Introduction Physics is the science that seeks to explain how the universe works. Physicists create theories to explain their observations of nature. These theories must make testable predictions. If the predictions prove false, the theory is modified or discarded. In this manner, physics evolves toward truth. Door Meten Tot Weten Kammerlingh Onnes, a low temperature physicist from Holland, proposed that this phrase (meaning through measurement to knowledge) be inscribed above the door of all physics labs. Every measurement has some uncertainty about it and is made relative to some standard or unit. When we measure the diameter of a CD with a vernier caliper to the nearest tenth of a millimeter, we report the observation as (12.00 0.01) cm. Note the number of decimal places in the measurement and stated uncertainty must agree. When the uncertainty in the final digit is one, this is often simply written 12.00 cm. We indicate the precision of the measurement by the number of significant figures recorded. An excellent reference for this topic is the Purdue web site http://www.physics.purdue.edu/phys152l/MA1/. We will always estimate our measurements to the nearest tenth of the smallest calibration of our measuring instrument. This estimated digit, uncertain by one, will be the final digit in our recorded measurement. Significant Figures Rules have been developed for using significant figures in measurements and in values calculated from measurements. These rules allow the uncertainty in a measurement or calculated quantity to be correctly reported. Rule 1: In numbers that do not contain zeros, all the digits are significant. Example: 3.14 has 3 significant figures. Rule 2: All zeros between significant digits are significant. Example: 1002.5 and 6.0004 each have five significant figures. Rule 3: Zeros to the left of the first nonzero digit are not significant. Example: 0.006 has only one significant figure. Rule 4: Zeros to the right of the last nonzero decimal place digit are significant. Example: 5.300 has four significant figures. Rule 5: Zeros to the right of the last nonzero digit in a number with no decimal point are not significant unless specially marked. Example: 3,600,000 has only 2 significant figures. To avoid confusion, express numbers in scientific notation. All digits are significant when expressed this way. Example: 3.6 X 104 has 2 significant figures and 4.00 X 106 has 3 significant figures. Constants in formulas like 2 in v = (2ax) are assumed to have an infinite number of significant figures. Addition and Subtraction The answer should be rounded to have no digits beyond the last digit position common to all the numbers being added or subtracted. Example: 15 + 34.2 + 0.0003 = 49.2003 on a calculator but we must round the answer to 49 as the first measurement was uncertain in the units position. Multiplication and Division The answer should be rounded to have the same number of significant digits as the least precise factor in the calculation. Example: 15 X 0.6 = 9.0 on a calculator but must be written as 9 (since 0.6 has one significant figure). Powers and Roots The answer has as many significant figures as the original number. Example: 5.002 = 25.0 Rounding We will follow the usual convention that in rounding a number with nonzero digits to the right of the place to which we are rounding, we round up if the first digit to be dropped is five or greater. SI Units We will use the International System of units in this course. An excellent resource for this topic is http://physics.nist.gov/cuu/Units/index.html. There are seven basic standard units in this system. The meter (m) is the standard of length, the kilogram (kg) the standard of mass, the second (s) the standard of time, the ampere (A) the standard of electrical current, the kelvin (K) the standard of temperature, the mole (mol) the standard of quantity, and the candela (cd) the standard of luminous intensity. All other units (velocity, in m/s for example) are defined in terms of theses basic units. Multiples of the base units are expressed using metric prefixes. For example, 1000 m = 1 kilometer = 1 km. A table of the metric prefixes is given below. Table of Metric Prefixes yotta zetta exa peta tera giga mega kilo hecto deka 1024 1021 1018 1015 1012 1012 109 103 102 101 Y Z E P T G M k h da yecto zepto atto femto pico nano micro milli centi deci 10-24 10-21 10-18 10-15 10-12 10-9 10-6 10-3 10-2 10-1 y z a f p n m c d Problem Solving We will solve a variety of story problems in this course. You should read the whole problem first. Write what you are asked to find (in words and symbols). Write what you are given (use the correct symbols and units). Find appropriate formulas. Solve algebraically for the required quantity. Make an order of magnitude estimate of the answer. Carry out the numerical part of the calculation, keeping one or two extra digits during the calculation but rounding your answer to the correct number of significant figures. Do not forget to include units in your calculation and answer. Factor - Label Use the factor-label method to convert and calculate with units. Treat the units as if you were working with numerical fractions. 25 cm X (1 m / 100 cm) = 0.25 m Order of Magnitude Estimates Round quantities to the nearest power of 10 and use the laws of exponents to estimate the magnitude of an answer. This may catch errors made entering numbers into a calculator. Math Review Physics expresses its laws in the language of mathematics. It is assumed that students in this course have completed second year algebra. We will review math topics as needed throughout the course. Appendix A of our text has a comprehensive review of the math we will need. Also see http://physics.nist.gov/cuu/Units/index.html and http://www.sisweb.com/math/tables.htm. Useful Symbols and Constants Our textbook contains math tables, a periodic table, and tables of selected constants. This material may also be found at the math sites listed above, http://www.webelements.com/, and http://physics.nist.gov/cuu/Constants/index.html. Greek characters, in addition to the familiar Roman characters, are used to represent the many quantities in physics formulas. The Greek alphabet is shown below. alpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu nu xi omicron pi rho sigma tau upsilon phi chi psi omega Each student on the first day of class receives a textbook (Physics, Principles with Applications, Fifth Edition by Giancoli), an Interactive Physics Player Workbook with computer disk for home use, and one copy each of the class rules and regulations, lab safety rules, and computer network use agreement. Be sure to sign your name in the text and workbook.

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