Units and Measurement Physics Mrs Coyle International Space

Units and Measurement Physics Mrs. Coyle International Space Station http: //apod. nasa. gov/apod/image/0706/iss_sts 117_big. jpg

It All Starts with a Ruler!!!

Math and Units • Math- the language of Physics • SI Units – International System – MKS • Meter m • Mass kg • Time s • National Bureau of Standards • Prefixes

SI Unit Prefixes - Part I Name Symbol Factor tera- T 1012 giga- G 109 mega- M 106 kilo- k 103 hecto- h 102 deka- da 101

SI Unit Prefixes- Part II Name Symbol Factor deci- d 10 -1 centi- c 10 -2 milli- m 10 -3 micro- μ 10 -6 nano- n 10 -9 pico- p 10 -12 femto- f 10 -15

The Seven Base SI Units Quantity Unit Symbol Length meter m Mass kilogram kg Temperature kelvin K Time second s Amount of mole Substance Luminous Intensity candela mol Electric Current a ampere cd

Derived SI Units (examples) Quantity unit Symbol Volume cubic meter m 3 Density Speed kilograms per kg/m 3 cubic meter per second m/s Newton kg m/ s 2 N Energy Joule (kg m 2/s 2) J Pressure Pascal (kg/(ms 2) Pa

SI Unit Prefixes for Length Name gigameter megameter kilometer decimeter centimeter millimeter micrometer nanometer picometer Symbol Gm Mm km dm cm mm μm nm pm Analogy 109 106 103 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12

Scientific Notation Mx n 10 • M is the coefficient 1<M<10 • 10 is the base • n is the exponent or power of 10

Other Examples: • 5. 45 E+6 • 5. 45 x 10^6 or

Numbers less than 1 will have a negative exponent. A millionth of a second is: 0. 000001 sec 1. 0 E-6 1 x 10 -6 1. 0^-6

Factor-Label Method of Unit Conversion • Example: Convert 5 km to m: • Multiply the original measurement by a conversion factor. NEW UNIT 85 km x 1, 000 m 1 km OLD UNIT = 85, 000 m

Factor-Label Method of Unit Conversion: Example • Example: Convert 789 m to km: 789 m x 1 km =0. 789 km= 7. 89 x 10 -1 km 1000 m

Convert 75. 00 km/h to m/s 75. 00 km x 1000 m x 1 h___ = 20. 83 m/s h 1 km 3600 s

Limits of Measurement • Accuracy and Precision

• Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

Example: Accuracy • Who is more accurate when measuring a book that has a true length of 17. 0 cm? Susan: 17. 0 cm, 16. 0 cm, 18. 0 cm, 15. 0 cm Amy: 15. 5 cm, 15. 0 cm, 15. 2 cm, 15. 3 cm

• Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Example: Precision Who is more precise when measuring the same 17. 0 cm book? Susan: 17. 0 cm, 16. 0 cm, 18. 0 cm, 15. 0 cm Amy: 15. 5 cm, 15. 0 cm, 15. 2 cm, 15. 3 cm

Example: Evaluate whether the following are precise, accurate or both. Accurate Not Precise

Significant Figures • The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

Centimeters and Millimeters

Finding the Number of Sig Figs: • When the decimal is present, start counting from the left. • When the decimal is absent, start counting from the right. • Zeroes encountered before a non zero digit do not count.

How many sig figs? 100 10302. 00 0. 001 10302 1. 0302 x 104

Sig Figs in Addition/Subtraction Express the result with the same number of decimal places as the number in the operation with the least decimal places. Ex: 2. 33 cm + 3. 0 cm 5. 3 cm (Result is rounded to one decimal place)

Sig Figs in Multiplication/Division • Express the answer with the same sig figs as the factor with the least sig figs. • Ex: 3. 22 cm x 2. 0 cm 6. 4 cm 2 (Result is rounded to two sig figs)

Counting Numbers • Counting numbers have infinite sig figs. • Ex: 3 apples

Solving Word Problems • Analyze – List knowns and unknowns. – Draw a diagram. – Devise a plan. – Write the math equation to be used. • Calculate – If needed, rearrange the equation to solve for the unknown. – Substitute the knowns with units in the equation and express the answer with units. • Evaluate – Is the answer reasonable?