General Physics 1.pdf

General Physics 1 c. Trailing zeros may or may not L1: Units, Physical Quantities, count when there is no demical Measurement, Graphical Presentation...

General Physics 1 c. Trailing zeros may or may not L1: Units, Physical Quantities, count when there is no demical Measurement, Graphical Presentation point Physical Quantities - numbers used d. Leading zeros don’t count to describe a physical phenomenon TYPES OF UNIT CONVERSION: quantitatively 1. Straightforward linear Nature of Physical Qualities: conversion - direct conversion 1. Fundamental Qualities - exist from 1 unit to another by themselves (mass, time, 2. Chain Conversion - multiplied length, temperature) in fractions (numerator: unit to 2. Derived Quantities - quantities convert into; denominator: unit dependent on other quantities to be converted) (area, speed, density) L2: Measurement Types of Physical Quantities: - Needed to formulate new A. Scalar Quantity - quantities concepts, theories, or laws, and with magnitude only (mass, verify existing ones distance, speed, energy) - Process of comparing an Unit Conversion - when units are not B. Vector Quantities - with unknown quantity to a standard consistent, converting to appropriate magnitude and direction quantity of the same physical ones is needed (velocity, acceleration, force) dimension Significant Figures - used to report Systeme Inernationale (SI) - universal - Process of assigning numbers value, measured or calculated, to the system used by scientific community and appropriate unit to a correct number of decimal places or physical quantity digits that will reflect the precision Precision - pertains to degree of value fineness of measurement taking into a. All non-zeros and any zeros account the ability of an instrument to sandwiched between nonzeros measure small quantities count - Degree of agreement of b. Trailing zeros count if there is measured values. The closer a decimal point the values to each other, the more precise the measurement Accurate - pertains to degree of a. Unavoidable because Best value: X̄ + δ agreement of measured value to there is uncertainty in STEP 1: create table with trial, and standard value; closer the mv to sv, the every physical measured value with its unit more accurate measurement STEP 2: find mean of all measured Percent error, %error - indicates Uncertainty - doubt that exist for every values nearness of a measured value to measurement, measures reported in STEP 3:calculate the standard standard value (gauge of accuracy of intervals deviation measurement) Best Value of Measurement - STEP 4: calculate the uncertainty consists best estimate and uncertainty value (δ) value (USED IN SINGLE STEP 5: write your conclusion MEASUREMENT) L3: Graphical Pressentation and μ = LC / 2; where LC is least count of Linear Fitting of Data X = measured value, s = standard instrumer Graph - illustration of a variable in value MULTIPLE MEASUREMENTS relation to another variable Errors - does not imply mistake or - Aid in visualizing relationship of blunder, but the deviation of measured two main variables: value to true value independent (x) and dependent 1. Systematic Error - measured (y) values tend to be either Equation of a line - linear ALWAYS larger or ALWAYS proportionality where the relationship of smaller than true value. As number of N (trials) increases, x and y is described by the equation: a. Caused by imperfect uncertainty decreases y = mx + b calibrations of an σs (standard deviation) is: m = slope (y/x) instrument or due to b = y-intercept varied response of instrument to different Linear Fitting - procedure of environmental determining general linear behavior of conditions a set of data or measurements 2. Random error - due to Linear regression limitations of measuring device X̄ = set of data/measured values and used or to uncertainties in X₁ = every measured value/s reading  STEP 3: Write the equation using y = mx + b STEP 4: Plot/graph the data Remember: scaling with unit, x & y label, broken line & no arrow STEP 5: Solve for R. STEP 6: Make a conclusion. STEP 7: Solve for R² 2. Coefficient of determination, STEP 8: depends on problem, predict Graphical analysis - there are two R² - square of correlation using linear equation statistical values that are used to coefficient used to determine L4: Vectors, Components of Vectors describe the linear relationship of x and strength of correlation of x and To represent vector quantity: y y. a. Bold letters - A, B, c, R 1. Pearson product moment a. Calculated by taking the b. Letter with arrow above correlation coefficient, R - square of R c. Colored straight line with used to determine type of b. Range of R² is from 0 to arrowhead correlation x and y exhibit. R is +1 Vectors - written in terms of magnitude calculated using formula: Value is: and direction. Ex.: 10m, 30° N of E Close to 1 (high) - x and y has strong Vectors with bar (| |) - only the linear relationship magnitude is needed Close to 0 (low) - x and y has a poor Rectangular coordinate system - linear correlation follows 360° in total Geographic coordinate system - R - range of values is from -1 to +1 R² also describes goodness of linear fit includes N/S/E/W Positive value of R: x increases, y or how reliable the linear fit equation is X-component (Ax) - parallel projection increases in showing general behavior of data of vector in x axis (East/West) Negative value of R: x increases, y Y-component (Ay) - parallel projection decreases STEP 1: Create a table with x and y of vector in y axis (North/South) values, xy, x², y², and their sums X and y component are drawn in STEP 2: Calculate m and b using the broken lines given formulas  Unit Vectors - has a magnitude of 1, to point/describe direction Caret - hat symbol used in place of the arrow Axî - x direction Ayĵ - y direction L5: Vector Addition Graphical Method - two ways to add vectors graphically: A. Parallelogram Method Step 1: Draw Vector 1 and Vector 2 such that their tails touch each To calculate for magnitude and other direction of vector: Step 2: Complete parallelogram by mirroring two sides. To solve for x and y components: Step 3: diagonal of the parallelogram - Using angle theta: that has the same tail as the Ax = Acosθ Where c = A (magnitude of vector) vectors represents the sum of Ay = Asinθ V1 and V2 When given angle is located in θ = arctan(Ay/Ax) B. Polygon Method - NE, NW, SE, SW Step 1: draw the first vector on a graph Where A is resultant vector Step 2: place the tail of each - Using opposite angle: subsequent vector at the head Ax = Asin(Opp. Angle) of the previous vector Ay = Acos(Opp. Angle) Step 3: resultant vector is then drawn When given angle is located in from the tail of the first vector to EN, ES, WN, WS the head of the final vector. Analytical Method - using analysis to solve resultant vectors A. Law of Sine and Cosine - used when triangles are not right triangles Where c is the resultant vector and C is the angle θ Where c is resultant vector and C is angle θ