1. Welcome Course: Regents Physics Room: 207 Teacher: Mrs. LaBarbera
google classroom code: ysslhjo
Post : Room 207, Tues. – Thurs. 1

2. Objectives Student information form Course guidelines Lab safety 2
Units – objectives
Define unit
List basic SI units and the quantities they describe.
Differentiate fundamental and derived units.
master the metric conversion techniques using SI prefixes.
Distinguish symbols for units and quantities.
Use dimensional analysis to check the validity of expressions.
A ____________________ is a standard quantity with which other similar quantities can be compared.
Example:
Meter, or mile for measuring ____________________.
Kilogram, pound for measuring ________________.
Liter or cubic meter for measuring _________________.
Second, minute, hour, or day for measuring ____________.
The SI system
The ____________________ provides standardized units for scientific measurements.
All quantities can be expressed by _______________ fundamental units.
Derived units
_______________________ are combinations of _________________________ of the fundamental units and are used to simplify notation.
the unit for _____________________ is m/s, which is a derived unit.
The unit for ________________ is watt, is also a derived unit because it is not on the list of the basic units.
Objectives
Student information form
Course guidelines
Lab safety
quantity
name
symbol
length
meter m
Mass
kilogram kg
Time
second s
Ele. current
ampere A
Temp.
Kelvin K
Amount of substance
mole
mol
Luminous intensity
candela cd 2

3. Lab - General guidelines
Conduct yourself in a responsible manner.
Perform only those experiments and activities for which you have received instruction and permission.
Be alert, notify the instructor immediately of any unsafe conditions you observe.
Work area must be kept clean.
Dress properly during a laboratory activity. Long hair should be tied back, jackets, ties, and other loose garments and jewelry should be removed.
When removing an electrical plug from its socket, grasp the plug, not the electrical cord. Hand must be completely dry before touching an electrical switch, plug, or outlet.
Report damaged electrical equipment immediately. Look for things such as frayed cords, exposed wires, and loose connections. Do not use damaged electrical equipment. 3

4. Topic 1 measurements and mathematics
SI Units
Tools for measurement
Uncertainty in measurement.
Scientific notation.
Evaluating experimental results
Graphing Data
Scalar and Vector Quantities
Solving equations using algebra

5. 1.1 SI Units - objectives Know:
basic SI units and the quantities they describe.
Derived units are multiplication or division of SI units
SI prefixes are prefixes combined with SI units to form a new unit that is larger or smaller than the base units by a multiple of 10.
Be able to
Differentiate basic and derived units.
Distinguish symbols for units and quantities.
Use dimensional analysis to determine the unit of an unknown quantity.

6. Units
A unit is a standard quantity with which other similar quantities can be compared.
All measurements must be made with respect to some standard quantity.

7. SI system Fundamental units
The SI system provides standardized units for scientific measurements. All quantities measured by physicists can be expressed in terms of the seven fundamental units.
Fundamental units
QUANTITY
NAME
SYMBOL
Length
meter m
Mass
kilogram kg
Time
second s
ele. current
ampere A
Temp.
Kelvin K
Amount of substance
mole
mol
Luminous intensity
candela cd

8. Electrical resistance
Derived units
A Derived unit is unit that is derived from COMBINATIONS (multiplying or dividing) of two or more of the fundamental units, they are used to simplify notation.
Derived Units
QUANTITY
NAME
SYMBOL
frequency
hertz Hz
force
Newton N
Energy, work
Joule J
Ele. charge
Coulomb C
Ele. potential
volt V
power
watt W
Magnetic flux
weber Wb
Electrical resistance
ohm Ω
resistivity
ohm∙meter
Ω∙m

9. SI prefixes Prefixes for Powers of 10
SI prefixes are prefixes (symbols such as T, G, M, k …). combined with SI units to form a new unit that is larger or smaller than the base units by a multiple of 10.
The symbols for the new unit consists of the symbol for the prefix followed by the symbol for the base unit.
Prefixes for Powers of 10
Prefix
Symbol
Notation
tera T
1012
giga G
109
mega M
106
kilo k
103
100
deci d
10-1
centi c
10-2
milli m
10-3
micro μ
10-6
nano n
10-9
pico p
10-12
Example:
2 Tm = 2 x 1012 m
Which means 2 terameter is 1012 times larger than 2 meter

10. To convert is to devide Prefixes for Powers of 10 Prefix Symbol
Notation
tera T
1012
giga G
109
mega M
106
kilo k
103
100
deci d
10-1
centi c
10-2
milli m
10-3
micro μ
10-6
nano n
10-9
pico p
10-12
1 Mg = _____ kg; 1 Mg = x kg
103
20 Tm = _________ mm
12 x10-2 Mm = _________ m
10 ng = _________ kg
14 μm = ________ nm

11. Differentiate symbols for quantity and unit
Symbols for quantities are denoted as italic fonts.
Symbols for units are denoted as non-italic fonts.
QUANTITY
SYMBOL
Length l
Mass m
Time t
Unit
SYMBOL
meter m
kilogram kg
second s
What is the difference?
15m = 30
d = 15 m
15 multiply by m equals to 30
d equals to 15 meters

12. DEMENSIONAL ANALYSIS
Analyzing units can help in solving problems. The units on the left side of an equation must always be equivalent to the units on the right side of the equation.
Quantities can be added or subtracted only if they have the same units.
5 kg + 2 kg = 7 kg
5 kg + 2 m : invalid

13. Using dimensional analysis to determine the unit of an unknown quantity.
Units (Dimensions) can be treated as algebraic quantities. Units can multiply or divide to form a new unit or cancel unit.
2 kg ∙ 5 m/s = 10 kg∙m/s
The units on the left side of an equation must always be equivalent to the units on the right side of the equation.

14. Example
If m represents mass in kg, v represents speed in m/s, and r represents radius in m. show that the force F in the equation F = mv2/r can be expressed in the unit kg∙ m/s2

15. Example
Which unit is equivalent to a newton per kilogram? ( 1 newton = 1 kg∙m/s2)
m/s2
W/m
J∙s
Kg∙m/s

16. example The formula for the period of a simple pendulum is as follows:
T is the period of the pendulum, l is the length, and g is the acceleration due to gravity. Determine the unit for T.

17. example: use dimensional analysis to determine the unit of a variable
What is the unit of v2/d ?, given the unit of v is m/s, and unit of d is m.

18. Homework is due
Read, print and sign the Lab Requirement Letter – both your signature and your parent/guardian’s signature.
Read, print and sign the Student Safety Agreement – both your signature and your guardian’s signature.
student information sheet
google classroom code: ysslhjo

19. 1.2 Select the tools for measurement
Be able to
Select appropriate equipment to make measurements of length, mass, time, force and angle
Draw a quantity with given scale
Determine the scale of a quantity shown
Apply trigonometric functions to determine the unknown.

20. Select proper equipment
quantity
tool
unit
Length, distance, height …
Meter stick, metric ruler,
Tape measurer
m, cm, mm, etc.
mass
Scale, triple beam balance,
kg, g, etc.
time
Timer, stop watch
photo gates
s, ms, min, etc.
force
Spring scale,
Force meter N
angle
protractor
degrees

21. Measuring length (meter)
What is the length of the object?
5.31 cm

22. Measuring mass (kg)
What is the mass of the object?
62.40 g

23. Measuring time (second)
What is the elapsed time in seconds?
Total of seconds

24. Measuring force (Newton)
What is the weight of the object?
20.1 N

25. Measuring an Angle (degree) from horizontal line
The bottom of the protractor must match the line from which the angle is to be measured and the hole must match the corner of the angle.
37.9o

26. Measuring an Angle (degree) from vertical line
The bottom of the protractor must match the line from which the angle is to be measured.
52.5o

27. Draw a quantity with given scale
On the diagram, starting at point A, draw a 28 N of force on the box. Use a scale of 1.0 cm = 10. N

28. Determine the scale of quantities shown
Use a metric ruler to determine the scale used in the diagram.

29. example
Using a metric ruler, determine the scale used in the vector diagram.

30. example
Use a protractor to measure angle θ. θ

31. Apply trigonometry to solve physics problems
Important trigonometry equations of a right triangle:
SOH CAH TOA
Pythagorean Theorem
a2 + b2 = c2 
SOH
CAH
TOA θ

32. Example 1 A block is positioned as shown.
A) How far is the block displaced horizontally?
B) what is the measurement of the angle of inclination of the plane to the horizontal?
c2 = a2 + b2
a2 = (1.25m)2 – (0.75m)2
b = 1.0 m
1.25 m c
0.75 m b θ a
B) sinθ = O/H = 0.75m / 1.25m
θ = sin-1(0.75/1.25) = 37o

33. Example 2
The diagram represents a ramp inclined to the horizontal at angle 30.o. If the upper end of the ramp is 37 cm above the horizontal, what is x?
SOH
tan30o = 37 cm / x
x = 64 cm
37 cm
30o x

34. Example 3
From the information provided by the following diagram, determine angle θ.
40 m/s
25 m/s θ

35. Example 4 x = (40 m)∙sin30o y = (40 m)∙cos30o x = 20 m x = 35 m
From the given diagram, find x and y.
40 m x
30o y
x = (40 m)∙sin30o
x = 20 m
y = (40 m)∙cos30o
x = 35 m

36. 1.3 Use significant figures in measurements and calculations
Know
the rules of determining significant figures.
Understand
Difference between accuracy with precision
Be able to
perform calculations with significant figures.

37. Accuracy and precision
The accuracy of a measurementof a measurement system is the degree of closeness of measurements of a quantityof a measurement system is the degree of closeness of measurements of a quantity to that quantity's true value.
The precision of a measurement is the degree to which repeated measurements under unchanged conditions show the same results.
Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.

38. example
Matt measures the total length of a lap around the school’s track to be m, m and m. If the accepted value for the path length is m,
Is Matt’s measurement accurate? Explain your answer
Is Matt’s measurement precise? Explain your answer

39. example
Mike measures the speed of red light in ice to be 2.00 x 108 m/s, 1.87 x 108 m/s, 2.39 x 108 m/s. If the accepted value for the speed is 2.25 x 108 m/s,
is Mike’s measurement accurate? Explain.
is Mike’s measurement precise? Explain.

40. The rule of determining significant figures
Significant figures (sig. figs) represent the level of certainty in a measurement.
In a measured value, the digits that are known with certainty plus the one digit whose value has been estimated are called SIGNIFICANT FIGURES or significant digits.
In this measurement, The length is 5.30 cm cm = 5.31cm. there are 3 sig. figs. The number of significant figures depends on how precise an instrument is.

41. Example: how long is the block?
Certain: 1.3 cm; Uncertain: 0.06 cm
Total length: 1.36 cm
3 sig. figs

42. Significant Digits: Rules
If a digit is non-zero, it is significant.
43.74 km has ___ sig figs;
If a digit is zero
Leading zeros are not significant
0.892 m has ___ sig figs; ms has ___ sig figs
Zeros between non-zero digits are significant
s has ____ sig figs; g has ___ sig figs
Ending zeros…
If there is a decimal point, zeros are significant
30.00 s has ____ sig figs; kg has ___ sig figs
If there is no decimal point, zeros are not significant
1000 mg has ___ sig figs; 20 mm has ___ sig figs

43. Significant Digits : Rules
All none-zeros are significant
Ignore all LEADING zero’s
Decimal
point?
YES NO
Count ALL remaining
digits as significant
Trailing zeros are not
significant

44. Significant Digits : Examples
How many significant digits in each?
456000
85067
0.204 3 2 4 5 3

45. Rules for calculating with sig. figs.

46. Examples
3.04 m m m =
0.028 kg kg =

47. Multiplication and division with measured values
When you multiply or divide, the answer has the same number of significant figures as the measurement having the smallest number of significant figures.
Example: what is the area of a rectangle that is 9.8 cm by 12.7 cm ?

48. 9/11 do now – 7th period
Practice packet #37

49. 1.4 Scientific notation - objectives
Know
the form of scientific notation.
Be able to
perform mathematical operations on numbers with scientific notation
Master the metric conversion techniques using SI prefixes.
Perform order of magnitude calculations

50. Scientific Notation
Scientific notation consists of a number equal to or greater than one and less than ten followed by a multiplication sign and the base ten raised to some integral power.
The general form of a number expressed in scientific notation is A x 10n, all the digits in A are significant.
Examples:
3.02 x 103
5.1 x 10-2
2 x 105

51. example
6,370,000 m has 3 significant digits, it can be expressed in scientific notation as ____________
N∙m2/kg2 has 3 significant digits, it can be expressed as _____________
Length of an ant is meters, which can be expressed in scientific notation as ______________.
Expand the number 9.56 x 10-3: _______________
Expand the number 1.11 x 107. _______________

52. Performing mathematic operations on numbers with scientific notation - EE Notation
3,000,000
Can be entered into the calculator as:
Not 3 x 10E6
3 x 10 ^ 6
3E6
BETTER METHOD
The calculator treats this as a
SINGLE number – no PARENTHESES
required!!!

53. Calculators : EE Notation Example
What is the quotient of 2.0 x 102 and 4.0 x 10-4 ?
Without EE notation:
You need parentheses
(2.0 x 10^2) / (4.0 x 10^-4)
With EE notation:
No parentheses needed
2E2 / 4E-4
Answer:
or 5.0 x 105 or 5E5
When performing calculations with scientific notation, the rules for significant figures apply

54. examples
Determine the area of a rectangle having a length of 41.5 cm and a width of 2.3 cm

55. Example – representing sig. figs with scientific notation
How many significant figures does 2014 m have?
Write 2014 with 1 significant figure.
Write 2014 with 2 significant figure.
Write 2014 with 3 significant figure.
Write 2014 with 5 significant figure. 4
2 x 103 m
2.0 x 103 m
2.01 x 103 m
x 103 m

56. Order of magnitude
Order of magnitude is a scale to measure how large or how small a number is. It is used to make approximate comparisons. Order of magnitude is based on power of 10.
For example:
an average man’s height is 1.75 m = 1.75 x 100 m in USA. We say the order of magnitude of average man’s height is 0.
an average car’s mass is about 1000 kg = 1.0 x 103 kg. We say the order of magnitude of average car’s mass is 3.
The average distance between Earth to the moon is x 108 m. the order of magnitude of the distance is 8

57. example
What is the order of the magnitude of the ratio of the Electrostatic constant to the Universal gravitational constant?
8.99x109 / 6.67x10-11 = 1.34x1020 20

58. Estimate using order of magnitude
In order to do estimations, we need to have an idea of length:
1000 m (The Burj Khalifa in Dubai, Mount Fuji)
100 m (102 m - length of high school track, The Great Pyramid)
10 m (101 m – school bus, blue whale)
1 m (100 m - baseball bat)
1 dm (10-1 m - height of a soda can)
1 cm (10-2 m – diameter of a penny)
1 mm (10-3 m - thickness of a credit card)
You also need to have an idea of mass:
1000 kg (103 kg – mass of a car)
100 kg (102 kg – a football player)
10 kg (101 kg – a book bag)
1 kg (100 kg – a text book)
100 g (10-1 kg – an apple. A golf ball, an egg)
10 g ( 10-2 kg – a pencil)
1 g (10-3 kg – paper clip)
1 apple ≈ 1 N
1 kg ≈ 2 lb
1 kg ≈ 10 N

59. 9/11 do now
Class work packet - #67

60. 1.5 Evaluating experimental results
Know
the definition of terms: Range and mean,
Be able to
calculate percent error.

61. Range and mean Range: difference between highest to lowest.
Mean: average of a set of measurements.
For example:
A student made seven measurements of the period of a simple pendulum of constant length: 1.34 s, 1.28 s, s, 1.28 s, 1.33 s, 1.33 s, and 1.28 s.
Determine the range
Determine the mean

62. Percent error
Measurements made during laboratory work yield an experimental value
Accepted value are the measurements determined by scientists and published in the reference table.
The percent error of a measurement can be calculated by equation:

63. example Percent error = 1.7%
In an experiment, a student determines that the acceleration due to gravity is 9.98 m/s2. If the accepted value is 9.81 m/s2, determine the percent error.
|experimental value – accepted value|
Percent error =
X 100%
accepted value
Percent error = 1.7%

64. 1.6 Graphing data Be able to represent data in graphical form
determine the mathematical relationships for the given graphs
determine the shape of graphs for the given mathematical relationships.

65. representing data in graphical form
The data collected in a physics experiment are often represented in graphical form. A graph makes it easier to determine whether there is a trend or pattern in the data.
Voltage vs. current

66. The graph include…
The title, labeled as dependent variable vs. independent variable.
The independent variable, the one the experimenter changes, is graphed on the x- or horizontal axis.
The dependent variable, the one that changes as the result of the changes made by the experimenter, is graphed on the y- or vertical axis.
The axes are labeled with the quantities and their units are given in the parenthesis.
An appropriate, linear scale that accommodates the range of data is determined for each axis.
The line of best fit can be a straight or curved line. This line usually does not pass through all measured points.
Extrapolation means extending the line beyond the region in which data was taken.

67. If the graph is a straight line, the slope often has a physical meaning
Voltage vs. current
In determining the slope of a line, you must use the data on the line of the best fit. The data can come from the data table only if those points lie on the line of best fit.

68. Example – find slope Time (s) Position (m) 0.0 1.0 18 2.0 40. 3.0 62
1.0 18
2.0
40.
3.0 62
4.0
80.
5.0
100.
The position of a moving car is recorded in the following table. Graph the data on the grid provided and draw the line of best fit. Determine the slope of the line.
Position vs. Time
100 80 60 40 20
Position (m)
Time (s)

69. Determine the mathematical relationships for given graphs
Period vs. length
Linear relationship: y = kx
Direct squared relationship: y = kx2
Direct square root relationship:
inverse relationship: y = k/x
inverse squared relationship: y = k/x2

70. Determine the shape of graphs for given mathematical relationships
Acceleration vs. mass
gravity vs. distance

71. 9/12 do now
Packet #84, 93

72. 1.7 Vector and scalar
know
The definition of a scalar and a vector.

73. Scalars vs. Vectors
Scalars are quantities that are fully described by a magnitude (or numerical value) alone.
Vectors are quantities that are fully described by both a magnitude and a direction.

74. examples
To test your understanding of this distinction, consider the following quantities listed below. Categorize each quantity as being either a vector or a scalar.
Quantity
Category
a. 5 m
b. 30 m/sec, East
c. 5 mi., North
d. 20 degrees Celsius
e. 256 bytes
f Calories

75. 1.8 Solving equations using algebra
Know
Axioms used for solving equations and order of operations
Be able to
solve an equation for an unknown quantity.
apply trigonometry to solve physics problems

76. Axioms used for solving equations
If equal are added to equals, the sums are equal.
If equal are subtracted from equals, the remainders are equal.
If equal are multiplied by equals, the products are equal.
If equal are divided by equals, the quotients are equal.
A quantity may be substituted for its equal.
Like powers or like roots of equals are equal.

77. Order in performing a series of operations
Simplify the expression within each set of parentheses
Perform exponents
Perform the multiplications and divisions in order from left to right.
Do the additions and subtractions from left to right
Force correct order using PARENTHESES in calculator

78. Algebra : Example #1
Solve for m1

79. Algebra : Example #2
Solve for r

80. Algebra : Example #3
Solve for vi

81. Lab – Measuring Immeasurable Heights
Purpose: How do you measure the height of some tall objects outside?
Material: protractor, tape measurer, Objects (LCD projector (in-class practice), scoreboard, bleachers, football field light fixture, batting cage, gym roof)
Object
Angle (o)
Distance from object (m)
Height of object (m)
LCD Projector
Scoreboard
Bleachers (top of announcer’s booth)
lights
Batting cage
Gym roof