The Science of Physics

Chapter 1

1-1: What is Physics?

Main Objectives: Identify activities and fields that involve the

major areas within physicsDescribe the processes of the scientific

methodDescribe the role of models and diagrams in

physics

What is Physics?

The goal of physics is to describe and explain the physical world using basic concepts, equations, and assumptionsThese principles can then be used to make

predictions about a broad range of phenomena Example: The same principles that can be used to

explain the motion of planets can be used to explain the motion of a baseball being thrown into the air

Pure vs. Applied Science

Many physicists study the laws of nature to satisfy their own curiosity about the natural worldPure science is when scientists working to

increase knowledge in a certain field

Pure vs. Applied Science

Many current forms of technology were only made possible through the application of scientific principles → this is applied science.Advances by those practicing pure science

have an affect on those practicing applied science and vice versa.

Physics is Everywhere The Physics of Cars

The Scientific Method

Scientists seek to understand, describe, and explain the natural worldThis involves an organized process of inquiry

and investigation

The Scientific Method

The scientific method is not necessarily a single procedure that is followed by scientists It is a collection of core

steps that are utilized in good scientific investigations

The Scientific Method

Physicists use models to represent key features of natural phenomena

Simple models that describe part of system are developed first so that they can be combined to represent complex phenomena model – a pattern, plan, representation, or description

designed to show the structure or workings of an object, system, or concept

Examples: mathematical models, diagrams, computer simulations, etc.

The Scientific Method system – a set of particles of interacting

components considered to be a distinct physical entity for the purposes of study

The Scientific Method Models can help build hypotheses

hypothesis – an explanation that is based on prior scientific research or observations and that can be tested

Hypotheses must be testable through experimentationcontrolled experiment – an experiment that

only tests one factor (variable) at a time by using the comparison of a control group with an experimental group

Galileo’s Though Experiment

Galileo’s Hypothesis: All objects fall at the same rate in the absence of air resistance

The Scientific Method

The best models/hypotheses can be used to make predictionsHowever, at any time there is the possibility

that an experiment will produce results that invalidate a certain model or hypothesis

A conclusion is only valid if it can be verified by others through experimentation

1-2: Measurements in Experiments

Main Objectives: List basic SI units and the quantities they

describeConvert measurements into scientific notationDistinguish between accuracy and precisionUse significant figures in measurements and

calculations

Accuracy and Precision

Good measurements in the lab are both correct and reproducible accuracy – how close a single measurement

comes to the actual dimension or true value of the quantity being measured

precision – the degree of exactness of a measurement

Example: 1.25 cm is a more precise measurement than 1.2 cm

Accuracy and Precision

All measurements made with instruments are really approximations that depend on the quality of the instruments and the skill of the person doing the measurement

The precision of the instrument depends on the how small the scale is on the device. The finer the scale the more precise the

instrument

SI Units The International System of Units, SI, is a

revised version of the metric system Correct units along with numerical values are

critical when communicating measurements. The are seven base SI units of which other SI

units are derived (derived units). Sometimes non-SI units are preferred for

convenience or practical reasons

Common SI Prefixes Units larger than the base unit

Tera T 10-12 = 0.000000000001 terameter (Tm)

Giga G 10-9 = 0.000000001 gigameter (Gm)

Mega M 10-6 = 0.000001 megameter (Mm)

Kilo k 10-3 = 0.001 kilometer (km)

Hecto h 10-2 = 0.01 hectometer (hm)

Deka da 10-1 = 0.1 decameter (dam)

Base Unit

100 = 1 meter (m)

Common SI Prefixes Units smaller than the base unit

Base Unit

100 = 1 meter (m)

Deci d 101 = 10 decimeter (dm)

Centi c 102 = 100 centimeter (cm)

Milli m 103 = 1000 millimeter (mm)

Micro μ 106 = 1,000,000 micrometer (μm)

Nano n 109 = 1,000,000,000 nanometer (nm)

Pico p 1012 = 1,000,000,000,000 picometer (pm)

Conversion Factors The same quantity can usually be measured

or expressed in many different ways. Examples:

1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies

1 m = 10 dm = 100 cm = 1000 mm

Whenever two measurements are equal, a ratio of these measurements will equal one Ratios of these equivalent (equal) measurements

are called conversion factors.

Conversion Factors In a conversion factor, the measurement in

the numerator (on the top) is equivalent to the measurement in the denominator (on the bottom.Example: “one meter per 100

centimeters”

1 m1 m 100 100 cmcm

Conversion Factors Because conversion factors are equal to one,

when a measurement is multiplied by a conversion factor, the size of a measurement stays the same.

Example: How many meters are in 0.68 km?1. Unknown: 0.68 km in meters

2. Known:

- 0.68 km

- 1 km = 1000 m → Conversion Factor:

3/4. Solution-Calculation:

1000 m1000 m 1 km1 km

0.68 km0.68 km x x 1000 m1000 m = 680 m = 680 m 1 1 km1 1 km

Scientific Notation

scientific notation – a number is written as the product of two numbers: a coefficient and a power of ten

Example: 36,000 is written in scientific notation as 3.6 x 104 or 3.6e4Coefficient = 3.6 → a number greater than or

equal to 1 and less than 10.Power of ten / exponent = 4 3.6 x 104 = 3.6 x 10 x 10 x 10 x 10 = 36,000

Scientific Notation

When writing numbers greater than ten in scientific notation the exponent is positive and equal to the number of places that the decimal has been moved to the left.

Scientific Notation

Numbers less than one have a negative exponent when written in scientific notation. Example: 0.0081 is written in scientific notation as

8.1 x 10-3

8.1 x 10-3 = 8.1/(10 x 10 x 10) = 0.0081

When writing a number less than one in scientific notation, the value of the exponent equals the number of places you move the decimal to the right.

Measurement and Uncertainty

Accurate measurements are an important part of physics, but no measurement is absolutely precise There is an uncertainty associated with every

measurement Uncertainty arises from various sources

Individual errors → Example: misusing equipment The limited accuracy of every measuring

instrument

Measurement and Uncertainty

The number of reliably known digits in a number is called the number of significant figuresSignificant figures in a measurement include

all of the digits that are known precisely plus one last digit that is estimated

23.21 → 4 significant figures 0.062 → 2 significant figures

Significant Figures - Rules1. Every nonzero digit in a recorded

measurement is significant.

- Example: 24.7 m, 0.743 m, and 714 m all have three sig. figs.

2. Zeros appearing between nonzero digits are significant.

- Example: 7003 m, 40.79 m, and 1.503 m all have 4 sig. figs.

Significant Figures - Rules3. Zeros appearing in front of all nonzero digits are

not significant; they act as placeholders and cannot arbitrarily be dropped (you can get rid of them by writing the number in scientific notation).

- Example: 0.0071 m has two sig. figs. And can be written as 7.1 x 10-3

4. Zeros at the end of the number and to the right of a decimal point are always significant.

- Example: 43.00 m, 1.010 m, and 9.000 all have 4 sig. figs.

Significant Figures - Rules

5. Zeros at the end of a measurement and to the left of the decimal point are not significant unless they are measured values (then they are significant). Numbers can be written in scientific notation to remove ambiguity.- Example: 7000 m has 1 sig. fig.; if those zeros were measured it could be written as 7.000 x 103 m

Significant Figures - Rules

6. Measurements have an unlimited number of significant figures when they are counted or if they are exactly defined quantities.

- Example: 23 people or 60 minutes = 1 hour

* You must recognize exact values to round answers correctly in calculations involving measurements.

Significant Figures in Calculations

In calculations involving measurements, an answer cannot be more precise than the least precise measurement from which it was calculated.Example: The area of a room that measures

7.7 m (2 sig. figs.) by 5.4 m (2 sig. figs.) is calculated to be 41.58 m2 (4 sig. figs.) – you must round the answer to 42 m2

Significant Figures in Calculations

The answer to an addition or subtraction problem should be rounded to have the same number of decimal places as the measurement with the least number of decimal places.Example: 34.61m – 17.3m = 17.31 → 17.3 (1

decimal place)

Significant Figures in Calculations

In calculations involving multiplication and division, the answer is rounded off to the number of significant figures in the least precise term (least number of sig. figs.) in the calculationsExample: 8.3m x 2.22m = 18.462 → 18mExample: 8432m ÷ 12.5 = 674.56 → 675m

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1-3: The Language of Physics

Main Objectives: Interpret data in tables and graphs, and

recognize equations that summarize dataCreate and identify different types of graphsManipulate algebraic equations to solve for

different variables

Organizing Data

Data can be organized in a variety of waysData is commonly organized in tables and

graphs which can be represented by equations that show the relationships between variables

Displaying Data - Graphing

An important step in analyzing data is to identify the independent variable (or manipulated variable) and the dependent variables (or responding variables). Independent variable – altered by the

experimenter; influence other variablesDependent variables – possibly change as a

result of changes in the independent variable.

Displaying Data - Graphing

See Figures 3.2 & 3.3 What is the independent variable? What

are the dependent variables?

What is the relationship between the independent variable and the dependent variables?

A Test of Galileo’s Hypothesis

Figure 3.2

A Test of Galileo’s Hypothesis

This graph can be summarized by the equation (change in position in m) = 4.9 x (time elapsed in s)2

or ∆y=4.9(∆t)2

Linear Relationships When there is a linear relationship

between two variables a graph of there relationship will be a straight line.

This relationship can be written as a linear equation → y = mx + bm is the slopeb is the y-intercept

Both are constants that can be found on the graph

Linear Relationships

Slope (m) – the ratio of vertical change (∆y) to horizontal change (∆x)

m = rise/run = ∆y / ∆x

y-intercept (b) – the point at which the line crosses the y-axis; it is the value of y when x is zero

Quadratic Relationships When a smooth line drawn through the data

points curves upward (not a straight line), the graphs are frequently parabolasThis indicates that the variables are related by

the equation: y = kxThis equation is one form of a quadratic

relationshipk is a constant that shows you how fast y

changes with x See Figure 3.3

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Inverse Relationships

Sometimes variables have an inverse relationship and form a hyperbola when graphed.

The general equation for an inverse relationship is xy = k or…

y = k(1/x) = kx-1

Manipulating Equations The way in which quantities/variables

relate to each other can be represented symbolically by an equation, as well as a graph.

Example: distance = speed x time

d = vt

You can use the rules of algebra to rearrange equations

Solve for v in the equation above

Solving Equations Using Algebra

When rearranging equations using algebra, any process that you do to one side of the equation you must do to the other side of the equationThe steps can be performed in any sequence,

but make sure you perform the same operations on both sides of the equation.

Solving Equations Using Algebra

Solve the following equations for x:ay/x = cb/s

y = mx + b

Units in Equations Most physical quantities have units and

numerical values When using quantities in equations you must

substitute the numerical value and the units Mathematical operations can be done on units

just as they can be done on numbers Make sure to use the same units for the same

type of measurement Example: If a problem involves length

measurements in meters (m) and centimeters (cm) convert them both to the same units

Units in Equations

Example: Solve for d using d = vt.

v = 11.0 m/s and t = 6.00 s