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Chapter 1LectureOutline

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•Why Study Physics?

•Mathematics and Physics Speak

•Scientific Notation and Significant Figures

•Units

•Dimensional Analysis

•Problem Solving Techniques

•Approximations

•Graphs

Chapter 1: Introduction

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§1.1 Why Study Physics?

Physics is the foundation of every science (astronomy, biology, chemistry…).

Many pieces of technology and/or medical equipment and procedures are developed with the help of physicists.

Studying physics will help you develop good thinking skills, problem solving skills, and give you the background needed to differentiate between science and pseudoscience.

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Gain an appreciation for the simplicity of nature.

Physics encompasses all natural phenomena.

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§1.2 Physics Speak

Be aware that physicists have their own precise definitions of some words that are different from their common English language definitions.

Examples: speed and velocity are no longer synonyms; acceleration is a change of speed or direction.

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§1.3 Math

Galileo Wrote:

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one is wandering in a dark labyrinth.

From Opere Il Saggiatore p. 171 by Galileo Galilei (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Galileo.html)

Basically, the language spoken by physicists is mathematics.

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x is multiplied by the factor m.

The terms mx and b are added together.

bmxy

Definitions:

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x is multiplied by the factor 1/a or x is divided by the factor a. The terms x/a and c are added together.

ca

xy

Example:

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Percentages:

Example: You put $10,000 in a CD for one year. The APY is 3.05%. How much interest does the bank pay you at the end of the year?

305,10$0305.1000,10$

The bank pays you $305 in interest.

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Example: You have $5,000 invested in stock XYZ. It loses 6.4% of its value today. How much is your investment now worth?

680,4$936.0000,5$

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The general rule is to multiply by

1001

n

where the (+) is used if the quantity is increasing and (–) is used if the quantity is decreasing.

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Proportions:

BA

BA

1

A is proportional to B. The value of A is directly dependent on the value of B.

A is proportional to 1/B. The value of A is inversely dependent on the value of B.

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Example: For items at the grocery store:

weightcost

The more you buy, the more you pay. This is just the relationship between cost and weight.

To change from to = we need to know the proportionality constant.

(weight)pound)per (cost cost

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Example: The area of a circle is .2rA

The area is proportional to the radius squared.2rA

The proportionality constant is .

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Example: If you have one circle with a radius of 5.0 cm and a second circle with a radius of 3.0 cm, by what factor is the area of the first circle larger than the area of the second circle?

8.2cm 3

cm 52

2

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21

2

1 r

r

A

A

The area of a circle is proportional to r2:

The area of the first circle is 2.8 times larger than the second circle.

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§1.4 Scientific Notation & Significant Figures

This is a shorthand way of writing very large and/or very small numbers.

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Example: The radius of the sun is 700,000 km.

Write as 7.0105 km.

Example: The radius of a hydrogen atom is 0.0000000000529 m. This is more easily written as 5.2910-11 m.

When properly written this number will be between 1.0 and 10.0

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From the box on page 5:

1. Nonzero digits are always significant.

2. Final ending zeroes written to the right of the decimal are significant. (Example: 7.00.)

3. Zeroes that are placeholders are not significant. (Example: 700,000 versus 700,000.0.)

4. Zeroes written between digits are significant. (Example: 105,000; 150,000.)

Significant figures:

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Note: be sure not to round off any of your calculated results until you are reporting your final answer.

Please see text example 1.2 for more information on significant figures.

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§1.5 Units

Some of the standard SI unit prefixes and their respective powers of 10.

Prefix Power of 10 Prefix Power of 10

tera (T) 1012 centi (c) 10-2

giga (G) 109 milli (m) 10-3

mega (M) 106 micro () 10-6

kilo (k) 103 nano (n) 10-9

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Dimensions are basic types of quantities that can be measured or computed. Examples are length, time, mass, electric current, and temperature.

A unit is a standard amount of a dimensional quantity. There is a need for a system of units. SI units will be used throughout this class.

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The quantities in this column are based on an agreed upon standard.

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Example: The SI unit of energy is the joule.

1 joule = 1 kg m2/sec2

Derived unit Base units

A derived unit is composed of combinations of base units.

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Units can be freely converted from one to another. Examples:

12 inches = 1 foot

1 inch = 2.54 cm

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Example: The density of air is 1.3 kg/m3. Change the units to slugs/ft3.

1 slug = 14.59 kg

1 m = 3.28 feet

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3slugs/ft 105.2

feet 3.28

m 1

kg 14.59

slug 1

m

kg 3.1

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§1.6 Dimensional Analysis

Dimensions are basic types of quantities such as length [L]; time [T]; or mass [M].

The square brackets are referring to dimensions not units.

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Example (text problem 1.84): Use dimensional analysis to determine how the period of a pendulum depends on mass, the length of the pendulum, and the acceleration due to gravity (here the units are distance/time2).

Mass of the pendulum [M]

Length of the pendulum [L]

Acceleration of gravity [L/T2]

The period of a pendulum is how long it takes to complete 1 swing; the dimensions are time [T].

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[Period] = [T] =

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§1.7 Problem Solving Techniques

Summary of the list on page 13:

•Read the problem thoroughly.•Draw a picture.•Label the picture with the given information.•What is unknown?•What physical principles apply?•Are their multiple steps needed?•Work symbolically! It is easier to catch mistakes.•Calculate the end result. Don’t forget units!•Check your answer for reasonableness.

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§1.8 Approximations

All of the problems that we will do this semester will be an approximation of reality. We will use models of how things work to compute our desired results. The more effects we include, the more correct our results will be.

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Example (text problem 1.44): Estimate the number of times a human heart beats during its lifetime.

Estimate that a typical heart beats ~60 times per minute:

timebeats/life 104.2

lifetime 1

years 75

year 1

days 365

1day

hours 24

hour 1

minutes 60

minute 1

beats 60

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§1.9 Graphs

Experimenters vary a quantity (the independent variable) and measure another quantity (the dependent variable).

Dependent variable here

Independent variable here

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Be sure to label the axes with both the quantity and its unit. For example:

Position (meters)

Time (seconds)

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Example (text problem 1.49): A nurse recorded the values shown in the table for a patient’s temperature. Plot a graph of temperature versus time and find (a) the patient’s temperature at noon, (b) the slope of the graph, and (c) if you would expect the graph to follow the same trend over the next 12 hours? Explain.

Time Decimal time Temp (°F)

10:00 AM 10.0 100.00

10:30 AM 10.5 100.45

11:00 AM 11.0 100.90

11:30 AM 11.5 101.35

12:45 PM 12.75 102.48

The given data:

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99.5

100

100.5

101

101.5

102

102.5

103

10 11 12 13

time (hours)

tem

p (

F)

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(a)

(b)

(c)

Reading from the graph: 101.8 F.

F/hour 9.0hr 0.10hr 0.12

F 0.100F 8.101slope

12

12

tt

TT

No.

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Summary

•Math Skills

•The SI System of Units

•Dimensional Analysis