Prof. Rizopoulos theprof211@outlook.com Course Introduction Day 1 Welcome to PHY 101 Prof. Rizopoulos theprof211@outlook.com Course Introduction

What Math Skills do I need to succeed? “Physics is the study of the physical or natural world” It is the most basic science… The study of motion, forces, energy, matter, heat, sound, light, waves, and the composition of matter.

Success Skills Conceptual (Why does this happen?) Problem Solving Data Analysis Lab Design Self-learning Observation

SI (System International) Base Units Fundamental units (also called base units) Length = meter (m) Mass = kilogram (kg) Time = seconds (s) A base unit is independent of other units. Other fundamental units include Temperature (K), Electric current (A), Luminous Intensity (candela (cd), Number of particles (mole) These are the seven fundamental properties upon which all measurements are based. Other fundamental units include Temperature (K), Electric current (A), Luminous Intensity (candela (cd)), Number of particles (mole) These are the seven fundamental properties upon which all measurements are based.

Derived Units Derived units - are combinations of fundamental units Examples Meters per second (m/s) used to measure ??? kilogrammeter squared per second squared (kgm2/s2) is used to measure energy (the Joule) kilogrammeter per second squared (kgm/s2) is used to measure force (the Newton)

Scientific Notation Numbers expressed as M x 10n Where: M is the “mantissa”, a number between 1 and 10. The mantissa must contain the correct number of sig figs. n is the exponent, an integer

Let’s Practice Express 0.0000578 in scientific notation. In your calculator, type in the number 4.567x108.

One more thing… Use your calculator to perform the following calculation (3.45x1012 kg) x (4.3x10-2 m/s2) Express your answer with the correct units.

Common Prefixes Look at your reference tables Example Front page, bottom left corner,”Prefixes for Powers of 10” Example 1 ns = 1 x 10-9 s 1 nm = 1 x 10-9 m We can make conversion factors!

Common Prefixes Practice: Answer: 1 ps = 1x10-12 s How many seconds are in 1 picosecond? Answer: 1 ps = 1x10-12 s What if we turn the question around? How many picoseconds are in one second? Answer: (1 ps / 1x10-12 s) = (1x1012 ps / s) Or… set it up using factor-label method… (1 s) x some conversion factor = ps Get conversion factor from prefixes table

Getting Conversion Factors From Prefixes Table We often need to change from one unit to another… we can do this using conversion factors. Here’s the key…Units are treated as mathematical factors, and can be divided out.

Let’s do it! Let’s convert 365 meters to km. On board

Why can’t I just move the decimal place? You can, but only if you’re going from one metric unit to another. What if you need to convert a derived unit, like km/hr to m/s?

Let’s do it! Let’s convert 100 km/hr to meters/second.

The Four Sig Fig Rules RULE #1- Non-zero digits are always significant Example How many sig figs in 2.735 m? Answer Four sig figs

The Four Sig Fig Rules RULE #2 - Zeros between two other significant digits are significant Example How many sig figs in the value 202.03 kg? Answer…. 5 sig figs

The Four Sig Fig Rules RULE #3 - All final zeros after the decimal point are significant Examples 0.002 kg has one sig fig 0.020 kg has two sig figs 0.200 kg has three sig figs For #’s less than one, leading zeros are not significant.

The Four Sig Fig Rules RULE #4 - Zeros used solely for spacing the decimal point are not significant (unless a decimal point is present) Examples 63400 seconds has three sig figs 63400. seconds has five significant figures

Adding and Subtracting w/Sig Figs The rule - Perform the operation, the round off to least precise value involved. Examples

Multiplying and Dividing w/ Sig Figs The rule - perform the operation, then round off answer to the same number of sig figs as the factor with the fewest sig figs. Examples

Physics Lab Measuring Length

Precision Precision is the degree of exactness (if that’s a word) to which the measurement of a quantity can be reproduced Precision is linked to significant figures Significant figures includes all known digits plus one estimated digit. Demo on overhead

% error = [(measured value - accepted value) / accepted value] x 100 Accuracy Accuracy is the extent to which a measured value agrees with the standard or accepted value. Accuracy is measured using percent error % error = [(measured value - accepted value) / accepted value] x 100

Assignment Homework #1

Estimating and “Order of Magnitude” “Order of Magnitude” is the power of 10 closest to a numerical quantity’s actual value Examples 1693 kg has an order of magnitude of 103 kg 8534 kg has an order of magnitude of 104 kg

Estimating and “Order of Magnitude” Useful for estimating answers or comparing quantities Practice - What is the order of magnitude in meters of a football field? Football field is 100 yards long. A yard is close to a meter. So its about 100 meters long… that’s 102 meters

Algebra Let’s pick a few equations off the reference tables and solve for an unknown…

Trigonometry (Reference Tables) SOH Sin  = opposite / hypotenuse CAH Cos  = adjacent / hypotenuse TOA Tan  = opposite / adjacent

Let’s Practice Angle = 300 Hypotenuse = 50 Newtons What is the y-component? What is the x-component?

One more practice Y-component = 20 m/s Hypotenuse = 50 m/s What is the angle?

Calculator Settings Make sure your calculator is always set to “degrees” mode for Regents Physics.

Graphing and Mathematical Relationships Some quick review Independent variable - the one the experimenter changes or controls directly Goes on X-axis Dependent variable - the one that changes as a result of changes made by the experimenter Goes on Y-axis

Graphing Work with a partner Get a ruler Use problem solving strategy in text page 27 as a guide. Make a graph using the sample problem data and graph paper.

Slope The slope of a graph often has physical meaning… Slope = Y / X We can pick any two points from our line of best fit to calculate the slope… On overhead Solve for slope on the overhead… Slope = dy / dx

Physical Significance of the Slope Velocity is the physical significance of the slope of this graph Units of slope will always be y-units over x-units, and the units of the slope help us identify its physical significance.

Linear Relationships This is an example of a linear relationship, because a straight line can be drawn through all data points Also called “direct” relationship or “directly proportional” An increase in one variable causes an increase in the other

Linear Relationships Equations for linear relationships take the general form… y = mx + b Where: m is the slope B is the y-intercept

Back to the Sample Problem For the graph of the sample problem… Y = (20 m/s) X + 0 Or… Position is equal to 20 m/s times the number of seconds.