Chapter 1 Study Guide (For Midterm)
Chapter 1 Study Guide (For Midterm) PHYS 111
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This 5 page Study Guide was uploaded by Wilson on Tuesday October 6, 2015. The Study Guide belongs to PHYS 111 at Indiana University of Pennsylvania taught by Dr. Haija in Summer 2015. Since its upload, it has received 376 views. For similar materials see Physics I Lecture in Physics 2 at Indiana University of Pennsylvania.
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Date Created: 10/06/15
Study Guide for Exam 1 PHYS 111 Chapter 1 Vectors Kinematics Sig Figs Trigonometric Functions Overview of Ch 1 Dimensions systems of units and powers of ten This chapter focuses on unit conversion as well as identifying how to multiply two units to produce a third Most of it is algebra along with a dose of problem solving Let s begin 0 Realize that there are many physical quantities The main three that we focus on are 1 Length m km cm yards feet 2 Mass lb N kg 3 Time sec milliseconds minutes 0 Time is standard across all systems Length and mass change based on a few systems be prepared to identify and convert based on this Consistency issues ie Distance velocity X time o 60 miles 20 mileshour X 3 hours 0 L L 39l39 X T The time value hours can be crossed out because it is in the numerator and denominator o I L L We have proved the distance formula s units are correct Three Systems of Units 1 MKS Sl system this is the international system and the one that we will primarily be using for mathematical equations It uses the units 0 Distance meters 0 Time seconds 0 Mass kg 0 Any units that vary from these need to be converted 2 C65 System centimeters grams seconds 3 Engineering System British System feet lbs second Powers of 10 0 Powers of ten is a way of representing either quite large or quite small numbers It can also be used to manipulate the number of sig gs present 1 EX 546432 miles 56432 X 104miles Notice that the decimal point moved four places to the left Therefore the power is 104 2 EX 00315 315 X 10393 0 Notice that the decimal point moved three places to the right Therefore the power is 10393 0 Also notice that there is one number before the decimal when we write numbers in this notation This notation is called scienti c notation Signi cant Figures 0 Sig gs can be tricky There are however a de ned set of rules that they always follow JUNl l 4 All nonzero numbers 19 are always signi cant All zeroes between nonzero numbers are always signi cant All zeroes which are simultaneously to the right of the decimal point and at the end of the number are always signi cant All zeroes which are to the left of a written decimal point and are in a number less than 10 are always signi cant 0 Let s look at some examples to clear things up These will go from easiest to hardest in terms of nding out the signi cant gures Please keep the rules above in mind 1 2 3 4 56732 5 sig gs none ofthese numbers are 0 They are all signi cant 5607032 7 sig gs the zeroes in this number are between nonzeroes This makes them signi cant 4300 2 sig gs these zeroes trail off and are not followed by a decimal They are not signi cant 00172 3 sig gs The two zeroes to the left of quot172 are not in front of the decimal and thus do not hold any signi cant However if we had a number 001720 there would be 4 sig gs because the trailing zero is after a decimal point 0 In Multiplication and Division 0 For multiplication and division know that your answer cannot have more sig gs than the number with the least amount of sig gs in the equation 0 EX 25 X 25 625 gtgt 63 25 has 2 sig gs so our answer must have 2 sig gs 0 EX 30 X 1500 45 Again we simplify for the lowest common denominator and our answer should have 2 sig gs 0 Addition and Subtraction 1 Instead of looking at the number of sig gs we observe the number of decimal places 0 Ex 251 16 2526 gtgt 253 0 There are no decimal places because one of our numbers being added has no decimal places 0 Again you always go by the number that has the fewest numbers after the decimal place This is because of the resolution of the numbers being used you cannot assume 251 actually means 2510000 It could be 2513 or 25109 or any other number Trigonometry 3 main functions Remember SOH CAH TOA o Trigonometry is the study of triangles We are visiting it to determine distances and angles These will later be used to add and subtract vectors 1 Sine oppositehypotenuse SOH ac 2 C056 adjacenthypotenuse CAH WC 3 Tane oppositeadjacent TOA ab 0 Remember that we will be using the A Cartesian plane 0 We will be working in 2D space with directions such as North West etc o In class the above three functions were converted to be in terms of x x is the given distance of a vector 0 Please look to the example below for how to use the Pythagorean Theorem and the trigonometric functions described earlier Remember that X and y are two coordinate components that de ne any position in the Xy plane The angle is always measured from the positive Xaxis o The X and y coordinates are independent of one another Knowing one does not give you enough information to predict the other Vectors o Vectors are physical quantities that may have direction and a value velocity displacement volume etc and other quantities have to be described by their value and direction 0 There are primarily 2 types 1 Scalars such as mass and time 2 Vectors such as velocity and force 0 We will mostly focus on the 2nOI type of vectors 0 Adding and Subtracting Vectors 1 Vectors are noted by a letter with an arrow over the top ie 6391 2 Vectors are depicted in terms of tail and head 0 Negative vectors will simply be the opposite direction with the same value o If a vector is multiplied by a number its direction stays the same so long as the number isn t negative and the force is multiplied by this number E r MW 2 o If two vectors are equal they must be equal in magnitude and direction 0 Note the picture to the right realize that b has the angle of 19 plus 180 o Realize that vectors form triangles and that you can apply trigonometric functions to these remember sin cos tan 0 Below please nd an application problem for the theoretical values posed above In depth equations include the by components method for the x and y axis I ve done an example problem below This is combining the concepts we have learned previously about angles and magnitudes o The formulas you should take away are included in the problem they are modi cations of the Pythagorean Theorem and the sin cos and tan formulas that have been mentioned previously
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