Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Why Study Physics? Mathematics and Physics Speak Scientific Notation and Significant Figures Units Dimensional Analysis Problem Solving Techniques Approximations Graphs Chapter 1: Introduction

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Gain an appreciation for the simplicity of nature. Physics encompasses all natural phenomena.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §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 ( and.ac.uk/~history/Mathematicians/Galileo.html) Basically, the language spoken by physicists is mathematics.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. x is multiplied by the factor m. The terms mx and b are added together. Definitions:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 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. Example:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 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? The bank pays you $305 in interest.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example: You have $5,000 invested in stock XYZ. It loses 6.4% of its value today. How much is your investment now worth?

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. The general rule is to multiply by where the (+) is used if the quantity is increasing and (–) is used if the quantity is decreasing.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Proportions: 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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example: For items at the grocery store: 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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example: The area of a circle is The area is proportional to the radius squared. The proportionality constant is .

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §1.4 Scientific Notation & Significant Figures This is a shorthand way of writing very large and/or very small numbers.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example: The radius of the sun is 700,000 km. Write as 7.0  10 5 km. Example: The radius of a hydrogen atom is m. This is more easily written as 5.29  m. When properly written this number will be between 1.0 and 10.0

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. From the “purple 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:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Note: be sure not to round off any of your results until you are reporting your final answer. Please see text example 1.2 for more information on significant figures.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §1.5 Units Some of the standard SI unit prefixes and their respective powers of 10. PrefixPower of 10PrefixPower of 10 tera (T)10 12 centi (c)10 -2 giga (G)10 9 milli (m)10 -3 mega (M)10 6 micro (  ) kilo (k)10 3 nano (n)10 -9

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. 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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. The quantities in this column are based on an agreed upon standard.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example: The SI unit of energy is the joule. 1 joule = 1 kg m 2 /sec 2 Derived unit Base units A derived unit is composed of combinations of base units.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Units can be freely converted from one to another. Examples: 12 inches = 1 foot 1 inch = 2.54 cm

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example: The density of air is 1.3 kg/m 3. Change the units to slugs/ft 3. 1 slug = kg 1 m = 3.28 feet

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example (text problem 1.74): 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/time 2 ). Mass of the pendulum [M] Length of the pendulum [L] Acceleration of gravity [L/T 2 ] The period of a pendulum is how long it takes to complete 1 swing; the dimensions are time [T].

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. [Period] = [T] =

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §1.7 Problem Solving Techniques Summary of the list on page 12: 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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §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.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example (text problem 1.34): Estimate the number of times a human heart beats during its lifetime. Estimate that a typical heart beats ~60 times per minute:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. §1.9 Graphs Experimenters vary a quantity (the independent variable) and measure another quantity (the dependent variable). Dependent variable here Independent variable here

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Be sure to label the axes with both the quantity and its unit. For example: Position (meters) Time (seconds)

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Example (text problem 1.39): 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. TimeDecimal timeTemp (°F) 10:00 AM :30 AM :00 AM :30 AM :45 PM The given data:

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. (a) (b) (c) Reading from the graph:  F. No.

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Summary Math Skills The SI System of Units Dimensional Analysis

Fisica Generale - Alan Giambattista, Betty McCarty Richardson Copyright © 2008 – The McGraw-Hill Companies s.r.l. Clicker Question for after slide 13: If you have one circle with a radius of 5 cm and a second circle with a radius of 3 cm, by what factor is the area of the first circle larger than the area of the second circle? (Use the fact that A  r 2.) A.0.60 B.1.67 C.2.78 D.8.73