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# Week 1 Notes 47136

UCI

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This 7 page Class Notes was uploaded by Emily Provenzano on Saturday October 3, 2015. The Class Notes belongs to 47136 at University of California - Irvine taught by TUCKER, L. in Summer 2015. Since its upload, it has received 11 views. For similar materials see BASIC PHYSICS I in Physics 2 at University of California - Irvine.

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Date Created: 10/03/15

Chapter 1 Physics Fundamentals How Physicists Think They make observations and use those observations to generate theories and use those theories to make predictions Significant Figures In a measurement one number is always the weakest link Decisions on where to cut off the measurement depends on how many significant figures or significant digits sd are pertinent to the precision of the original measurement Multiplication Division The number of significant digits in the answer is the number of significant digits in the number in the multiplication division that has the least significant digits is the least precise EXAMPLE 1678 35 1678 has 45d 35 has 25d 25d lt 43d so the answer has 25d because that is the smaller number So although the quotactualquot answer is 1678 35 5873 it has to be cut off after two significant digits and the last one is rounded So the answer is 59 Addition Subtraction The number of decimal places in the answer is the number of decimal places in the number in the multiplication division that has the least decimal places is the least precise EXAMPLE 10626 952 10626 has 3 numbers after the decimal place 952 has only 1 number after the decimal place So 952 will be the quotlimiting reagentquot to use chemistry terms or because it has the lower amount of numbers after the decimal place that determines the number the answer should have It is important to note here that 952 has 35d and the answer has 45d This is okay because the answer is determined by number of decimal places not by number of significant digits Exact Numbers exact numbers are those that are given exact quantity and don t limit the measurement For example if you are told to double 8353 then the answer would be 16706 Even though this is actually the calculation 2 8353 and 2 has only 15d it is an exact number so it s number of significant digits is not counted in defining the answer EXAMPLE How many significant figures are in the answer to the following expression Assume that 7quot is an exact number 7 201 953 EXPLANATION By orders of operation you do the multiplication first so you do 7 201 1402 DO NOT DO SIG FIGS OR ROUND UNTIL THE END Then you add the 140 1402 to the 953 Since 953 has less numbers after the decimal 95 3 places then 1402 does it limits the number in the final answer 1093 If counted the number of significant figures in the answer is 4sd How is this possible if the numbers in the problem have either K 1093 1sd or 3sd ADDITIONAL EXCERCISES How many significant figures are in the following numbers 1 900 2 10500 3 40 4 300 5 1000000001 ANSWERS 11 23 32 4 3 510 Uncertainty Uncertainty limit of how precise you can take a measurement Make sure that the number has the same amount of decimal places as the uncertainty i uncertainty units EXAMPLE 84 i 02cm EQUATION Uncertainty uncertaintymeasurement X 100 EXAMPLE 84 i 02cm O 2 Note that the answer has only 1sd because 02 only 39 X 100 238 has 15d 84 c Sm Precise Language It s good to note that physicists use very precise language and so the word choice used has been thought out and means exactly what it says Read questions very carefully on tests and quizzes to make sure you catch things Order of Magnitude Orders of magnitude only have one significant figure EXAMPLE Orders of magnitude of the number of minutes in a year 106 107 500000 are all good answers because they have only 1sd Dimensional Analysis Three major base units of mechanics 1 Length 2 Time 3h4ass Base Unit Variable Units of SI Unit Length L L m Time t t 5 Mass m m kg EXAMPLE I represents the ow of particles per area time I1L2 t n represents concentration of particles n 1L3 x represents distance F L What are the units of D in DAnAx EXPLANATION The negative sign does not effect the units so that can be taken out and that makes the equation DAnAx Changes in quantities Asomething have the same units as the quantities themselves so those can be taken out which leaves I Dn X Then if you substitute in the above equations for n and x you get 1L2tD 1L3DL Then you solve for D and get D LZt and in SI units that equates to mZs Dimensional analysis can only determine if a relationship is wrong the units can be correct and the answer may still be wrong RANDOM OTHER UNRELATED EXAMPLE If speed is doubled in the following equation what is the effect on d assume acceleration stays constant dspeed22accelerationD ds22a normally but if speed is doubled then dZs22a 4sZZa 4 sZZa so compared to the original equation the doubled equation is 4 times it So the answer is If you double speed in the equation d goes up by a factor of 4 Displacement Displacement is a change in position If a person starts at Point A and travels all around and ends up at Point B the displacement between the two points is the length of a line drawn straight from Point A to Point B ignoring the path actually taken Vectors vs Scalars Scalar is a number with magnitude but no direction For example the number 5 a speed of 100mph the number of cats you own and 200F are all scalars Vectors have both direction and magnitude For example 5 miles to the east and 8 Newtons to the right are both examples of vectors Vector Addition Vectors are drawn as arrows The side with the arrowhead is called the quottipquot and the side without the head is called the quottailquot TiptoTail Method When arrows are lined up so that the tip of one arrow aligns with the tail of another you can draw another vector from the tail of the first one to the tip of the last one and this line is called the resultant vector and represents Resultant the displacement between the two vectors Vector The resultant vector is shown here in red Subtracting Vectors Subtracting vectors is the same thing as adding negative vectors A negative vector has the same magnitude as the positive version with the opposite direction EXAMPLE E F G H What does vector H look like EFV EXPLANATION Using the tip to tail method the first thing to do is put E and F tip to tail F E Then G needs to be ipped to become a negative vector and added to the end F G E ANSWER Then you draw a vector from the tail of E to the tip of G F G E Component Vectors Component vectors are two vectors one parallel to the X axis and one parallel to the y axis that add to crate the desired resultant vector The vectors don t have to be on the axis just parallel to either the y or x axis and therefore should create a 90 angle between them EXAMPLE The vector A is made up of the addition of the component vectors AX and Ay AX is parallel to the x axis and Ay is parallel to the y axis Overall A AX Ay A A X A V V Unit Vectors Unit vectors are vectors with a length of 1unit They add up to create component vectors This is a good way to find a resultant vector because you can add up the units in the x component and y components to get the component vectors of the resultant vector you want The x components are represented by an i with a hat and the y components are represented by a j with a hat EXAMPLE E e If E has an X component of 3 and a y component of 2 F has an X component of 2 and a y component of 0 G has an X component of 3 and a y component of 2 F What are the components of the red resultant vector EXPLANATION First ip the signs of both of the components of the G vector to make it negative Then add the X components and separately add the y components ANSWER i 8 j 4 Position displacement one dimension These graphs plot position X vs time t where position is on the y aXis and time is on the X EXAMPLE This graph shows starting at position 4 moving to position 1 at a strolling pace and staying there for awhile and then running to position 3 A 4 21V A V V Instantaneous Velocity Instantaneous velocity is the velocity of an object in an infinitely small amount of time A positionA time V ArAt ms positive velocity moves in a positive direction and negative velocity moves in a negative direction Average velocity Average velocity takes into account the beginning and ending location and it is the change in position over that allotted amount of time Therefore if you start at point A run 100 miles in 100 minutes and end at point A your average velocity is still Omph Speed Speed is the magnitude of velocity and it is always positive Make sure you know on a velocity versus time graph that points with a negative velocity at a higher magnitude are still quotfasterquot than those of a lower negative magnitude because speed doesn t have a direction

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