Welcome. Please take a Syllabus - physics.wm.eduphysics.wm.edu/~hancock/109/notes/class1.pdf · graphically. It gives us picture of a function. There are an infinite number of function.

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Practical Physics - Physics 109 (CRN 20728)

MWF 9:00 – 9:50 Small 111

Welcome. Please take a Syllabus

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Instructor: A. Dayle Hancock Office: Small 239Office hours: MW 10:00 - 11:00 or by AppointmentPhone: (757) 221-7844 e-mail: [email protected] web: http://physics.wm.edu/~hancock/109

Text: 'How Things Work' 5th edition by Bloomfield.The textbook is available in the W&M bookstore.

Grade: The final class grades will be curved if necessary. The weighting of the final average will be:

Quizzes 50%Homework (Wiley Plus) 25%Final exam (comprehensive) 25%

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Quizzes:The quizzes will be given on every other Friday during the last half of the regularly schedule class period.The first quiz will be January 31st.

Quiz questions are typically multiple choice questions orshort answer. A quiz typically has 16 or 17 questions.

The low quiz grade will be dropped from the final quiz average.

The quiz schedule is shown on the syllabus.

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Homework: Wiley Plus is the online homework system. You can purchase the text 'bundled' with Wiley PlusIn the W&M bookstore or you can purchase Wiley PlusOnline. The URL (web address) for the class Wiley PlusPage is:

http://edugen.wileyplus.com/edugen/domain/dmn73888/ Homework is normally due on Thursday night at 11:00 pm.

The first homework will be due January 23rd enroll inWiley plus as soon as possible.

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Final Exam: The final exam is required of all students. The final exam will be comprehensive. The final exam is scheduled for April 28th during the first period (9 am).

Laboratory: The first 110 lab is the week of January 27-31. No preparation is require for the first lab. You do not have to be enrolled in the lab. Labs meet in Small 224 on Monday (11:00 am and 2:00pm), Tuesday (3:30 pm) and Wednesday (2:00 pm). The lab manual is available in the bookstore. Pdf files of the manual are on the lab web page:

http://physics.wm.edu/~labs/110/

You must bring a hard copy of the experiment with you to the lab.

January 27

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Science is organized common sense about the universe around us.

Nature does not always work the way we thing it should.

Science is based on 'rational thinking' (logic).

Science is quantitative (numbers).

Science is built on math.

With a quantitative understanding of nature, civilization has 'advanced' to modern medicine, electronics, complex machinery etc.

What is Science?

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To understand something about the world, you have to to quantify the information i.e., put a number on it.

Examples: making an apple pie (how many apples?)or the orbit of Mars (how many days?)

Quantifying nature leads immediately to units e.g, how many kilograms (mass) of apples to make a pie.

While this country uses 'English units', most of theworld and science uses SI (French for 'Système International') or metric units.

All the units we will encounter can be reduced to distance (meter), mass (kilograms), time (seconds) and chage (Coulombs).

Quantifying Nature and Units

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● A major advantage of metric units is the power of ten prefixes.

Charge is something we will encounter with electricity. By the way, there are no English units for electricity. A volt is a metric unit.

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Math - Numbers

Math is the foundation of science. You have to put anumbers on things to do science!

A number can be an integer (counting numbers like -1 or 5) or fractions (½ or 0.5) which are called rational numbers. Rational numbers can be expressed as ratios of two integers. As a decimal the pattern of digits will repeat like2/3 as 0.6666666... )

Some numbers are irrational like π (3.14159...) and can not be expressed as a ratio of integers. There are others like 'e' (2.718...). There are many more irrational numbers thanthere are rational numbers.

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Math – Notation and Algebra

A equal sign (=) divides an algebraic expression into two sides. An expression can contain:

Integer numbers (-5, 7, 137 ), rational numbers (½, 0.675, etc) or irrational numbers (π, etc).

Variables are just letters for some number we want to find. They can be normal letters (x, y, etc). In science we also use Greek letters (α, β, ∆, etc).

Operators tell us what to do with the numbers or variables.Common operators are + (add), - (subtract). Note that two variables together or a number and a variable together means multiplication i.e. 3x. Parentheses are used to group things together like (3 + 6) ÷ 2 = 4.5.

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Math – Algebra

The most important rule in algebra is what you do to one side of an equation, you must do to the other side of the equation.

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Math – FunctionsA function is just a rule that tell us how to get one quantity if we know another quantity. A simple function for 'y' might be add 1 to x: y = x + 1

If we plot (graph) y verses x we can represent the function graphically. It gives us picture of a function. There are an infinite number of function. My favorite is y = ex.

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Slopes and Rates of Change

How something changes (like a function) is often useful. Physics and modern math started when Newton and Leibniz co-developed calculus which is about rates of change

For a straight line this is called the slope of the line is:

Slope = change y

change x=

∆y

∆x

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Slopes and Rates of Change

Even if the line is not straight, we can think about the slope of a line that is tangent to the function at some point. The slope will always exist if the function is 'nice'.

We will use this concept when we talk about 'instantaneous' velocity and acceleration.

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Area under a curve – Adding up how much

Sometime we wan to know how much of something happened over time e.g. how far did something move.This idea is closely connect to slopes and rates of change.

We will view this kind of problem from the viewpoint ofArea under a curve. If we consider a flat line, the answerIs easy. It is just the area of a square.

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Area under a curve – Summing how much

We can expand this idea is the line is not flat. Consider a line with a non zero slope. Then the area is just the area of a square and a triangle. The area of a triangle is just ½ the height times the base.

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Vectors

Vectors are mathematical objects that have direction and magnitude. We can graphically represent a vector with a line segment with an arrow head on one end. The length of the line segment is the magnitude (amount) and the arrow shows the direction.

If we want to add vectors that are in the same direction (or opposite direction) we just add (or subtract) the magnitudes.

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Vectors

What if the vectors are not parallel (or anti-parallel)? If the vectors are perpendicular, we can use the Pythagorean theorem:

The magnitude of the sum of A and B is given by the relation:

Sum2 = A2 +B2

Later we will find how to find the direction.

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Vectors

We can add any two vectors graphically by placing them 'head to tail' with the sum being from the tail of the first to the head of the last:

Normally, you would not want to draw vectors to scale using a ruler and protractor. We can add vectors usingTrigonometry by finding the components of a vector and adding the compents to get the components of the sum (resultant).

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Trigonometry

Trigonometry relates the sides of right triangles.

For an angle θ, the trig functions are defined as:

Note the side which side is adjacent or opposite depends on the angle.

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Vector Addition with components

We can add vectors using the components of of vectors. Components are the 'projection' of vectors onto a coordinate system. We will normally use Cartesian coordinate (x – y). The x and y components can be foundIf you know the magnitude and angle of the vector:

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Vector Addition with components

To find the sum of two vectors, find the x and y components of each vector. Add the x components of each vector to get the x component of the sum (resultant). Do the same for the the y components to get the y component of the sum.

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Vector Addition with components

Finally, to get the resultant vector in terms of magnitude and direction (angle) we use the Pythagorean theorem for the magnitude:

C = (Cx2 + Cy

2) ½

For the angle the angle, we can use the 'arctangent' or inverse tangent trig function:

θ = tan-1 ( )Cx

Cy

Note that tan-1 means the angle which has the tangent of (Cy/Cx ) and not

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tan θ