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# Study Guide Chapter 1 (For Midterm) PHYS 111

IUP

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This 5 page Study Guide was uploaded by Wilson on Monday October 5, 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 50 views. For similar materials see Physics I Lecture in Physics 2 at Indiana University of Pennsylvania.

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Date Created: 10/05/15

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 39l39 The time value hours can be crossed out because it is in the numerator and denominator o J L L We have proved the distance formula s units are correct Three Systems of Units 1 MKS SI 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 CGS 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 figs present 1 Ex 546432 miles 56432 x 104miles 0 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 scientific notation Significant Figures 0 Sig figs can be tricky There are however a defined set of rules that they always follow 1 All nonzero numbers 19 are always significant 2 All zeroes between nonzero numbers are always significant 3 All zeroes which are simultaneously to the right of the decimal point and at the end of the number are always significant 4 All zeroes which are to the left of a written decimal point and are in a number less than 10 are always significant 0 Let s look at some examples to clear things up These will go from easiest to hardest in terms of finding out the significant figures Please keep the rules above in mind 1 56732 5 sig figs none of these numbers are 0 They are all significant 2 5607032 7 sig figs the zeroes in this number are between nonzeroes This makes them significant 3 4300 2 sig figs these zeroes trail off and are not followed by a decimal They are not significant 4 00172 3 sig figs The two zeroes to the left of quot172 are not in front of the decimal and thus do not hold any significant However if we had a number 001720 there would be 4 sig figs 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 figs than the number with the least amount of sig figs in the equation 0 EX 25 X 25 625 63 I 25 has 2 sig figs so our answer must have 2 sig figs 0 Ex 30 x 1500 45 I Again we simplify for the lowest common denominator and our answer should have 2 sig figs 0 Addition and Subtraction 1 Instead of looking at the number of sig figs we observe the number of decimal places 0 EX 251 16 2526 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 CosG adjacenthypotenuse CAH bc 3 TanG oppositeadjacent TOA ab 0 Remember that we will be using the 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 define 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 2ncl type of vectors 0 Adding and Subtracting Vectors 1 Vectors are noted by a letter with an arrow over the top ie a 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 o If two vectors are equal they must be equal in magnitude and direction 0 Note the picture to the right gt realize that b has the angle of 1 plus 180 o Realize that vectors form triangles and that you can apply trigonometric functions to these remember sin cos tan 0 Below please find 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 modifications of the Pythagorean Theorem and the sin cos and tan formulas that have been mentioned previously

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