Chapter 2 Welcome to Grade 11 Physics SI

Chapter 2 Welcome to Grade 11 Physics SI units and Scientific Notation

Units of Measurement • Measurements involve NUMBER and UNIT • Represent a quantity: has magnitude, size, or amount • Gram = unit of measurement • Mass = quantity

Units of Measurement • Scientists around the world agree on one system… – International System of Units (le Systeme International d’Unites) – SI units – Built from seven base units

SI Fundamental or Base Units

Metric prefix • Prefixes – powers of ten

Mass • • • Measures quantity of matter SI unit: kilogram, kg ______ kg = _____ g gram used for smaller masses Weight: measure of gravitational pull

Length • • • SI unit: meter, m Longer distances: kilometer, km _______ km = _______ m Shorter distances: centimeter, cm _______ m = ____ cm

Derived Units, like Volume • SI unit: m 3 • A derived unit: combination of base units by multiplying or dividing • SI unit for Area: l x w = m x m = m 2 • Volume: l x w x h = m x m = m 3 • Also: liters (L), m. L, dm 3 and cm 3 • 1 L = 1 dm 3 = 1000 m. L = 1000 cm 3

Derived Units

Scientific Notation • Put the numbers in the form a x 10 n • a has one # to left of decimal • If # is bigger than 1 + exponent • If # is less than 1 - exponent

Scientific Notation Review: • Write in scientific notation 32, 700 0. 0003412 • Change to a decimal 3. 901 x 10 -6 4. 755 x 108

Significant Figures (sig figs) • How many numbers mean anything? • When we measure, we can (and do) always estimate between the smallest marks. 1 2 3 4 5

Significant figures (sig figs) • Better marks better estimate. • Last number measured actually an estimate 1 2 3 4 5

Sig Figs • What is the smallest mark on the ruler that measures 142. 15 cm? • 142 cm? • 140 cm? • Does the zero mean anything? (Is it significant? ) • They needed a set of rules to decide which zeroes count.

Sig Figs. • • • 405. 0 g 4050 g 0. 450 g 4050. 05 g 0. 0500060 g

Sig Figs • Only measurements have sig figs. • Counted numbers are exact – infinite sig figs • A dozen is exactly 12

Problems • • 50 has only 1 significant figure if it really has two, how can I write it? Scientific notation 5. 0 x 101 2 sig figs • Scientific Notation shows ALL sig figs

Rounding rules • Round 454. 62 to four sig figs – to three sig figs – to two sig figs – to one sig fig

Sig figs. • How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0. 0485 g • 0. 004085 g • 40. 004085 g

Density • Density = mass D=m volume V • Units: g/cm 3 or g/m. L but SI unit is kg/m 3 • derived unit • Used to identify substances • Varies with temperature • As temp. increases density…

Density

Density Examples • If a metal block has a mass of 65. 0 grams and a volume of 22 cubic centimeters, what is the density of the block? • D=m V • D = 65. 0 g = 3. 0 g/cm 3 22 cm 3

Density Examples • Aluminum has a density of 2. 7 g/cm 3. What volume of aluminum has a mass of 60 grams? • D=M V 20 cm 3

Unit Conversions

Conversion factors • Given information in one unit need to find the equivalent in another unit • “A ratio of equivalent measurements. ” • Start with two things that are the same. 1 m = 100 cm • Can divide by each side to come up with two ways of writing the number 1.

Conversion factors 1 m 100 cm = 100 cm

Conversion factors 1 m 100 cm = 1

Conversion factors 1 m 100 cm = 1 m 1 m = 1 100 cm 1 m

Conversion factors 1 m 100 cm = 1 100 cm 1 m

Conversion Factors • Unique way of writing the number 1. • Does NOT change the VALUE, it changes the UNITS.

Write the conversion factors for the following • kilograms to grams • 1 L = 1 dm 3 = 1000 m. L = 1000 cm 3

More Unit Conversions More Involved

Derived Unit Conversions • 54. 3 cm 3 = ______ m 3

Derived Unit Conversions • 625 g/m. L = ______ kg/m 3

Where do these measurements come from? Recording Measurements

Making Good Measurements • We can do 2 things: 1. Repeat measurement many times - reliable measurements get the same number over and over - this is PRECISE

Making Good Measurements 2. Test our measurement against a “standard”, or accepted value - measurement close to accepted value is ACCURATE

Measurements are Uncertain 1. Measuring instruments are never perfect 2. Skill of measurer 3. Measuring conditions 4. Measuring always involves estimation – Flickering # on balance – Between marks on instrument

Estimating Measurements

Error • • Probably not EXACTLY 6. 35 cm Within. 01 cm of actual value. 6. 35 cm ±. 01 cm 6. 34 cm to 6. 36 cm

Calculating Percent Error • Compares your measurement to accepted value • Negative if measurement is small • Positive if measurement is big

Calculating Percent Error • What is the % error for a mass measurement of 17. 7 g, given that the correct value is 21. 2 g?

Direct Proportions • Two quantities are directly proportional if dividing one by the other gives a constant • y x “y is proportional to x” • General Equation • y=k x

Direct Proportions • Solve for y: y=k x • Look familiar? • Eqn for a straight line: y = mx + b • Slope is the constant

Direct Proportion

Inverse Proportions • Two quantities are inversely proportional if their product is a constant • “y is proportional to 1 divided by x” • General eqation: xy = k • Example: speed and travel time

Inverse Proportion Graph is called “hyperbola”

Calculations • Convert 3. 23 x 104 kg to g. Give answer with correct sig. figs.

Calculations • What is the mass of an object with a density of 25. 98 g/m. L and a volume of 4. 2 m. L? • What is the density of a 430 g object that takes up 25. 5 cm 3?