A Physics Toolkit: Basic Math & Science Skills

Slides:



Advertisements
Similar presentations
A Physics Toolkit Chapter Physics Energy, matter and their relationship Understanding the physical world Careers –Scientists, astronomers, engineers,
Advertisements

Physics 1.2.
Measurement and Calculation Unit 2. The Fundamental SI Units (la Système Internationale, SI) Physical QuantityNameAbbreviation Mass Length Time Temperature.
Measurements and Calculations
Review and Introductory Topics. Measurements  In science, System Internationale (SI) is used.  See Table 2-2 for prefixes –Giga through pico (some examples)
DO NOW Without using your book what are the three branches of Natural Science? Earth and Space, Life, Physical.
Introduction to Chemistry.  No eating or drinking!  Wear goggles at all times!  Use common sense!
CHAPTER 1&2 NOTES KONICHEK. I.Science- The organized study of events in the universe. A. Universe- all matter, space, time, and energy B. Event- a happening.
1-1 What is Physics?  What does Physics mean? "Physics" is from the Greek root physik (science of nature) and Latin physica (natural science).  It’s.
DATA.
Measurements and Calculations
Chapter 2: Scientific Method Cartoon courtesy of NearingZero.net.
Chapter 2 Standards of Measurement Objectives:  Understand Mass and Weight (2.1)  Identify the metric units of measurement (2.6)  Explain what causes.
In this section you will:
Measurement and Calculation Unit 2. The Fundamental SI Units (le Système International, SI) Physical QuantityNameAbbreviation Mass Length Time Temperature.
INTRODUCTION The “stuff” every Physics student should know…
Measurement. Physics  A branch of science that involves the study of the physical world: energy, matter, and how they are related.
1. Linear Graphs Graphing data shows if a relationship exists between two quantities also called variables. If two variables show a linear relationship.
Physical Science Methods and Math Describing Matter The Scientific Method Measurements and Calculations 1.
INTRODUCTION TO CHEMISTRY CHAPTERS 1 AND 2. 1.) WHAT IS CHEMISTRY?  The study of matter and the changes that matter undergoes.
1 Honors Physics A Physics Toolkit. 2 Honors Physics Chapter 1 Turn in Contract/Signature Lecture: A Physics Toolkit Q&A Website:
1 Chemistry Chapter 1 Scientific method and Data management Chemistry- Matter and Change Glencoe.
Intro to Physics (Chapter 1). PHYSICS is an attempt to describe in a fundamental way, the nature and behavior of the world around us. is about the nature.
Physics Chapter 1: The Science of Physics.  Physics Is Everywhere!  Motion  Heat  Sound  Light  Electricity.
Physics Why does sound not travel in a vacuum? Why is the gravitational force of the Earth not able to pull a magnet off the refrigerator? How does a.
In this chapter you will:  Use mathematical tools to measure and predict.  Apply accuracy and precision when measuring.  Display and evaluate data graphically.
AP PHYSICS 1 SUMMER PACKET Table of Contents 1.What is Physics? 2.Scientific Method 3.Mathematics and Physics 4.Standards of Measurement 5.Metric System.
Chapter 2: Measurements and Calculations Ch 2.1 Scientific Method Steps to the Scientific Method (1) Make observations-- Use your 5 senses to gather.
Uncertainty in Measurement What is the Difference Between Accuracy and Precision? Accuracy: how close a measurement comes to the true accepted value.
1-1 What is Physics?  "Physics" is from the Greek root physik (science of nature) and Latin physica (natural science).  It’s the scientific study of.
Chapter 1 The Nature of Science.
The Nature of Science Sections 1.2 and 1.3
The Scientific Method
Introduction To Chemistry
Math in Physics Math skills are essential to physics.
Measurement.
Mathematical Toolkit Chapter 2 Pg
Science Skills Chapter 1.
Measurements and Calculations
Section 2.1 Units and Measurements
Why are measurement units important? Why do we use significant digits?
Why are measurements and calculations essential to a Physics study?
Mathematics and Physics
2015 Physics WoF Start the year right with a .
Chemical Foundations Chapter 1.
Pre-AP Chemistry Measurements and Calculations.
Lab Skills Physical Quantities Uncertainty SI Units Prefixes
Introduction: Matter and Measurement
Chapter 1: A Physics Toolkit
Graphs in Physics.
SCIENCE UNIT 3 THE PHYSICS OF MOTION !
Prof. Rizopoulos Course Introduction
Metric Systems and Significant Figures
Lab Skills Physical Quantities Uncertainty SI Units Prefixes
DATA.
Chapter 1 A Physics Toolkit.
Click the mouse or press the spacebar to continue.
Unit 0: Orientation to Class The Structure of Physics
Mathematics and Physics
Chapter 2 Data Analysis 2.1 Units of Measurement
ACCURACY AND PRECISION
Solve Apply the concepts to this problem.
Scientific Measurement
ACCURACY AND PRECISION
Measurements in Experiments
2016 Physics WoF Start the year right with a .
Introduction to Chemistry and Measurement
Chapter 2 A Mathematical Toolkit
What are the SI base units for time, length, mass, and temperature?
Scientific Measurements
Presentation transcript:

A Physics Toolkit: Basic Math & Science Skills Chapter 1 A Physics Toolkit: Basic Math & Science Skills

Mathematics and Physics

What is Physics? branch of science that studies the physical world involves the study of energy, matter, and how the two are related The goal of this course is not to make you a physicist. It is to give you an idea of the way physicists view the world; to have the satisfaction of understanding and even predicting the outcome of the things that are happening all around you.

Scientific Methods Scientific Law Scientific Theories A rule of nature that sums up related observations to describe a pattern in nature. Laws do not explain WHY these phenomena occur, they simply describe them. An explanation based on many observations supported by experimental results. Theories may serve as explanations for laws. A law only describes what happens, not why. A theory is the best available explanation of why things work the way they do. A theory must be well-supported. The Law of Universal Gravitation gives the relationship between the gravitational force the distance and masses of two objects. The theory of universal gravitation explains that all the mass in the universe is attracted to other mass. Laws and Theories may be revised or rejected over time.

SI Units The 7 base units are listed in the table to the right. You need to know these! Base Quantity Base Unit Symbol Length meter m Mass kilogram kg Time second s Temperature kelvin K Amount of a Substance mole mol Electric Current ampere A Luminous Intensity candela cd To share results, it’s practical to use units that everyone recognizes. The worldwide scientific community (and most countries) presently use an adapted version of the metric system, called SI. Uses 7 base quantities. You are going to see many derived units also this year. Derived units come from the combination of these 7 base units in different ways.

Prefixes Used with SI Units Symbol Multiplier Scientific Notation nano- n 0.000000001 10-9 micro- μ 0.000001 10-6 milli- m 0.001 10-3 centi- c 0.01 10-2 deci- d 0.1 10-1 kilo- k 1,000 103 mega- M 1,000,000 106 giga- G 1,000,000,000 109 You probably already know from chem. that its much easier to convert units in the SI system because all you have to do is multiply or divide by the appropriate power of 10. Prefixes are used to change SI units by powers of 10. You need to know these too!

Dimensional Analysis The method of treating units as algebraic quantities that can be cancelled. How? Choose a conversion factor that will make the units you don’t want cancel, and the units you do want stay in the answer. Example: How many meters are in 30 kilometers? Conv. Factor 1 km = 1000 m 30 km x Try This One: Convert 36 km/hr to m/s. 1000 m 1 km = 30,000 m

Significant Figures Sig figs are the valid digits in a measurement. answers cannot be more precise than the least precise measurement in calculations All answers on tests, quizzes, labs, etc. must have the proper amount of sig figs.

Determining the Number of Sig Figs in a Measurement Sig Fig Rules Determining the Number of Sig Figs in a Measurement Remember these four rules: Nonzero digits are always significant. All final zeros after the decimal point are significant. Zeros between two other significant digits are always significant. Zeros solely used a placeholders are NOT significant.

Operations Using Sig Figs Addition & Subtraction Example: To add or subtract measurements: perform the operation round off the result to correspond to the least precise value involved Add 24.686 m + 2.343 m + 3.21 m. Just add the measurements. 24.686 m + 2.343 m + 3.21 m = 30.239 m Round to the least precise measurement. 3.21 m is the least precise, so… round to two decimal places: 30.24 m

Operations Using Sig Figs Multiplication & Division Example: To multiply or divide measurements: perform the operation note measurement with the least number of sig figs round the product or quotient to this number of digits Multiply 3.22 cm by 2.1 cm. Just multiply the measurements. 3.22 cm x 2.1 cm = 6.762 cm2 Round the product to the same number of digits as the measurement with the least amount of sig figs. 3.22 cm has 3, 2.1 cm has 2, so, round to 2 digits  6.8 cm2

Measurement

Measurement A comparison between an unknown quantity and a standard.

Characteristics of Measured Values Precision Accuracy The degree of exactness of a measurement. Depends on the instrument and the technique used to make the measurement. Describes how well the results of a measurement agree with the accepted value as measured by skilled experimenters. Precision – How close measurements are to one another. Depends on tool – as you can probably guess, the device that has the finest division on its scale will produce the most precise measurements. Accuracy – How close the measurements are to the correct value.

Techniques of Good Measurement Know how to use the instrument you are using to obtain measurements. Use the instrument correctly. Handle instruments with care, to avoid damage. Always “zero” the instrument if necessary. Look straight at the markings at eye-level to avoid a parallax. Parallax – the apparent shift in the position of an object when it is viewed from different angles.

Graphs in Physics

Linear Graphs You can see if a relationship exists between two quantities, also called variables, by graphing the data. If two variables show a linear relationship they are directly proportional to each other. Examine the following graph:

Linear Graphs Dependent Variable Independent Variable

Linear Graphs – Slope of a Line The slope of a line is a ratio between the change in the y-value and the change in the x- value. This ratio tells whether the two quantities are related mathematically. Calculating the slope of a line is easy!

Linear Graphs – Slope of a Line y x y2 Rise = Δy = y2 – y1 Slope = Rise Run y1 Run = Δx = x2 – x1 Slope = y2 – y1 x2 – x1 x1 x2

Linear Graphs – Equation of a Line Once you know the slope then the equation of a line is very easily determined. Slope Intercept form for any line: y = mx + b y-intercept (the value of y when x =0) slope Of course in Physics we don’t use “x” & “y”. (We could use F and m, or d and t, or F and x etc.)

Linear Graphs: Area Under the Curve Sometimes it’s what is under the line that is important! Work = Force x distance W = F x d How much work was done in the first 4 m? How much work was done moving the object over the last 6 m?

Non Linear Relationships Not all relationships between variables are linear. Some are curves which show a square or square root relationship In this course we use simple techniques to “straighten the curve” into a linear relationship. This is called linearizing.

Non Linear Relationships This is not linear. It is an exponential relationship. Try squaring the x-axis values to produce a straight line graph Equation of the straight line would then be: y = x2

Non Linear Relationships This is not linear. It is an inverse relationship. Try plotting: y vs 1/x. Equation of the straight line would then be: y = 1/x

Meaning of Slope from Equations Often, in physics, graphs are plotted and the calculation and meaning of the slope becomes an important factor. We will use the slope intercept form of the linear equation described earlier. y = mx + b

Meaning of Slope from Equations Unfortunately physicists do not use the same variables as mathematicians! d = ½ x a x t2 For example: is a very common kinematic equation. where d = displacement, a = acceleration and t = time

Meaning of Slope from Equations d t Physicists may plot a graph of d vs t, but this would yield a non-linear graph in this case: d t2 To linearize the curve Square the time

d = ½at2 Meaning of Slope from Equations But what would the slope of a d vs t2 graph represent? Let’s look at the equation again: d = ½at2 {d is plotted vs t2} y = mx + b d is y and t2 is x… so whatever is before t2 must be equal to the slope of the line! slope = ½ a {and don’t forget about the units! m/s2}

Meaning of Slope from Equations Now try These. A physics equation will be given, as well as what is initially plotted. Tell me what should be plotted to linearize the graph and then state what the slope of this graph would be equal to. Plot a vs v2 to linearize the graph Example #1: a = v2/r a v Let’s re-write the equation a little: a = (1/r)v2 Therefore plotting a vs. v2 would let the slope be: Slope = 1/r

Meaning of Slope from Equations Example #2: F = 2md/t2 F t Plot F vs 1/t2 to linearize the graph F 1/t2 Slope = 2md Go on to the worksheet on this topic

Classwork Start the Linearization Worksheet in class and finish for homework.