium atom
The current standard cesium clock was built and is housed at the National Institute of Standards and Technology Laboratory in Boulder, Colorado

11. Approximate Values
Various tables in the text show approximate values for length, mass, and time: See Page 3
Note the wide range of values
Lengths – Table 1.1
Masses – Table 1.2
Time intervals – Table 1.3

12. Prefixes Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific abbreviation
See table 1.4 found on page 4
Common prefixes to remember:
109 giga, G 106 mega, M 103 kilo, k
101 deka, da deci, d centi, c
10-3 milli, m micro,  nano, n

13. Structure of Matter Matter is made up of molecules
the smallest division that is identifiable as a substance
Bodies of mass smaller than the molecule will not have characteristics of a unique substance; e.g. protons, neutrons, electrons
Molecules are made up of atoms
correspond to elements

14. More structure of matter
Atoms are made up of
nucleus, very dense, contains
protons, positively charged, “heavy”
neutrons, no charge, about same mass as protons
protons and neutrons are made up of quarks
orbited by
electrons, negatively charges, “light”
fundamental particle, no structure

15. Structure of Matter

16. Structure of Matter
Quarks – up, down, strange, charm, bottom, and top.
Up, Charm, and Top have a charge of + ⅔ that of a proton.
Down, Strange, and Bottom have a charge of - ⅓ that of a proton.
The proton has two up quarks and one down quark. ⅔ + ⅔ - ⅓ = + 1.
The neutron has two down quarks and one up quark. - ⅓ - ⅓ + ⅔ = 0.
The other quarks are indirectly observed and not well understood.

17. Dimensional Analysis Technique to check the correctness of an equation
Dimensions (length, mass, time, combinations) can be treated as algebraic quantities
add, subtract, multiply, divide
Both sides of equation must have the same dimensions

18. Dimensional Analysis, cont.
Cannot give numerical factors: this is its limitation
Dimensions of some common quantities are listed in Table 1.5 on page 5.
Example: [a] = [v]/[t]; L/T = {x}/{t2} T
a = x/t2
x = at2

19. Uncertainty in Measurements
There is uncertainty in every measurement, this uncertainty carries over through the calculations
need a technique to account for this uncertainty
We will use rules for significant figures to approximate the uncertainty in results of calculations

20. Significant Figures A significant figure is one that is reliably known
All non-zero digits are significant
Zeros are significant when
between other non-zero digits
after the decimal point and another significant figure
can be clarified by using scientific notation

21. Operations with Significant Figures
When multiplying or dividing two or more quantities, the number of significant figures in the final result is the same as the number of significant figures in the least accurate of the factors being combined

22. Operations with Significant Figures, cont.
When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum
If the last digit to be dropped is less than 5, drop the digit
If the last digit dropped is greater than or equal to 5, raise the last retained digit by 1

23. Examples of Significant Digits
Addition & Subtraction – The resulting answer is to have the same degree of precision as the least precise number used in the calculation.
Ex – 0.57 = 3.0 not 3.03
= 7.8 not 7.75
Multiplication & Division - The resulting answer is to have the same number of significant digits as the number with the least precise number of significant digits.
Ex ÷ 3.0 = 0.67 not
2.5 x 3.2 = 8.0 not 8

24. Reading Quiz
The quantity 2.67 x 103 m/s has how many significant figures? 1 2 3 4 5
Answer: C

25. Answer The quantity 2.67 x 103 m/s has how many significant figures? 14 5
Answer: C
Slide 1-8

26. Importance of Measurements
Data collection and interpretation are essential skills in physics
Repeatability to obtain measurements and the degree of uncertainty of correctness are very important

27. Importance of Measurements
Precision – The repeatability of the measurement using a given instrument
Example:
If a board is measured four times and the results are 8.81 cm, 8.78 cm, 8.85 cm, 8.82 cm then the precision of the measurement is ± 0.1 cm.
The value beyond the 0.1 cm level is an estimate between 8.8 and 8.9 cm.

28. Importance of Measurements
Accuracy – The degree of closeness a measurement is to the true and correct value.
Example:
If the ruler used to take the measurements stated previously was manufactured with a 2% error, the accuracy of the 8.8 cm measurement would be 2% or 8.8 x 0.02 = ± cm or ± 0.2 cm .

29. Importance of Measurements
Estimated Uncertainty – Expressing the measurement with the degree of determined precision of the measurement
Example:
8.8 ± 0.1 cm is the estimated uncertainty because the measurement was 8.8 cm and the level of precision was determined to be ± 0.1 cm

30. Importance of Measurements
Percent Uncertainty – The ratio of the uncertainty of the measured value to the measured value multiplied by 100.
Example:
Uncertainty → 0.1 cm
Measured value → 8.8 cm
% uncertainty = (0.1/8.8) x 100 = 1%

31. Importance of Measurements
Percent uncertainty Example - A family heirloom diamond is loaned to a friend to show her family. Before giving her the diamond you weigh it and get g on a scale of ± 0.05g accuracy. Upon return the diamond weighs 8.09 g. Is this your diamond?
Answer – The mass before release was 8.17± 0.05g meaning the weight range was 8.12 – 8.22 g. The mass after return was 8.09 ± 0.05g meaning the weight range was 8.04 – 8.14 g. Since these ranges overlap (8.12 – 8.14) there is no concern about discrepancy.

32. Percent Error
The calculation of % error from the determined data is an integral part of the analysis of physics.
% error = |accepted value – measured value|x 100
accepted value
Example: Determination of gravity
Measured value 9.68 m/s 2
Accepted value 9.80 m/s 2
% error = 9.80 – x 100 = 1.22%
9.80

33. Mean, Variance, & Standard Deviation
The mean, is the average of the measured values divided by the number of values.
The variance,  2, equals
The standard deviation of the measurements equals , or the square root of the variance.

34. Example of Statistical Analysis
You are measuring the time needed for a frictionless car to go down a fixed ramp that has a length of 1.45 meters that is set at an angle so that you attempt to determine the value of the gravity constant. The measurements are taken on six test runs with the following results. Determine the mean value of g; determine the variance and standard deviation of your measurements and explain what the results tell you about the value that you determine for g.

35. Example of Statistical Analysis
Prepare a table with all of the necessary data and calculations. Remember that acceleration is equal to: a=v/t; v=x/t;
s m/s m/s 2 t v g
(g – g’)
(g – g’)2
0.36s
4.03
11.19
1.39
1.93
0.40s
3.63
9.06
-0.74
0.55
0.38s
3.82
10.04
0.24
0.06
0.37s
3.92
10.59
0.79
0.62
0.39s
3.72
9.53
-0.27
0.07

36. Example of Statistical Analysis
s m/s m/s 2 t v g
(g – g’)
(g – g’)2
0.36s
4.03
11.19
1.39
1.93
0.40s
3.63
9.06
-0.74
0.55
0.38s
3.82
10.04
0.24
0.06
0.37s
3.92
10.59
0.79
0.62
0.39s
3.72
9.53
-0.27
0.07
g’=9.80 m/s2 g
= ( ) 6
= 9.91 m/s2

37. Example of Statistical Analysis
The data demonstrated that our measurement for the value of g was only 0.11m/s2 away from the accepted value. This was good accuracy.
The standard deviation of 0.87 means that our data within the range of (8.93 to 10.67) was 68.3% certain to contain the correct value. This is one standard deviation away from the value, 9.80.
The percent error is (|9.91 – 9.80|/9.80)x100% = 1.12%

38. Summary of Formulas measurement
Accuracy – (measurement) x (% error of device)
Precision – one power of ten less than the given measurements
Estimated uncertainty – measurement  accepted level of precision
Percent Uncertainty –
% uncertainty = uncertainty x 100
measurement
Percent error –
% error = |accepted value – measured value| x 100
accepted value

39. Sample Problems
What is the % uncertainty in the measurement 3.76  0.25?
Answer: (0.25/3.76) x 100% = 6.6%
What is the % uncertainty in the measurement 11.3  0.9?
Answer: (0.9/11.3) x 100% = 8%

40. Sample Problems
In calculating the area of a piece of notebook paper you get measurements of (21.1  .1) cm for the width and (27.5  .2) cm for the length. Determine the area and the uncertainty. If the actual value of the area is 603 cm2, determine the percent error from your calculation.
Uncertainty x uncertainty
Measurements x uncertainties of other measure
measurements
Answer: (21.1)(27.5)  {(21.1)(.2) + (27.5)(.1) + (.1)(.2)} =
( ) = (580  7) cm2
% error = (603 – 580) x 100 = 3.8%
603

41. Sample Problems
An airplane travels at 950 km/h. How long in seconds does it take to travel 1 km?
Answer: (950 km/h)(1h/3600sec) = .26 km/sec; t= 1 km/.26 km/s = 3.8 s
Use dimensional analysis to determine if the equation
vf 2 = vo 2 + 2as is consistent.
Answer: [L]2 = [L]2 + [L][L]
[T] [T]2 [T]2
[L]2 = [L]2
[T] [T]2 The equation is consistent.

42. Conversions
When units are not consistent, you may need to convert to appropriate ones
Units can be treated like algebraic quantities that can “cancel” each other
See the inside of the front cover for an extensive list of conversion factors
Example:

43. Examples of various units measuring a quantity

44. Order of Magnitude Approximation based on a number of assumptions
may need to modify assumptions if more precise results are needed
Order of magnitude is the power of 10 that applies
Examples: 27~30, ~

45. Coordinate Systems Used to describe the position of a point in space
Coordinate system consists of
a fixed reference point called the origin
specific axes with scales and labels
instructions on how to label a point relative to the origin and the axes

46. Types of Coordinate Systems
Cartesian – (x,y) or (x,y,z)
Plane polar - (r,) y s r  x

47. Cartesian coordinate system
Also called rectangular coordinate system
x- and y- axes
Points are labeled (x,y)

48. Plane polar coordinate system
Origin and reference line are noted
Point is distance r from the origin in the direction of angle , ccw from reference line
Points are labeled (r,)

49. Trigonometry Review

50. More Trigonometry Pythagorean Theorem
To find an angle, you need the inverse trig function
for example,
Be sure your calculator is set appropriately for degrees or radians

51. Problem Solving Strategy

52. Problem Solving Strategy
Read the problem
Identify the nature of the problem
Draw a diagram
Some types of problems require very specific types of diagrams

53. Problem Solving cont. Label the physical quantities
Can label on the diagram
Use letters that remind you of the quantity
Many quantities have specific letters
Choose a coordinate system and label it
Identify principles and list data
Identify the principle involved
List the data (given information)
Indicate the unknown (what you are looking for)

54. Problem Solving, cont. Choose equation(s)
Based on the principle, choose an equation or set of equations to apply to the problem
Substitute into the equation(s)
Solve for the unknown quantity
Substitute the data into the equation
Obtain a result
Include units

55. Problem Solving, final Check the answer Do the units match?
Are the units correct for the quantity being found?
Does the answer seem reasonable?
Check order of magnitude
Are signs appropriate and meaningful?

56. Problem Solving Summary
Equations are the tools of physics
Understand what the equations mean and how to use them
Carry through the algebra as far as possible
Substitute numbers at the end
Be organized

57. Homework Assignment Pages 19 – 22
Problems: 5, 7, 8, 11, 17, 21, 31, 41, 42, 52.