Mathematics in Physics Chapter 2 Mathematics in Physics

Metric System

A system of Measurements that is based on the power of ten or multiples of ten

SI International System

The system of measurements that has been adopted by the scientific world based on the metric system

Basic Units

Length meter m Mass kilogram kg Time second s Temp. kelvin K Matter mole mol Current amp A Lum. Int. candela cd

Drill A bird flies east for 30 min at 20 mph, then flies west for 45 min at 16 mph, then flies east for 75 min at 4 mph. How far is the bird from its original position?

SI Prefixes

Nano n 0.000000001 10-9 micro m 0.000001 10-6 milli m 0.001 10-3 centi c 0.01 10-2 deci d 0.1 10-1 kilo k 1000 103 mega M 1,000,000 106 giga G 1,000,000,000 109

Scientific Notation

M x 10n 1.00...  M < 10 n = an integer

M x 10n M is the coefficient n is the exponent

Convert each of the following to scientific notation: 620,000,000 0

Addition & Subtraction in Scientific Notation

When adding w/o calculator change all additives to the same power of ten add coefficients power of ten remains constant 3 x 104 + 4 x 105 0.3 x 105 + 4 x 105 When adding with calculator all scientific notations must be within parentheses 3 x 104 + 4 x 105 (3 x 104) + (4 x 105)

When subtracting w/o a calculator change all numbers to the same exponent subtract coefficients keep exponents constant When subtracting with a calculator place all scientific notations within parentheses

Add: 4.10 x 1016 3.4 x 10-186 5.2 x 1015 6.20 x 10-185

Subtract: 4.10 x 1016 3.4 x 10-186 5.2 x 1015 6.20 x 10-185

Add: Subtract: 2.25 x 1016 3.40 x 10-18 7.7 x 1015 - 6.2 x 10-19

Multiplication & Division in Scientific Notation

When multiplying w/o a calculator multiply coefficients add exponents When multiplying with a calculator place all scientific notations within parentheses

When dividing in w/o a calculator divide coefficients subtract exponents When dividing in with a calculator place all scientific notations within parentheses

Multiply: 4.10 x 10126 2.0 x 10-186 3.0 x 1015 1.20 x 1018

divide: 4.40 x 1016 6.4 x 10186 2.2 x 1015 3.20 x 10-185

Compute: 4.40 x 10-6 6.4 x 10186 2.0 x 1015 3.20 x 1085 x

Measurement Uncertainties

Accuracy

How close the measurement is to the correct measurement

Precision

How well one can repeat the same results in a measurement

Significant Digits

The valid digits in a measurement removing all digits that have too much uncertainty to count

Determine Sig Dig: 215 21.5 21500 21.500 0.000 215 205 0.000 215 000 000

Conversion Factors Ratios = 1

100 cm 1 m = 1 1 m 100 cm = 1

Conversion Factors When you multiply any number by a conversion factor, the number’s magnitude does not change

1 nm 10-9 m = 1 1 mm 10-6 m = 1

1mm 10-3 m = 1 1 cm 10-2 m = 1

1km 103 m = 1 1 Mm 106 m = 1

1Gm 109 m = 1 109 m 1 Gm = 1

1 mm 10-3 m 44 m x = 44 x 103 mm = 4.4 x 104 mm

Drill: Convert: 1) 53 mm to km 2) 80 Gbytes to Mbytes 3) 44 mg to ng 4) 62 cm to km

Parallax

Differences in a measurement due to the angle of observation

Common Units m = mass in (kg) t = time in (s) d = displacement in (m)

Common Units v = velocity in (m/s) a = acceleration in (m/s2) F = force in (N) N = Newton = kgm/s2

Common Units W = work in (J) J = Joules = kgm2/s2 P = Power in (W) W = Watts = kgm2/s3

Graphing Data

Convert: 1) 44 mm to km 2) 21 ms to Ms 3) 64 cg to ng

Convert: 1) 3.5 mm3 to m3 2) 3.6 km/hr to m/s

A measure of mass per unit volume Density A measure of mass per unit volume

Density (D) (r) r = m/V

Calculate the density of 750 g of a substance occupying 12 Calculate the density of 750 g of a substance occupying 12.5 mL of space.

Convert: 1) 23 cm/ms to km/ns 2) 56 mg/nL to kg/ML

Convert: 1800 km/hr to mm/ns

Convert: 47 mg/nL to mg/mL

Calculate the density in g/cm3 of a 0 Calculate the density in g/cm3 of a 0.62 Mg chunk of metal that has dimensions of 12.5 mm by 4.0 m by 2.0 x 10-3 km. V = lwh r = m/V

Convert: 144 km/hr to mm/ns

Convert: 250 kg/m3 to mg/cm3

Convert: 1)1800 miles/hr to mm/ns 2.54 cm = 1 inch

Drill: Convert: 4.6 mg/nL to Mg/m3 1 mL = 1 cm3

Convert: 2.5 x 108 miles/year to mm/ms 2.54 cm = 1.00 inch

Name & describe the seven basic units

Name & give the multiple for: k, m, M, m, n, c, & G

Calculate the density in g/mL of 7. 520 x 104 kg of stuff occupying 2 Calculate the density in g/mL of 7.520 x 104 kg of stuff occupying 2.5 x 103 m3 of space.

Calculate the volume in kL of an rectangular prism with a length of 25 cm, width of 40.0 mm, & a height of 33500 mm.

Review Lab Due Monday