PHY - Unit 0 - Lessons 1 2 3 - Class PPT Rev

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Unit 0: Physics and its Mathematics

What is Physics?

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Physics is the study of the most fundamental interactions between time, space, energy and matter.

VCU Department of Physics

Science develops through theuse of hypotheses, models, and theories. Explanations of how things work.

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Unit 0: Physics and its Mathematics

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Unit 0: Physics and its Mathematics

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Unit 0: Physics and its Mathematics

Physics in action

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Unit 0: Physics and its Mathematics

Physics Classroom Flickr Galleries:

Kinematics:http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/

Newton’s Laws of Motion:http://www.flickr.com/photos/physicsclassroom/galleries/72157625278916478/with/3521203176

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Projectile Motion:http://www.flickr.com/photos/physicsclassroom/galleries/72157625381723822/#photo_4902799284

Work, Energy & Power:http://www.flickr.com/photos/physicsclassroom/galleries/72157625199307955/

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Unit Objectives:

Students will be able to…1. Understand the Areas of Physics and Course Topics2. Review Algebra Skills needed for success3. Significant Figures - Understand and apply Significant

Figures in calculations4. Dimensional Analysis - Perform Dimensional Analysis

of measurement units and their conversion

Unit 0: Physics and its Mathematics

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Lesson 1: Course Topics

First Nine Weeks Second Nine Weeks

0. Introduction 6. Rotational Motion and Gravity

1. Motion in One Dimension 7. Vibrations and Mech. Waves

2. Two Dimensional Motion 8. Light and EM Waves Properties

3. Force and Newton’s Laws 9. Electrostatics

4. Work, Energy and Power 10. Magnetism

5. Momentum and Collisions 11. Modern Physics

Planned

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Lesson 1: Algebra Review

Lesson Objectives

Students will be able to…

• Review and practice algebra skills needed for success

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Lesson 1: Algebra Review

MATH PRE TEST!

PhysicsUnits of Measure:

Physics uses the International System of Units (SI) to measure most physical quantities and perform most of its calculations.

PhysicsFundamental Units

Unit Quantitymeter (m) length kilogram (kg) masssecond (s) timeampere (A) electric currentKelvin (K) temperaturemole (mol) amount of sub.candela (cd) luminous int.

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meter (m) length kilogram (kg) masssecond (s) time

These three units make upa subset call the MKS system.

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A derived unit is a combination of fundamental units.

m/s2 Kgm/s2

Units like cm or m3 are not derivedunits.

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Slide 17

Fig. T1.4, p.5

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All units except the kilogram are defined in terms of natural phenomena.

The kilogram is the mass of a platinum-iridium metal cylinder.

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Slide 19

Fig. 1.1a, p.4

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1 meter is the distance light travels in 1/299 792 458 second in a vacuum.

1 second is the time for 9 192 631 770 vibrations of a cesium-133 atom

Unit definitions:

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Slide 21

Fig. 1.1b, p.4Cascade Atomic Clock

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All measurements are subject to uncertainty. These can be due to the expertise of the investigator, the instrument, and parallax.

PhysicsParallax is the apparent shift in the position of an object when it is viewed from various angles.

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Mr. Huff - NKHS - 2010/201124

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Lesson 2: Significant Figures Review

Lesson Objectives

Students will be able to…

• Understand and apply Significant Figures in measurements and calculations

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Lesson 2: Significant Figures Review

Significant Figures

Challenge – solve the following problem...

A 7,560 kg car traveled at a constant speed for 1.80 hours over a distance of 22.06 kilometers. What is the car’s average momentum if:

momentum = mass x speed

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Lesson 2: Significant Figures Review

Significant Figures

Communicating our uncertainty ...

• Rules for zeros - how do we count zeros?

• Rules for operations – how do we round?

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Lesson 2: Significant Figures Review

Significant Figures

Rules for zeros:

Complete the Worksheet Problems

Rules for Zeros Examples

Non-zero digits are always significant 103.230002All final zeros after the decimal point are significant

12.740 ; 0.0420

Zeros between two other sig dig are always significant.

10.0 ; 2004 ; 6.000

Zeros used for spacing the decimal point are not (?) significant

100 ; .00000233

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Lesson 2: Significant Figures Review

Significant Figures

Rules for operations and rounding:

• If you add or subtract, round answer to same number of decimal places as the term with the least number of decimal places.

• If you multiply or divide two numbers, round answer to the number of significant figures as the term with the fewest sig digs.

Complete the Worksheet Problems

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22.4+10.6895

33.0895 33.1

Do the addition

0.00259+2.5

2.50259 2.5

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12.06 X 7.1 85.626 86

0.02471 X 3 0.07413 0.07

200.1 X 0.0025 0.50025 0.50

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Lesson 2: Significant Figures Review

Scientific Notation

How many significant figures does the measurement of 100 mm have?

However, what if whoever performed the measurement was accurate to within 1 mm?

To eliminate possible confusion, we can report the above measurement as 1.00 x 102 mm.

Physics What is scientific Notation?

• Scientific notation is a way of expressing really big numbers or really small numbers.

• It is most often used in “scientific” calculations where the analysis must be very precise.

Scientific Notation slides from presentation by Jenny Erickson

Physics Scientific notation consists of two parts:

• A number between 1 and 10

• A power of 10

N x 10x

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Changing standard form to scientific notation.

Physics To change standard form to scientific notation…

• Place the decimal point so that there is one non-zero digit to the left of the decimal point.

• Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

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• If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Physics Example 1

• Given: 289,800,000• Use: 2.898 (moved 8 places)• Answer: 2.898 x 108

Physics Example 2

• Given: 0.000567• Use: 5.67 (moved 4 places)• Answer: 5.67 x 10-4

Physics To change scientific notation to standard form…

• Simply move the decimal point to the right for positive exponent 10.

• Move the decimal point to the left for negative exponent 10.

(Use zeros to fill in places.)

Physics Example 3

• Given: 5.093 x 106

• Answer: 5,093,000 (moved 6 places to the right)

Physics Example 4

• Given: 1.976 x 10-4

• Answer: 0.0001976 (moved 4 places to the left)

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Precision

Precision is the degree of exactness to which the measurement of a quantity can be reproduced.

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Precision is also the agreement among several measurements that have been made in the same way.

Deviation is used to report precision.

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Accuracy

The extent to which a measured value agrees with the standard value of a quantity.

Accuracy is reported with relative error.

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Relative Error

Error Calculations:

EO A

Ar | |

Er -- Relative ErrorO -- Observed ValueA -- Accepted Value

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Lesson 3: Dimensional Analysis

Lesson Objectives

Students will be able to…

• Perform Dimensional Analysis including solving single, fractional and exponential unit conversion problems using standard units

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Lesson 3: Dimensional Analysis

Units - The Big Idea

Units identify what a specific number represents.

42 ?!?

Without the units attached, the number is meaningless.

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Lesson 3: Dimensional Analysis

Units - The Big Idea

• Every calculation and answer must include units.

• The standard for the course are Metric or SI Units Examples: meters, kilograms, seconds, Newtons

• Not sure how to attack a problem?You can often find the appropriate equation by

thinking about the correct units for the answer.

Handout Fact Sheet

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Lesson 3: Dimensional Analysis

Dimension ConversionSingle Unit conversions –

1. How many feet long is a 100 m football pitch? (that’s a soccer field to most of you)

2. How many kilometers is 5.5 miles?

3. How many seconds are in 2.2 hours?

Do Problems on Worksheet 4-8

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Lesson 3: Dimensional Analysis

Dimension ConversionFractional Unit Conversions -

9. Convert 63.89 meters per hour into meters per second

10. Convert 1.05 km/h into kilometers per second

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Lesson 3: Dimensional Analysis

Dimension ConversionFractional / Multiple Unit Conversions -

11. Convert 23.5 meters per second into miles per hour

12. Convert 60.2 miles per hour in kilometers per second

Do Problems on Worksheet 13 - 16

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Summary:Significant Figures –• All solutions must utilize the right number of

significant digits• Basic rules exist for zeros, rounding and * & /Dimensional Analysis• All solutions must have correct units – no naked

numbers!• Conversions must be done for common units

Unit 0: Physics and its Mathematics

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Graphical Relationships

Linear Inverse Quadratic

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xLinear relationships have the form y=mx+b

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X

Δy

Δx

m is the slopem = y/xb is the y intercept

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XInverse relationships have the form xy = k or y = k/x

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XThe graph of an Inverse is a hyperbola.

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XQuadratic relationships have the form y = kx2

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XThe graph of a Quadratic relationships is a parabola.