Serway AP Physics. Chapter 1

Transcription

1 Serway AP Physics Chapter Units must be defined to for measuring quantities. Units such as kg, m and sec are common in physics. The fundamental units are length (m), mass (Kg), and time (sec) which is from the 1960 Systeme International. Length- During the construction of the pyramids, a handy measuring device was used-the cubit. It was the length from a man's elbow to the farthest point of the fingers. Amazing the pyramids were built at all. By 1799 meter was ordained the standard length, originally defined as 1/ the distance from equator to north pole along the prime meridian. It was made out of a platinum iridium bar housed under controlled environmental conditions. But if the bar had to be moved, just touching it could affect its measurement, as well as temperature changes affecting its length and volume. The 1960 standard is wavelengths of orange-red light from krypton-86. Currently it is distance traveled by light in one second in a vacuum during time interval 1/ s. There were 29 platinum-iridium meters constructed of which the US holds #27. The meter comes from the greek word metron (to measure). Mass-Weight was initially the value of an absolute volume of pure water where 1g=1/100m 3. Weight varies by location around the world as discovered accident in 1671 with J. Richer's water clock that ran slow 2.5 minutes per day in Africa as compared to Europe. Therefore it was important to recognize that mass would never change in the universe, and that weight varied according to force impressed upon it. The kilogram was born in It is roughly the size of a shot glass. 39 mm tall, and 39 mm in diameter. The US has #20 and a duplicate #4 at NIST. They have only made the trip to Paris 4 times in 100 years. SI unit for mass is the kilogram. It is housed at Sevres France at the International Bureau of Weights and Measures. Fig 1.1 pg 2. Weight- was initially the value of an absolute volume of pure water where 1g=1/100m 3. Weight varies by location around the world as discovered accident in 1671 with J. Richer's water clock that ran slow 2.5 minutes per day in Africa as compared to Europe. Mass- it was important to recognize that mass would never change in the universe, and that weight varied according to force impressed upon it. The kilogram was born in It is roughly the size of a shot glass. 39 mm tall, and 39 mm in diameter. The US has #20 and a duplicate #4 at NIST. They have only made the trip to Paris 4 times in 100 years. Time-3000 years ago the Egyptians divided day and night into 12hrs each The Babylonians had 60 as a base in their arithmetic, and sometime during the 14 th century with the development of the mechanical clock, broke hours into 60 minutes, 60 minutes into 60 seconds. By 1656 Christian Huygens developed a pendulum accurate to 10s/day. By 1967 the second was defined 9,192,631,770 vibrations of Cs-133. Earth is gradually slowing as it spins. As gravity drops, time moves faster like Colorado clocks running 15 ns faster than Paris. Other systems use similar units. Gaussian is the cgs (centimeter, gram, second) Us Customary (foot, slug, second)

2 Table 1.4 illustrates some common prefixes used in physics. A List of the Metric Prefixes Multiplier Prefix Symbol Numerical Exponential yotta Y 1,000,000,000,000,000,000,000, zetta Z 1,000,000,000,000,000,000, exa E 1,000,000,000,000,000, peta P 1,000,000,000,000, tera T 1,000,000,000, giga G 1,000,000, mega M 1,000, kilo k 1, hecto h deca da no prefix means: deci d centi c milli m micro nano n pico p femto f atto a zepto z yocto y Dimensional Analysis When multiplying numbers and units, the left side of the equation must equal the right. A x t is the same as t x A. xa/t= a=x/t. Etc.See table 1.5 pg Uncertainty In mathematical operations involving significant figures, the answer is reported in such a way that it

3 reflects the reliability of the least precise operation. Let's state that another way: a chain is no stronger than its weakest link. An answer is no more precise that the least precise number used to get the answer. Let's do it one more time: imagine a team race where you and your team must finish together. Who dictates the speed of the team? Of course, the slowest member of the team. Your answer cannot be MORE precise than the least precise measurement. The following rule applies for multiplication and division: The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer. This means you MUST know how to recognize significant figures in order to use this rule. Example #1: 2.5 x The answer to this problem would be 8.6 (which was rounded from the calculator reading of 8.55). Why? 2.5 has two significant figures while 3.42 has three. Two significant figures is less precise than three, so the answer has two significant figures. Example #2: How many significant figures will the answer to 3.10 x have? You may have said two. This is too few. A common error is for the student to look at a number like 3.10 and think it has two significant figures. The zero in the hundedth's place is not recognized as significant when, in fact, it is has three significant figures. Three is the correct answer has three significant figures. Note that the zero in the tenth's place is considered significant. All trailing zeros in the decimal portion are considered significant. Another common error is for the student to think that 14 and 14.0 are the same thing. THEY ARE NOT is ten times more precise than 14. The two numbers have the same value, but they convey different meanings about how trustworthy they are.

4 Four is also an incorrect answer given by some. It is too many significant figures. One possible reason for this answer lies in the number This number has four significant figures while 3.10 has three. Somehow, the student (YOU!) maybe got the idea that it is the GREATEST number of significant figures in the problem that dictates the answer. It is the LEAST. Sometimes student will answer this with five. Most likely you responded with this answer because it says on your calculator. This answer would have been correct in your math class because mathematics does not have the significant figure concept. Example #3: 2.33 x x 2.1. How many significant figures in the answer? Answer - two. Which number decides this? Answer - the 2.1. Why? It has the least number of significant figures in the problem. It is, therefore, the least precise measurement. Example #4: (4.52 x 10 4) (3.980 x 10 6). How many significant figures in the answer? Answer - three. Which number decides this? Answer - the 4.52 x Why?

5 It has the least number of significant figures in the problem. It is, therefore, the least precise measurement. Notice it is the 4.52 portion that plays the role of determining significant figures; the exponential portion plays no role.math With Significant Figures Addition and Subtraction In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. Let's state that another way: a chain is no stronger than its weakest link. An answer is no more precise that the least precise number used to get the answer. Let's do it one more time: imagine a team race where you and your team must finish together. Who dictates the speed of the team? Of course, the slowest member of the team. Your answer cannot be MORE precise than the least precise measurement. For addition and subtraction, look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do: 1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the left of the decimal place are not used to determine the number of decimal places in the final answer.) 2) Add or subtract in the normal fashion. 3) Round the answer to the LEAST number of places in the decimal portion of any number in the problem. WARNING: the rules for add/subtract are different from multiply/divide. A very common student error is to swap the two sets of rules. Another common error is to use just one rule for both types of operations. ROUNDING Rounding of significant figures carries a certain degree of controversy and people will argue with you based on what they were taught at some point in their education. For example I learned from my chemistry course in college that when rounding a number that is followed by a 5, for example , one should round up to the even number, 1.12 or not round up if the number was already even. More recently I have been told from statisticians that I respect that this procedure removes the rounding bias.

6 They explain that without bias half of the time the number is rounded up. Others always round up in this situation regardless of whether the number is even or odd. My position on this subject is use the even odd rule. Another painful detail that can cause controversy is that if the number following the 5 is not a zero, for example , the number should be rounded up. Examples: A) rounded to four significant figures is B) rounded to four significant figures is C) rounded to four significant figures is D) rounded to four significant figures is