ii) Approximately how many inches in a meter? How many yards in a meter? ii) Approximately how many seconds in a year?

Transcription

1 Math Diagnostic Test and Giancoli Assignment AP Physics 1 and 2 AP Physics B Summer Assignment: Turn this in by the first Tuesday of the school year. All questions should be answered by reading the explanations, performing simple calculations, and by completing a modest amount of research using the Internet. Check out a text online through Bellevue West High School: Giancoli Physics this information can be found under AP Homework at Mrs. Elliott s Website. Read Physics: Giancoli Introduction - Chapter 1 Part 1 Scientific Measurement, Uncertainty and Units 1. Physics Units: In everyday life you use units all the time feet and inches for your height, miles for the distance you drove yesterday, pounds for your weight, minutes for the time left in class, dollars per hour for the pay at your job, years of your life. Scientists agreed some time ago on a single set of units called, Scientific International, so that when they calculated some result of a physical process, they could express that in the same units as any scientist anywhere in the world. 2. Fundamental Units: The fundamental or base units are meters for length, seconds for time, and kilograms for mass. They are independent of each other. Look up each unit, define it as a scientist would define it, and in terms of everyday units you use: a) Meter (abbreviated m ): i) Modern definition: ii) Approximately how many inches in a meter? How many yards in a meter? b) Second(abbreviated s ): i) Modern definition: ii) Approximately how many seconds in a year? c) Kilogram (abbreviated kg ): i) Modern definition: ii) Approximately what does a kilogram weigh in pounds? What is your mass in kilograms? iii) What is the difference between mass and weight?

2 iv) If you took a 1-kilogram lab weight to the Moon, would it still have the same mass as on Earth? Would it weigh the same on a fish scale? 3. Derived Units: Certain physics units are composed by combining fundamental units. What are the units for the following? a) Velocity or speed: (distance per time) b) Acceleration: (rate of change of velocity) c) Force: (you may have to search for Newton s second law) 4. Significant Digits: The instruments we measure things with have limits on their precision. For example, a meter stick can reasonably expected to measure to a precision of a millimeter, but not a micrometer. The smallest graduation on a meter stick is a millimeter. We can even estimate a length measurement to within perhaps a half of a millimeter, but that s about all. For a piece of metal that is actually m in length, the best we could do in measuring it with a meter stick is m, or if we were really careful, we could estimate m. All non-zero digits to the right of the highest order non-zero digit are significant. Zeroes to the right of the lowest order non-zero digit are significant only if there is a decimal point shown in the number. For example, there are two significant digits in 120, but three significant digits in 120., four significant digits in 120.0, and four significant digits in In multiplying or dividing numbers, the number of significant digits we can claim for the result is the smallest number of significant digits in the original numbers. In addition and subtraction, we cannot gain significance over the significance of the number with the largest magnitude. For example, = 114. Note that I rounded the sum up in the least significant digit. Record the following results to the appropriate number of significant digits, using scientific notation if that eases the task of writing the number: 75,000 x = x 567 = = 2.30 / 0.90 = = General rule: Don t worry too much about significant digits, unless you carry too few (like only one when you could have carried three) or too many (like all ten digits from your calculator display regardless of the precision of the inputs). In the first case, you lost significance, in the second case you wasted time writing down extra digits, and

3 you implied a greater degree of precision in a calculation than you actually have a right to. In general, I recommend you carry three significant digits in your calculations. Some physical constants are written to only two significant digits, leaving off a zero in the third digit. For example, the acceleration due to gravity at the Earth s surface is written as 9.8 m/s 2, but is actually 9.80 m/s 2 if we were to include the next digit in the actual measured value. The charge on an electron is commonly written 1.6 x C, but would be written 1.60 x C if we included the next digit of the actual measured value. Other constants and most measured values of variables will generally be given to three significant digits, hence my general rule above. 5. Scientific Notation: When numbers are very large or very small, it is easier to express them in scientific notation. For example, it is easier to express as 3.12x10 7 or to express as 8.86x10-9. Usually, in forming the scientific notation for a number, we put the decimal point after the first non-zero digit. It is okay to leave numbers as large as 1000 or as small as 0.001, but please do not make me count more than three powers of ten. The diameter of a hydrogen atom is about meters, but please write it 1x10-10 m. You already mastered scientific notation in math and chemistry. Please review the rules for forming and combining exponents. Convert the following numbers either to or from scientific notation: = = = 1.26 x 10 9 = x 10-4 = x 10-3 = 1.87 x 10 3 x 6.67 x 10 4 = (4.11 x 10 7 ) / (56.2 x 10-8 ) = 6. Prefixes: In many cases, the measure of something involves so many of some unit or such a small fraction of some unit that it is more convenient to use a prefix with that unit. For example, a millimeter is one-thousandth of a meter, and is a more convenient unit for measuring the diameter of a pencil lead. Please have a working knowledge of the following prefixes: Prefix Abbreviation Multiplier centi- c (e.g., centimeter = cm) 10-2 milli- m (e.g., millisecond = ms) 10-3 micro- µ (e.g., microfarad = µf) 10-6 nano- n (e.g., nanometer = nm) 10-9

4 pico- p (e.g., picocoulomb = pc) kilo- k (e.g., kilojoule = kj) 10 3 mega- M (e.g., megawatt = MW) 10 6 giga- G (e.g., gigavolt = GV) 10 9 Convert the following to or from their prefixed forms, using both standard and scientific notation. For example, volts (V) = 25 mv (millivolts) = 25 x 10-3 V, and 74 µc (microcoulombs) = C = 74 x 10-6 C : 1300 MW = W = W 550 nm (nanometers) = m = m F (farads) = nf = F 0.65 g (standard unit of mass for chemists) = kg (standard unit of mass for physicists) = kg 12.5 mj (millijoules) = J = J

5 21. Which of these lines has the largest slope? 22. Which (one or more) of these graphs represent(s) a direct proportion? 23. Which (one or more) of the graphs in question 2 represent(s) a linear function? 24. Which (one or more) of these graphs represent(s) the function y = ax 2, where a is any real nonzero number?

6 25. Which (one or more) of these graphs represent(s) the function x = 2t 2? 26. Calculate the distance on the graph from point (1,1) to point (5,3). Good sources of math review material is Hypermath.