Physics

A Mathematical Science

Science

An organized way of studying our surroundings

Technology

Applied scienceUsing discoveries to create useful products

PhysicsStudy of matter and energy and their relationships Experimental

Research using equipment Theoretical

Construction of theory using mathematics to explain experimental data

Basic to all other sciences Chemistry, engineering, architecture,

medicine A few laws describe most physical

relationships

Traits Helpful to a Physicist:

KnowledgeInsightCreativityImaginationPatience

Scientific Method

Recognize the

ProblemForm a

Hypothesis

Test the Hypothesis

Draw Conclusions

Use observations

Conduct the experimentDesign an experiment

Collect data

Make predictions

Revise/ repeat experiment

Measurement

Definition of the base unit

SI Base Unit

Other common units

Length: distance light travels in 1/300,000,000s

meter km, cm, mm

Mass: mass of a Pt-Ir cylinder

gram kg, mg

Temperature:

0 K = -273 °C Kelvin

Time: period of radiation of Cesium-133

second

ms, min, h

Data Analysis

Chapter 2

Measurement

quantitative description Requirements: Know property attempting to measure Must have a standard for comparison Must have a method of comparison

International System of Measurement

SICreated by the French in 1795Used by most countriesUnits are related to powers of 10No fractions are used

Powers of ten

Peta - 1015 Tera - 1012 Giga - 109

Mega - 106

Kilo - 103

Hecto - 102

Deka - 101

Deci – 10-1

Centi – 10-2

Milli – 10-3

Micro – 10-6

Nano – 10-9

Pico – 10-12

Femto - 10-15

SI base units Unit Quantity Instrumen

t

Meter Length – distance between two points

meter stick

Kilogram

Mass – amount of matter

balance

Kelvin Temperature – how hot or cold an object is relative to others (avg. KE of particles)

thermometer

Second Time – interval between two events

clock

SI base units

Unit Quantity Instrument

Mole Amount of a substance(6.02 x 1023)

Count (calculated from mass)

Candela

Light Intensity – amount of light that falls on 1 m2 of surface

Light meter

Ampere

Electrical current – number of charges moving past a point in 1 second

Ammeter

Derived units

made from basic units Volume: amount of space occupiedVolume may determined by: Calculating from dimensions Graduated cylinder – if liquid Water displacement – if irregular in shape

Acceptable units: L, mL, m3, cm3, dm3

Determining Volume from Dimensions

V = l x w x h

= 1 dm3 = 1 L

1000 cm3 = 1000 mL

1 cm3 = 1 mL

1 dm1 dm

1 dm

Other Derived UnitsDensity – mass per unit volume D = m/V units: g/cm3

can be used to identify an unknown sample of matter

Weight – measure of force of gravity between 2 objects W = mg Newton (kg·m/s2) Measured with a spring scale

Scientific Notation

way to express extremely large or small numbers as powers of ten

M x 10n M = # between 1 and 10

n = any whole number

+n – # is larger than 1

-n – # is smaller than 1

Examples:

123456778 = 1.23456778 x 108

0.0000456 = 4.56 x 10-5

Operations:

To add or subtract, exponents must be the same. Adjust exponents

and decimal place Add or subtract M’s Keep n the same Adjust exponent and

decimal on final answer if needed

Example: 2 x 102 + 3 x 103

2 x 102 30 x 102

= 32 x 102

= 3.2 x 103

Operations

To multiply: multiply M’s Add n’s

To divide: Divide M’s Subtract n’s

Example: (2.0 x 102)(3.0 x

103)

= 6.0 x 10(2 + 3)

= 6.0 x 105

Using a Calculator for Scientific Notation

Locate or This stands for “x 10”Example: (2.0 x 102)(3.0 x 103) Enter “2.0 EE 2 times 3.0 EE 3 = ” 6.0 x 105 should appear on the display

Use the +/- key to enter negative exponentsIf the answer does not appear in sci. not., check the mode or punch SCI.

EE EXP

Solving Problems Using Dimensional Analysis

AKA: factor-label method, conversion factors, bridge methodUnits are treated as factors Multiply by a series of factors to cancel the unwanted unitsNo need to memorize lists of formulas You do have to know the conversion factors

Factors are equivalent.

1 m or 1 min

100 cm 60 s

Ex: ? m = 500 cm

? m = 500 cm

100 cm

1 m

= 5 m

Arrange factors to cancel unwanted unitsMultiply by numbers on the top of the barDivide by numbers on the bottomIf the units match on each side of the =, the problem should be correct.

Uncertainties of Measurement:

All instruments are subject to external forces and interpretation by people

Accuracy and Precision:

Describe the reliability of a measurementAccuracy: how close a measurement is to the correct value May be expressed as percent error

% error = accepted value – experimental value x 100

accepted value

Accuracy and Precision:

Precision: how close repeated measurements are to each other Depends on the exactness of the

instrument scale Measurements are recorded using

the correct number of significant digits

Parallax

Apparent shift in position of an object when viewed from various angles Meter reading Graduated cylinder reading

Significant digits

All definitely known digits plus one estimated digit.The number of sig. digs. should be observed in all calculations using measurements.Rules for determining number of sig digs in a recorded measurement are on page 39. Nonzero digits Captured zeroes Zeros after a decimal and after a number

Examples

300 m 1 sig dig303 m 3 sig digs3030 m 3 sig digs30.0 m 3 sig digs0.3 m 1 sig dig0.0003 m 1 sig dig0.00300 m 3 sig digs0.03030 m 4 sig digs

Reading Instrument Scales

Reading Instrument Scales

Reading Instrument Scales

Reading Instrument Scales

Rounding Off Numbers

If adding or subtracting measurements, round your answer to the least number of decimal places.

If multiplying or dividing measurements, round your answer to the least number of significant digits.

Problems – pages 27-28

Solving Equations Using Algebra

Isolate unknown on the left side of the equation before plugging in known values when possibleRemember the order of operations.Perform same operations to both sides of equationExample: Solve the following expression for b.

3y = 6x + 2ab2

Units in Equations:

Operations performed on numbers are also performed on unitsProper units = correct answer Good check method

Measurements of the same type must have the same units Make conversions using dimensional

analysis Example: 6 cm + 5 m + 2 mm

Representing Data observations →charts → graphs

→equationsGraph – visual display Circle – parts of a whole (percents) Bar – how one quantity varies with another Line – (same as bar)

Determine relationship (verbal or equation) Determine slope (rate of change of y to x) Interpolate – read between data points Extrapolate – read beyond data points (predict)

Variables

Independent – one manipulated in an experiment Plotted on the x-axis

Dependent – changes as a result of manipulating independent variable Plotted on the y-axis

Linear Relationships

Data points form a straight lineEquation: y = mx + b Slope (m) = rise/run y-intercept (b) =

value of y when x = 0

Direct relationship: As x increases, y

increases x

Parabolic Relationship

Data forms an upward curve (parabola)Equation: y = kx2

K = constant = y/x2

Power curve: as x increases, y increases more each time

x

y is greater for each increment of x

Root Curve

Data points form a an upward curve which levels offEquation: y = kx

Inverse Relationship

Data points slope downward (hyperbola)Equation: y = k/xAs x increases, y decreases

x

Identify these relationships: