Welcome Course: Regents Physics Room: 207 Teacher: Mrs. LaBarbera Email: diana.labarbera@valleycentralschools.org google classroom code: ysslhjo Post : Room 207, Tues. – Thurs. 1

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

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

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

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.

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.

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

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

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

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

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

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

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.

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

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

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.

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.

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

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.

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

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

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

Measuring time (second) What is the elapsed time in seconds? Total of 115.15 seconds

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

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

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

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

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

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

example Use a protractor to measure angle θ. θ

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

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

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

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

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

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.

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.

example Matt measures the total length of a lap around the school’s track to be 402.3 m, 402.3 m and 402.5 m. If the accepted value for the path length is 402.3 m, Is Matt’s measurement accurate? Explain your answer Is Matt’s measurement precise? Explain your answer

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.

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 + 0.01 cm = 5.31cm. there are 3 sig. figs. The number of significant figures depends on how precise an instrument is.

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

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; 0.00008 ms has ___ sig figs Zeros between non-zero digits are significant 3.0025 s has ____ sig figs; 0.305 g has ___ sig figs Ending zeros… If there is a decimal point, zeros are significant 30.00 s has ____ sig figs; 0.030 kg has ___ sig figs If there is no decimal point, zeros are not significant 1000 mg has ___ sig figs; 20 mm has ___ sig figs

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

Significant Digits : Examples How many significant digits in each? 456000 0.0093 2.150 85067 0.204 3 2 4 5 3

Rules for calculating with sig. figs.

Examples 3.04 m + 4.134 m + 6. 1 m = 0.028 kg + 0.0023 kg =

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 ?

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

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

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

example 6,370,000 m has 3 significant digits, it can be expressed in scientific notation as ____________ 0.000 000 000 066 7 N∙m2/kg2 has 3 significant digits, it can be expressed as _____________ Length of an ant is 0.004 meters, which can be expressed in scientific notation as ______________. Expand the number 9.56 x 10-3: _______________ Expand the number 1.11 x 107. _______________

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!!!

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: 500000 or 5.0 x 105 or 5E5 When performing calculations with scientific notation, the rules for significant figures apply

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

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 2.0140 x 103 m

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 3.84 x 108 m. the order of magnitude of the distance is 8

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

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

9/11 do now Class work packet - #67

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

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, 1.26 s, 1.28 s, 1.33 s, 1.33 s, and 1.28 s. Determine the range Determine the mean

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:

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%

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.

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

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.

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.

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) 0 1.0 2.0 3.0 4.0 5.0 Time (s)

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

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

9/12 do now Packet #84, 93

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

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.

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. 4000 Calories

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

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.

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

Algebra : Example #1 Solve for m1

Algebra : Example #2 Solve for r

Algebra : Example #3 Solve for vi

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