Corner Brook Regional High School

Measurement and Calculations Significant Digits Scientific Notation Converting between Units Accuracy vs. Precision Scalar Quantities Distance Calculations Speed Calculations Distance-Time Graph Speed Time Graph Vector Quantities Displacement Calculations Velocity Calculations Acceleration Calculations Vector Diagrams

Chapter 9 Intro, 9.2, 9.5, 9.6, 9.7, 9.10 Chapter 10 Intro, 10.2, 10.3, 10.4, 10.7 Chapter 11 Intro, 11.1, 11.3, 11.5, 11.7

What is Physics What is Physics? Sheldon s Version When a physics teacher knows their stuff!

DEFINITION: The study of motion, matter, energy, and force. Branches include: MECHANICS (motion and forces) WAVES (sound and light) ENERGY (potential and kinetic, thermodynamics) MODERN (quantum physics, nuclear physics)

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Before we jump into physics we need to look at some the skills you will need. For example we need to be able to take measurements of things. Mass/Weight Distance Time

CERTAINTY Defined as the number of significant digits plus one uncertain (estimated) digit The last digit of any number is always UNCERTAIN, as measurement devices allow you to estimate. EXAMPLE: 2.75 m The 5 is uncertain

TAKE THE FOLLOWING MEASUREMENT and determine the certain digits and the uncertain digit. ANSWER:

TAKE THE FOLLOWING MEASUREMENT and determine the certain digits and the uncertain digit. ANSWER: 8.05 the 5 is uncertain, it was estimated 11

1. EXACT VALUES EXACT VALUES have an INFINITE ( ) NUMBER of SIGNIFICANT DIGITS. TWO TYPES: COUNTED VALUES directly counted Ex: 20 students, 3 dogs, 5 fingers DEFINED VALUES always true, constant measures Ex: 60 s/min, 100 cm/m, 1000 m/km

2. ZEROS ALL NUMBERS in a value are SIGNIFICANT EXCEPT LEADING ZEROS, and TRAILING ZEROS WITH NO DECIMAL. VALUE 600 606 600.0 0.60 0.606 660 NUMBER OF SIG FIGS

3. MULTIPLYING and DIVIDING WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS. EXAMPLE: 6.15 x 8.0 = 8.4231 2 =

3. MULTIPLYING and DIVIDING WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS. EXAMPLE: 6.15 x 8.0 = 8.4231 2 = 16

4. ADDING AND SUBTRACTING WHEN ADDING(+) and SUBTRACTING(-), ANSWER has SMALLEST NUMBER of DECIMAL PLACES. EXAMPLE: 104.2 + 11 + 0.67 =

4. ADDING AND SUBTRACTING WHEN ADDING(+) and SUBTRACTING(-), ANSWER has SMALLEST NUMBER of DECIMAL PLACES. EXAMPLE: 104.2 + 11 + 0.67 = 116 18

5. ROUNDING When ROUNDING, if the number is 5 or GREATER, ROUND UP. Remember, round only once! VALUE 61.3 s 12.70 m/s 36.5 km 99.0 m/s 2 46.4 min ROUND to 2 SIG FIGS

5. ROUNDING When ROUNDING, if the number is 5 or GREATER, ROUND UP. Remember, round only once! VALUE 61.3 s 12.70 m/s 36.5 km 99.0 m/s 2 46.4 min ROUND to 2 SIG FIGS 20

34.497

A convenient way of expressing very large and small numbers. Expressed as a number between 1 and 10 and multiplied by 10 x (x = exponent). LARGE numbers exponent is # of spaces to the LEFT SMALL numbers NEGATIVE exponent is # of spaces to the RIGHT

ROUND THE FOLLOWING to 2 SIGNIFICANT DIGITS. VALUE SCIENTIFIC NOTATION 100 m 3500 s 926,000,000,000 h 0.0043 m 0.0000000001246 s 0.1 m/s 2

ROUND THE FOLLOWING to 2 SIGNIFICANT DIGITS. VALUE SCIENTIFIC NOTATION 100 m 3500 s 926,000,000,000 h 0.0043 m 0.0000000001246 s 0.1 m/s 2 24

DO Worksheets 1,2, 3 (p. 4-6)in your handout for homework.

From the Physics Worksheets Booklet 29

0.0300 31

WHEN ADDING(+) and SUBTRACTING(-), ANSWER has SMALLEST NUMBER of DECIMAL PLACES. WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS. 32

Scientific Notation 34

5 x 10-3 5.05 x 10 3 8 x 10-4 1 x 10 3 1 x 10 6 2.5 x 10-1 2.5 x 10-2 2.5 x 10-3 5 x 10 2 5 x 10 3 1500 0.0015 0.0375 375 220,000 0.335 0.00012 10,000 0.1 4 35

BASE UNIT A unit from which other units may be derived, including units for the following: Length Mass Time metres, m kilogram, kg second, s Temperature kelvin, K In science, we use SI BASE UNITS, from the INTERNATIONAL SYSTEM OF UNITS. DERIVED UNIT A unit which is derived from base units. Ex: m/s

METRIC PREFIXES Values placed in front of the base units. PREFIX SYMBOL FACTOR giga G 10 9 mega M 10 6 kilo k 10 3 hecta h 10 2 deca da 10 1 SI BASE UNITS deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9

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To convert, using the following system: TO THE RIGHT multiply by 10 TO THE LEFT divide by 10 G M k h da SI BASE UNITS d c m μ n DIVIDE BY 10 MULTIPLY BY 10

EXAMPLES: 1.6 m = μm 340 N = hn

EXAMPLES: 1.6 m = 1.6 x 10 6 = 1,600,000 μm (micro-meter) 340 N = 340 /100 = 3.4 hn (hecta-newton) 43

EXAMPLES: 1250 cm = km 4.7 Gg = ng

EXAMPLES: 1250 cm = 1250/100000 =.0125 km (1 km = 1000m and 1 m=100 cm) 4.7 Gg = 4.7 x 10 18 ng Do the metric hops! 45

In addition to using metric prefixes, we also convert between SI UNITS and other accepted systems of measurement. Here are some helpful CONVERSION FACTORS you should know when studying MOTION: 1 km = 1000 m 1 h = 3600 s 1 m/s = 3.6 km/h

..and where did that number come from. So again. 1 meter/second = 3.6 km/hr 47

CONVERT THE FOLLOWING: 23 min = h 0.47 h= s

CONVERT THE FOLLOWING: 23 min = 23/60 =.3833 =.38 h 0.47 h= 1700 s WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS. 49

CONVERT THE FOLLOWING: 4.5 km/h = m/s 30.2 m/s = km/h

CONVERT THE FOLLOWING: WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS 4.5 km/h = m/s 30.2 m/s = km/h 51

DO WORKSHEETS 4 and 5 (p. 10-11 in your handout) for homework.

Pages 4 and 5 of Work Book Divide Multiply 55

Let s convert 1000 km to cms. That s 5 hops to the right, so multiply by 10 5 1000 x 10 5 = 100,000,000 cms in 1000 km 1000 km x 1000 m x 100 cm = 100,000,000 cm 1 km 1 m 56

#2. 250 x 10-9 which is the same as 2.5 x 10-7.00000025 (2.5 x 10-4 ) 57

4 spaces to the left 9 spaces to the right 58

WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS. 60

WHEN ADDING(+) and SUBTRACTING(-), ANSWER has SMALLEST NUMBER of DECIMAL PLACES. WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS. 62

REMEMBER TO READ ALL INSTRUCTIONS! ROUND FIRST!!!! Ex: 0.00987 0.0099 63

1 m/s = 3.6 km/h 1 h = 3600 s 65 min = 0.045 days 1 km = 1000 m 1 d = 1440 min (60 x 24) WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS. 64

UNIT 3 QUIZ 1 Significant Digits, Rounding, Scientific Notation, Converting Between Units Closed Book Quiz Similar to Worksheet 5 CLASS QUIZ DATE:

Accuracy measures how close a measurement is to an ACCEPTED or TRUE VALUE. It is expressed as a PERCENT VALUE (%). Often, poor accuracy is a result of flaws in equipment or procedure. EXAMPLE: Accepted Value a g = 9.80 m/s 2 Experimental Value a g = 9.50 m/s 2 Accuracy = 96.9 %

Precision measures the reliability, repeatability, or consistency of a measurement. It is expressed as the accepted value ± a discrepancy. Often, poor precision is a result of flaws in techniques by the experimenter. EXAMPLE: Accepted Value a g = 9.806 m/s 2 Experimental Value a g = 9.50 m/s 2 Precision = 9.80 m/s 2 ±.306

EXAMPLE: Describe the ACCURACY and PRECISION of each of the following results.

QUALITITATIVE DESCRIPTIONS Describing with words. These descriptions are made using the 5 senses. Example: colour of a solution odor of a chemical product sound of thunder QUANTITATIVE DESCRIPTIONS Describing with numbers (i.e., quantities). These descriptions are made by counting and measuring. Example: height of a building speed of an airplane

POINTS to REMEMBER: Whatever you do to ONE SIDE of an EQUATION, you must do to the OTHER SIDE. Do not move the item you are trying to isolate. Move EVERYTHING ELSE!!! Do the opposite to move a variable. For example, to move a variable that is multiplied, divide by it.

Rearrange the following equations to solve for the variable indicated: a = v Solve for v. t

Rearrange the following equations to solve for the variable indicated: a =v Solve for v t Cross multiply: v = a x t Multiply both sides by t: t x a = v x t = t x a =v t 74

y = mx + b Solve for m.

y =mx + b Solve for m. Subtract b on both sides: y b = mx + b b y b = mx Divide both sides by X: y b = mx so m = y b x x x 76

DO WORKSHEET 6 (page 14 in your handout) for homework.

Rearrange the following equations and solve for the variable indicated. a) a = v solve for t: t at = v and t = v a 80

b) Solve for n: c = n (cross multiply) v cv = n 81

c) Solve for M n = m M nm = m M = m n 82

d) Solve for R PV = nrt PV = nrt nt nt PV = R nt 83

e) Solve for X y = mx + b y b = mx +b b y b = mx y b = x m 84

f) Solve for r C = 2 r C = r 2 85

g) Solve for a: d = 1aT 2 2 2d = 1aT 2 2 2 2d = at 2 2d = at 2 T 2 T 2 86

h) Solve for T d = 1aT 2 2 2d = at 2 2d = T 2 a 2d = T a 87

i) Solve for ΔT V2 = V1 + aδt V2 V1 = a ΔT V2 V1 = ΔT a 88

j) d = (V i + V f )T 2 Solve for V f 2d = (V i + V f )T 2d = (V i + V f )T x 1 T T 2d=V i + V f T 2d V i T = V f 89