Chapter 1 Lecture Outline Chapter 1: Introduction §1.1 Why Study Physics
Flood, Michelle, Features Writer has reference to this Academic Journal, PHwiki organized this Journal Copyright © The McGraw-Hill Companies, Inc. Permission required as long as reproduction or display. Chapter 1 Lecture Outline Why Study Physics Mathematics in addition to Physics Speak Scientific Notation in addition to Significant Figures Units Dimensional Analysis Problem Solving Techniques Approximations Graphs Chapter 1: Introduction §1.1 Why Study Physics Physics is the foundation of every science (astronomy, biology, chemistry ). Many pieces of technology in addition to /or medical equipment in addition to procedures are developed with the help of physicists. Studying physics will help you develop good thinking skills, problem solving skills, in addition to give you the background needed to differentiate between science in addition to pseudoscience.
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Gain an appreciation as long as the simplicity of nature. Physics encompasses all natural phenomena. §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 in addition to velocity are no longer synonyms; acceleration is a change of speed or direction. §1.3 Math Galileo Wrote: Philosophy is written in this gr in addition to book, the universe, which st in addition to s continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language in addition to read the characters in which it is written. It is written in the language of mathematics, in addition to its characters are triangles, circles, in addition to other geometric figures without which it is humanly impossible to underst in addition to a single word of it; without these, one is w in addition to ering in a dark labyrinth. From Opere Il Saggiatore p. 171 by Galileo Galilei (http://www-gap.dcs.st- in addition to .ac.uk/~history/Mathematicians/Galileo.html) Basically, the language spoken by physicists is mathematics.
x is multiplied by the factor m. The terms mx in addition to b are added together. Definitions: x is multiplied by the factor 1/a or x is divided by the factor a. The terms x/a in addition to c are added together. Example: Percentages: Example: You put $10,000 in a CD as long as 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.
Example: You have $5,000 invested in stock XYZ. It loses 6.4% of its value today. How much is your investment now worth The general rule is to multiply by where the (+) is used if the quantity is increasing in addition to () is used if the quantity is decreasing. 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.
Example: For items at the grocery store: The more you buy, the more you pay. This is just the relationship between cost in addition to weight. To change from to = we need to know the proportionality constant. Example: The area of a circle is The area is proportional to the radius squared. The proportionality constant is . Example: If you have one circle with a radius of 5.0 cm in addition to 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 The area of a circle is proportional to r2: The area of the first circle is 2.8 times larger than the second circle.
Example 1.1, p 4 Effect of Increasing Radius on the Volume of a Sphere The volume of a sphere is given by the equation V = 4/3 pr3, where V is the volume in addition to r is the radius of the sphere. If a basketball has a radius of 12.4 cm in addition to a tennis ball has a radius of 3.20 cm, by what factor is the volume of the basketball larger that the tennis ball Practice Problem 1.1 Power Dissipated by a Lightbulb The electric power P dissipated by a lightbulb of resistance R is P = V2/R, where V represents the line voltage. During a brownout, the line voltage is 10.0% less than its normal value. How much power is drawn by a lightbulb during the brownout if it normally draws 100.0 W (watts). Assume that the resistance doesnt change.
Follow up problem A spherical balloon is partially blown up in addition to its surface area is measured. More air is then added, increasing the volume of the balloon. If the surface area of the balloon exp in addition to s be a factor of 2.0 during this procedure, by what factor does the radius of the balloon change
Strategy Relate the surface area S to the radius r using Solution Find the ratio of the new radius to the old. The radius of the balloon increases by a factor of 1.4. Assignment 1 p. 19 2, 5, 6, in addition to 9. §1.4 Scientific Notation & Significant Figures This is a shorth in addition to way of writing very large in addition to /or very small numbers.
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 in addition to 10.0 From the box on page 5: Nonzero digits are always significant. Final ending zeroes written to the right of the decimal are significant. (Example: 7.00.) Zeroes that are placeholders are not significant. (Example: 700,000 versus 700,000.0.) Zeroes written between digits are significant. (Example: 105,000; 150,000.) Significant figures: Example 1.2 For each of these values, identify the number of significant figures in addition to rewrite each in its st in addition to ard scientific notation. 409.8 s 0.058700 cm 9500 g 950.0 x 101 mL
Practice Problem 1.2 State the number of significant figures in each of these measurements in addition to rewrite them in st in addition to ard scientific notation. 0.00010544 kg 0.005800 cm 60200 s Significant Figures in Calculations When two or more quantities are added or subtracted, the result is as precise as the least precise of the quantities. If the quantities are written in scientific notation with different powers of ten, first rewrite them with the same power of ten. After adding or subtracting, round the result, keeping only as many decimal places as are significant in all of the quantities that were added or subtracted. When quantities are multiplied or divided, the result has the same number of significant figures as the quantity with the smallest number of significant figures. In a series of calculations, rounding to the correct number of significant figures should only be done at the end, not at each step. Rounding at each step would increase the chance that roundoff error could snowball in addition to have an adverse effect on the accuracy of the final answer. Its a good idea to keep at least two extra significant figures in calculations, then round at the end. Example in addition to Practice Problem 1.3 Significant Figures in Addition. Calculate the sum 44.56005 s + 0.0698 s + 1103.2 s. Significant Figures in Subtraction. Calculate the difference 568.42 m 3.924 m in addition to write the result in scientific notation. How many significant figures are in the result
Summary Math Skills The SI System of Units Dimensional Analysis
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