Head first physics

In this chapter, you’ll expand your math skills by making substitutions to work out a key equation of motion for a curved displacement-time graph of a falling object.. 305 You can work

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Download at WoweBook.Com

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Advance Praise for Head First Physics

“If you want to learn some physics, but you think it’s too difficult, buy this book! It will probably help,

and if it doesn’t, you can always use it as a doorstop or hamster bedding or something I wish I had a

copy of this book when I was teaching physics.”

— John Allister, physics teacher

“Head First Physics has achieved the impossible - a serious textbook that makes physics fun Students all

over will be thinking like a physicist!”

— Georgia Gale Grant, freelance science writer, communicator and broadcaster

“Great graphics, clear explanations and some crazy real world problems to solve! This text is full of

strategies and tips to attack problems It encourages a team approach that’s so essential in today’s work

world.”

— Diane Jaquith, high school physics, chemistry and physical science teacher

“This is an outstandingly good teacher masquerading as a physics book! You never feel phased if you

don’t quite understand something the first time because you know it will be explained again in a different

way and then repeated and reinforced ”

— Marion Lang, teacher

“This book takes you by the hand and guides you through the world of physics.”

— Catriona Lang, teacher

“Head First Physics really rocks - I never thought it was possible to enjoy learning physics so much! This

book is about understanding and not about rote learning, so you can get to grips with the physics and

remember it much better as a result.”

— Alice Pitt-Pitts

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Praise for other Head First academic titles

“Head First Statistics is by far the most entertaining, attention-catching study guide on the market By presenting the material in an engaging manner, it provides students with a comfortable way to learn an otherwise cumbersome subject The explanation of the topics is presented in a manner comprehensible

to students of all levels.”

— Ariana Anderson, Teaching Fellow/PhD candidate in Statistics, UCLA

“Head First is an intuitive way to understand statistics using simple, real-life examples that make learning fun and natural.”

— Michael Prerau, computational neuroscientist and statistics instructor, Boston University

“Thought Head First was just for computer nerds? Try the brain-friendly way with statistics and you’ll change your mind It really works.”

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Praise for the Head First Approach

“There are books you buy, books you keep, books you keep on your desk, and thanks to O’Reilly and the

Head First crew, there is the ultimate category, Head First books They’re the ones that are dog-eared,

mangled, and carried everywhere Head First SQL is at the top of my stack Heck, even the PDF I have

for review is tattered and torn.”

— Bill Sawyer, ATG Curriculum Manager, Oracle

“Elegant design is at the core of every chapter here, each concept conveyed with equal doses of

pragmatism and wit.”

— Ken Goldstein, Executive Vice President, Disney Online

“I feel like a thousand pounds of books have just been lifted off of my head.”

—Ward Cunningham, inventor of the Wiki and founder of the Hillside Group

“This book’s admirable clarity, humor and substantial doses of clever make it the sort of book that helps

even non-programmers think well about problem-solving.”

— Cory Doctorow, co-editor of Boing Boing

Author, Down and Out in the Magic Kingdom

and Someone Comes to Town, Someone Leaves Town

“It’s fast, irreverent, fun, and engaging Be careful—you might actually learn something!”

—Ken Arnold, former Senior Engineer at Sun Microsystems

Co-author (with James Gosling, creator of Java), The Java Programming

Language

“I received the book yesterday and started to read it and I couldn’t stop This is definitely très ‘cool.’ It is

fun, but they cover a lot of ground and they are right to the point I’m really impressed.”

— Erich Gamma, IBM Distinguished Engineer, and co-author of Design

Patterns

“One of the funniest and smartest books on software design I’ve ever read.”

— Aaron LaBerge, VP Technology, ESPN.com

“I ♥ Head First HTML with CSS & XHTML—it teaches you everything you need to learn in a ‘fun

coated’ format.”

— Sally Applin, UI Designer and Artist

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Other related books from O’Reilly

Statistics HacksTM

Statistics in a Nutshell

Mind HacksTM

Mind Performance HacksTM

Your Brain: The Missing Manual

Other books in O’Reilly’s Head First series

Head First JavaTM

Head First Object-Oriented Analysis and Design (OOA&D)Head First HTML with CSS and XHTML

Head First Design Patterns

Head First Servlets and JSP

Head First EJB

Head First PMP

Head First SQL

Head First Software Development

Head First JavaScript

Head First Ajax

Head First Statistics

Head First PHP & MySQL (2008)

Head First Algebra (2008)

Head First Rails (2008)

Head First Web Design (2008)

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Beijing • Cambridge • Kln • Sebastopol • Taipei • Tokyo

Heather Lang, Ph.D.

A learner’s companion to mechanics and practical physics

Wouldn’t it be dreamy if

there was a physics book that

was more fun than going to the

dentist, and more revealing than

an IRS form? It’s probably just a

fantasy

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Head First Physics

by Heather Lang, Ph.D.

Printed in the United States of America.

Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472.

O’Reilly Media books may be purchased for educational, business, or sales promotional use Online editions are

also available for most titles (safari.oreilly.com) For more information, contact our corporate/institutional sales department: (800) 998-9938 or corporate@oreilly.com.

Series Creators: Kathy Sierra, Bert Bates

Cover Designers: Louise Barr, Steve Fehler

Production Editor: Brittany Smith

Printing History:

September 2008: First Edition.

The O’Reilly logo is a registered trademark of O’Reilly Media, Inc The Head First series designations,

Head First Physics, and related trade dress are trademarks of O’Reilly Media, Inc.

Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks Where those designations appear in this book, and O’Reilly Media, Inc., was aware of a trademark claim, the designations have been printed in caps or initial caps.

While every precaution has been taken in the preparation of this book, the publisher and the authors assume no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein.

No pizza delivery guys were harmed in the making of this book

ISBN: 978-0-596-10237-1

[M]

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This book is dedicated to anyone who made me laugh while writing it!

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the author

Author of Head First Physics

Heather studied physics in Manchester,

gaining a first class honours degree She likes explaining how stuff works and persuading people to send her chocolate in the post Her first foray into science communication was via the BaBar Particle Physics Teaching Package She followed this up with a Ph.D in the grey area between physics and biochemistry, but got fed up of sharing a fridge with petri dishes and moved on from the lab into education and Head First Physics

When not explaining how stuff works, Heather likes to play extreme sports such as chess and cricket, play with sliders on a sound desk, or play the fool while running school chess clubs (in the name of teaching of course)

Heather Lang

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table of contents

ix

Table of Contents (Summary)

Table of Contents (the real thing)

Your brain on Physics Here you are trying to learn something, while here your brain is doing you a favor by making sure the learning doesn’t stick Your

brain’s thinking, “Better leave room for more important things, like which wild

animals to avoid and whether naked snowboarding is a bad idea.” So how do you

trick your brain into thinking that your life depends on knowing physics?

Intro

1 Think Like a Physicist: In the beginning 1

2 Making It All Mean Something: Units and Measurements 17

3 Scientific Notation, Area, and Volume: All Numbers Great and Small 55

4 Equations and Graphs: Learning the Lingo 95

6 Displacement, Velocity, and Acceleration: What’s Going On? 203

7 Equations of Motion (Part 1): Playing with Equations 237

8 Equations of Motion (Part 2): Up, Up, and Back Down 283

9 Triangles, Trig and Trajectories: Going Two-Dimensional 335

10 Momentum Conservation: What Newton Did 391

11 Weight and The Normal Force: Forces for Courses 437

12 Using Forces, Momentum, Friction and Impulse: Getting On With It 471

14 Energy Conservation: Making Your Life Easier 559

15 Tension, Pulleys and Problem Solving: Changing Direction 603

17 Circular Motion (Part 2): Staying on Track 663

18 Gravitation and Orbits: Getting Away From It All 715

19 Oscillations (Part 1): Round and Round 761

20 Oscillations (Part 2): Springs ‘n’ Swings 797

21 Think Like a Physicist: It’s the Final Chapter 839

i Appendix i: Top Six Things We Didn’t Cover 863

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x

You can get a feel for what’s happening by being a part of it 4 Use your intuition to look for ‘special points’ 6 The center of the earth is a special point 8 Ask yourself “What am I ALREADY doing as

Where you’re at - and what happens next? 11

In the beginning

think like a physicist

1 Physics is about the world around you and how everything

in it works As you go about your daily life, you’re doing physics all the time! But the thought of actually learning physics may sometimes feel like falling

into a bottomless pit with no escape! Don’t worry this chapter introduces how

to think like a physicist You’ll learn to step into problems and to use your intuition to spot patterns and ‘special points’ that make things much easier

By being part of the problem, you’re one step closer to getting to the solution

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2

It’s the best music player ever, and you’re part of the team! 18

So you get on with measuring the myPod case 19 When the myPod case comes back from the factory, it’s way too big 20 There aren’t any UNITS on the blueprint 22 You’ll use SI units in this book (and in your class) 25 You use conversion factors to change units 29 You can write a conversion factor as a fraction 30 Now you can use the conversion factor to update the blueprint 33 What to do with numbers that have waaaay too many

How many digits of your measurements look significant? 37 Generally, you should round your answers to three significant digits 39 You ALREADY intuitively rounded your original

you need the right number of significant digits 51

Units and measurements

making it all MEAN something

How long is a piece of string? Physics is based on making

measurements that tell you about size In this chapter, you’ll learn how to use

units and rounding to avoid making mistakes - and also why errors are OK

By the time you’re through, you’ll know when something is significant and

have an opinion on whether size really is everything.

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3

So how long before things go really bad? 57 Power notation helps you multiply by

Your calculator displays big numbers using scientific notation 63 Scientific notation uses powers of 10 to write down long numbers 64 Scientific notation helps you with small numbers as well 68 You’ll often need to work with area or volume 72 Look up facts in a book (or table of information) 73 Prefixes help with numbers outside your comfort zone 74 Scientific notation helps you to do calculations with

200,000,000 meters cubed bugs after only 16 hours is

Be careful converting units of area or volume 84

So the bugs won’t take over unless the guys sleep in! 86 The “Converting units of area or volume” Question 87

All numbers great and small

scientific notation, area, and volume

The Bumper Book of Bugs

In the real world, you have to deal with all kinds of numbers, not just the ones that are easier to work with. In this chapter, you’ll

be taking control of unwieldy numbers using scientific notation and discovering why rounding a large number doesn’t mean having to write a zillion zeros at the end You’ll also use your new superpowers to deal with units of area and volume - which is where scientific notation will save you lots of grief (and time) in the future!

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4

You need to work out how to give the customer their delivery time 97

If you write the delivery time as an equation,

Use variables to keep your equation general 99 You need to work out Alex’s cycling time 101 When you design an experiment, think about what might go wrong! 105 Conduct an experiment to find out Alex’s speed 108 Write down your results in a table 109 Use the table of distances and times to work out Alex’s speed 111 Random errors mean that results will be spread out 113

A graph is the best way of taking an average of ALL your results 114 Use a graph to show Alex’s time for ANY distance 117 The line on the graph is your best estimate for

how long Alex takes to cycle ANY distance 118 You can see Alex’s speed from the steepness

Alex’s speed is the slope of the distance-time graph 122 Now work out Alex’s average speed from your graph 123 You need an equation for Alex’s time to give to the web guys 125 Rearrange the equation to say " time = something" 126 Use your equation to work out the time it takes

So just convert the units, and you’re all set right? 131 Include the cooking time in your equation 133

A graph lets you see the difference the stop lights made 137 The stop lights change Alex’s average speed 139 The “Did you do what they asked you” Question 146

Learning the lingo

equations and graphs

Communication is vital. You’re already off to a good start

in your journey to truly think like a physicist, but now you need to

communicate your thoughts In this chapter, you’re going to take your

first steps in two universal languages - graphs and equations - pictures

you can use to speak a thousand words about experiments you do and

the physics concepts you’re learning Seeing is believing.

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dealing with directions

Displacement is different from distance 155 Distance is a scalar; displacement is a vector 157 You can represent vectors using arrows 157

The “Wheat from the chaff ” Question 166

If you can’t deal with something big, break it down

Velocity is the ‘vector version’ of speed 174

You need to allow for the stream’s velocity too! 176

If you can find the stream’s velocity, you can figure

It takes the boat time to accelerate from a standing start 180

Vector, Angle, Velocity, Acceleration = WINNER!!! 187 I’m ready - what’s first?

Time, speed, and distance are all well and good, but you really need DIRECTION too if you want to get on in life.

You now have multiple physics superpowers: You’ve mastered graphs and equations, and

you can estimate how big your answer will be But size isn’t everything In this chapter, you’ll be learning about vectors, which give direction to your answers and help you to find easier shortcuts through complicated-looking problems.

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You want an instantaneous velocity, not an average velocity 213 You already know how to calculate the slope of a straight line 218

A point on a curved line has the same slope as its tangent 218 The slope of something’s velocity-time graph

Success! You worked out the velocity after 2.0 s -

Now onto solve for the displacement! 234

What’s going on?

Displacement, Velocity, and Acceleration

It’s hard to keep track of more than one thing at a time When something falls, its displacement, velocity, and acceleration are all important at the same time So how can you pay attention to all three without missing anything? In this chapter, you’ll increase your experiment, graph, and slope superpowers in preparation for bringing everything together with an equation or two.

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Graphs and equations both represent the real world 240 You’re interested in the start and end points 241 You have an equation for the velocity -

See the average velocity on your velocity-time graph 249 Test your equations by imagining them with different numbers 251

You know how high the crane should be! 254 But now the Dingo needs something more general 255

Get rid of the variables you don’t want by making substitutions 259

You derived a useful equation for the cage’s displacement! 264

Check your equation by trying out some extreme values 268

The “Units” or “Dimensional analysis” Question 276

Playing With Equations

Equations of motion (part 1)

It’s time to take things to another level.

So far, you’ve done experiments, drawn graphs of their results, and worked out equations from them But there’s only so far you can go since sometimes your graph isn’t a straight

line In this chapter, you’ll expand your math skills by making substitutions to work out

a key equation of motion for a curved displacement-time graph of a falling object And you’ll also learn that checking your GUT reaction to an answer can be a good thing.

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You can use one graph to work out the shapes of the others 293

Is a graph of your equation the same shape

Fortunately, ACME has a rocket-powered hovercraft! 305

You can work out a new equation by making a substitution for t 308 Multiply out the parentheses in your equation 311 You have two sets of parentheses multiplied together 312 You need to simplify your equation by grouping the terms 315 You can use your new equation to work out the stopping distance 317 There are THREE key equations you can use

You need to work out the launch velocity that gets

You need to find another way of doing this problem 326 The start of a beautiful friendship 330 The “Sketch a graph” or “Match a graph” Question 331 The “Symmetry” and “Special points” Questions 332

Up, up, and back down

equations of motion (part 2)

What goes up must come down. You already know how to

deal with things that are falling down, which is great But what about the other half of the bargain - when something’s launched up into the air? In this chapter, you’ll add a third key equation of motion to your armory which will enable you to deal with (just about) anything! You’ll also learn how looking for a little symmetry can turn impossible tasks into manageable ones.

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9

Pythagoras’ Theorem lets you figure out the sides quickly 343 Sketch + shape + equation = Problem solved! 345 Camelot we have ANOTHER problem! 348 Relate your angle to an angle inside the triangle 351 Classify similar triangles by the ratios of their side lengths 354 Sine, cosine and tangent connect the sides and

How to remember which ratio is which? 357

The horizontal component of a projectile’s velocity is constant 372 The same method solves both problems 375

Going two-dimensional

triangles, trig and trajectories

Ladder

WallEnd of ladder

is nowhere near top of wall

Bottom of

ladder is at

edge of moat

Moat filled with water

15.0 m 15.0 m 15.0 m

So you can deal with one dimension But what about real life?

Real things don’t just go up or down - they go sideways too! But never fear - you’re

about to gain a whole new bunch of trigonometry superpowers that’ll see you spotting right‑angled triangles wherever you go and using them to reduce complicated‑looking problems into simpler ones that you can already do.

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You can’t do everything that’s theoretically possible -

Sieges-R-Us has a new stone cannonball, which they claim will increase the range! 400 Massive things are more difficult to start and stop 402

A stone cannonball has a smaller mass -

so it has a larger velocity But how much larger? 407

How are force, mass and velocity related? 411 Vary only one thing at a time in your experiment 414 Mass × velocity - momentum - is conserved 418

A greater force acting over the same amount of time

Write momentum conservation as an equation 421 Momentum conservation and Newton’s Third Law are equivalent 422 You’ve calculated the stone cannonball’s velocity,

Use proportion to work out the new range 430 The “Proportion” Question (often multiple choice) 434

What Newton Did

momentum conservation

No one likes to be a pushover. So far, you’ve learned to deal with objects that are already moving But what makes them go in the first place? You know that something

will move if you push it - but how will it move? In this chapter, you’ll overcome inertia as

you get acquainted with some of Newton’s Laws You’ll also learn about momentum, why it’s conserved, and how you can use it to solve problems.

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Is it really possible to lose weight instantly?! 439 Scales work by compressing or stretching a spring 440

The relationship between force and mass involves momentum 444

If the object’s mass is constant, Fnet = ma 446 The scales measure the support force 449

The machine reduces the support force 452 Force pairs help you check your work 454

A surface can only exert a force perpendicular (or normal) to it 458 When you slide downhill, there’s zero perpendicular acceleration 461 Use parallel and perpendicular force components to deal with a slope 463

Forces for courses

weight and the normal force

Sometimes you have to make a statement forcefully

In this chapter, you’ll work out Newton’s 2nd Law from what you already know about momentum conservation to wind up with the key equation, F

net = ma Once you

combine this with spotting Newton’s 3rd Law force pairs, and drawing free body diagrams, you’ll be able to deal with (just about) anything You’ll also learn about why mass and weight aren’t the same thing, and get used to using the normal force to

support your arguments.

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In real life, the force of friction is present 484 Friction depends on the types of surfaces that are interacting 488

Be careful when you calculate the normal force 489 You’re ready to use friction in the game! 491 Including friction stops the players from sliding forever! 492 The sliding players are fine - but the tire drag is causing problems 493 Using components for the tire drag works! 497

The game’s great - but there’s just been a spec change! 506 For added realism, sometimes the players should slip 509 You can change only direction horizontally on a

The game is brilliant, and going to X-Force rocks! 511 Newton’s Laws give you awesome powers 512

Getting on with it

using forces, momentum, friction and impulse

It’s no good memorizing lots of theory if you can’t apply it

You already know about equations of motion, component vectors, momentum conservation, free body diagrams and Newton’s Laws In this chapter, you’ll learn

how to fit all of these things together and apply them to solve a much wider range

of physics problems Often, you’ll spot when a problem is like something you’ve seen before You’ll also add more realism by learning to deal with friction - and will see why it’s sometimes appropriate to act on impulse.

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Do an experiment to determine where to position the fulcrum 521 Zero net torque causes the lever to balance 525 Use torque to lift the sword and the stone! 530 The “Two equations, two unknowns” Question 533

So you lift the sword and stone with the lever

When you move an object against a force, you’re doing work 538 The work you need to do a job = force × displacement 538 Which method involves the least amount of work? 539

Energy is the capacity that something has to do work 542 Lifting stones is like transferring energy from one store to another 542 Energy conservation helps you to solve problems

Will energy conservation save the day? 547 You need to do work against friction as well as against gravity 549 Doing work against friction increases internal energy 551

It’s impossible to be 100% efficient 553

Getting a lift

torque and work

You can use your physics knowledge to do superhuman feats.

In this chapter, you’ll learn how to harness torque to perform amazing displays of strength,

by using a lever to exert a much larger force than you could on your own However, you

can’t get something for nothing - energy is always conserved and the amount of work you do to give something gravitational potential energy by lifting it doesn’t change.

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Forces and component vectors solve the first part

but the second part doesn’t have a uniform slope 563

The kinetic energy is related to the velocity 567 Calculate the velocity using energy conservation

You’ve used energy conservation to solve the second part 571

In the third part, you have to apply a force to stop a moving object 571 Putting on the brake does work on the track 573 Doing work against friction increases the internal energy 574 Energy conservation helps you to do

complicated problems in a simpler way 579 There’s a practical difference between

Momentum conservation will solve an inelastic collision problem 587 You need a second equation for an elastic collision 587 Energy conservation gives you the second equation that you need! 589 Factoring involves putting in parentheses 591 You can deal with elastic collisions now 592

In an elastic collision, the relative velocity reverses 593 There’s a gravity-defying trick shot to sort out 594 The initial collision is inelastic - so mechanical energy isn’t conserved 596 Use momentum conservation for the inelastic part 597

Making your life easier

energy conservation

Why do things the hard way when there’s an easier way?

So far, you’ve been solving problems using equations of motion, forces and component vectors And that’s great - except that it sometimes takes a while to crunch through the

math In this chapter, you’ll learn to spot where you can use energy conservation as a

shortcut that lets you solve complicated-looking problems with relative ease.

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It’s a bird it’s plane no, it’s a guy on a skateboard?! 604

Michael and the stack accelerate at the same rate 608

Look at the big picture as well as the parts 617 But the day before the competition 619 Using energy conservation is simpler than using forces 621

Changing direction

tension, pulleys and problem solving

The center of the target is 15.0 m from the foot of the pier.

Skateboard is pulled along

the pier by the rope.

When the skateboard reaches the end of the pier, Michael continues with velocity v.

v

The mass has just

hit the surface

The competition takes

place when the tide is

in and the sea is 110 m

below the top of the pier.

Here’s what SHOULD happen

Sometimes you need to deal with the tension in a situation

So far, you’ve been using forces, free body diagrams and energy conservation

to solve problems In this chapter you’ll take that further as you deal with ropes,

pulleys, and yes, tension Along the way, you’ll also practise looking for familiar

signposts to help navigate your way through complicated situations.

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A circle’s radius and circumference are linked by π 637 Convert from linear distance to revolutions 639 Convert the linear speeds into Hertz 641

So you set up the machine but the wheel turns too slowly! 643 Try some numbers to work out how things relate to each other 645 The units on the motor are radians per second 646 Convert frequency to angular frequency 651

You can increase the (linear) speed by increasing the wheel’s radius 657

From α to ω

circular motion (part 1)

The center of the target is

15.0 m from the foot of the pier.

Skateboard is pulled along

the pier by the rope.

When the skateboard reaches the end of the pier, Michael

continues with velocity v.

v

The mass has just

hit the surface

and hit the bullseye.

The competition takes

place when the tide is

in and the sea is 110 m

below the top of the pier.

Here’s what SHOULD happen

Hey kiddo, this Kentucky Hamster Derby is big business, and we gotta get the training schedule absolutely spot on!

Billionaire hamster owner

Distance (km) Speed (km/h) Total number

of revolutions Motor setting ( )

15.0 3.0 10.0 4.0 2.0 5.5

0 5 10 15 20 25

You say you want a revolution? In this chapter, you’ll learn

how to deal with circular motion with a crash course in circle anatomy, including what the radius and circumference have to do with pies (or

should that be πs) After dealing with frequency and period, you’ll need

to switch from the linear to the angular But once you’ve learned to use radians to measure angles, you’ll know it’s gonna be alright.

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When you’re in freefall, objects appear to float beside you 666 What’s the astronaut missing, compared to when he’s on Earth? 667 Can you mimic the contact force you feel on Earth? 669 Accelerating the space station allows you

You can only go in a circle because of a centripetal force 674 Centripetal force acts towards the center of the circle 677 The astronaut experiences a contact force when you

What affects the size of centripetal force? 679 Spot the equation for the centripetal acceleration 681 Give the astronauts a centripetal force 683 The floor space is the area of a cylinder’s curved surface 686

Angling the track gives the normal force a horizontal component 697 When you slide downhill, there’s no perpendicular acceleration 698 When you turn a corner, there’s no vertical acceleration 699 How to deal with an object on a slope 700 The “support force” required for a vertical circle varies 704 Any force that acts towards the center of the circle

Staying on track

circular motion (part 2)

The astronauts are tir ed

of floating They want

gravity in space!

Ever feel like someone’s gone off at a tangent? That’s exactly what

happens when you try to move an object along a circular path when there’s not enough centripetal force to enable this to happen In this chapter, you’ll learn exactly what

centripetal force is and how it can keep you on track Along the way, you’ll even solve some pretty serious problems with a certain Head First space station So what are you waiting for? Turn the page, and let’s get started.

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The surface area of the sphere is the same as

Earth’s gravitational force on you becomes weaker

Gravitation is an inverse square law 735 Now you can calculate the force on the spaceship

The potential energy is the area under the force-displacement graph 743

If U = 0 at infinity, the equation works for any star or planet 745

Use energy conservation to calculate the astronaut’s escape velocity 747

We need to keep up with our astronaut 751 The centripetal force is provided by gravity 754 With the comms satellites in place, it’s Pluto (and beyond) 757 The “gravitational force = centripetal force” Question 758

Getting away from it all

gravitation and orbits

So far, you’ve been up close and personal with gravity - but what happens to the attraction as your feet leave the ground? In this chapter, you’ll learn that

gravitation is an inverse square law, and harness the power of gravitational potential

to take a trip to infinity and beyond Closer to home, you’ll learn how to deal with orbits - and learn how they can revolutionize your communication skills.

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The screen for the game is TWO-DIMENSIONAL 769

So we know what the duck does but where exactly is the duck? 773 Any time you’re dealing with a component vector,

The second player sees the x-component of the duck’s displacement 783

We need a wider definition of cosine, too 784 sine and cosine are related to each other 785

What’s the duck’s velocity from each player’s point of view? 789 Get the shape of the velocity-time graph from

the slope of the displacement-time graph 790

Round and round

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20

The plant rocker needs to work for three different masses of plant 798

A spring will produce regular oscillations 799 Displacement from equilibrium and

strength of spring affect the force 801

A mass on a spring moves like a side-on view of circular motion 805

A mass on a spring moves with simple harmonic motion 806 Simple harmonic motion is sinusoidal 809 Work out constants by comparing a situation-specific

The “This equation is like that one” Question 813 Anne forgot to mention something 815

But now the plant rocker’s frequency has changed 822 The frequency of a horizontal spring depends on the mass 824 Will using a vertical spring make a difference? 824

A pendulum swings with simple harmonic motion 830 What does the frequency of a pendulum depend on? 831

The “How does this depend on that” Question 836

springs and pendulums that move with simple harmonic motion to get the

ultimate “I rule” experience without having to repeat yourself too much.

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21

The round-trip looks like simple harmonic motion 842 But what time does the round-trip take? 843 You can treat the Earth like a sphere and a shell 845 The net force from the shell is zero 850 The force is proportional to the displacement, so your trip is SHM 853 The “Equation you’ve never seen before” Question 855 You know your average speed - but what’s your top speed? 857 Circular motion from side-on looks like simple harmonic motion 858

It’s the final chapter

think like a physicist

It’s time to hit the ground running Throughout this book, you’ve been

learning to relate physics to everyday life and have absorbed problem solving skills as you’ve gone along In this final chapter, you’ll use your new set of physics tools to dig

into the problem we started off with - the bottomless pit through the center of the earth The key is the question: “How can I use what I know to work out what I don’t know (yet)?”

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xxxi

i

#1 Equation of a straight line graph, y = mx + c 864

#2 Displacement is the area under the velocity-time graph 866

look at as we went along, but are still important and useful.

It’s difficult to remember something when you’ve only seen it once

Equations are a major way of describing what’s going on in physics Every time you use equations to help solve a problem, you naturally start to become familiar

with them without the need to spend time doing rote memorization But

before you get to that stage, it’s good to have a place you can look up the equation you want to use That’s what this equation table appendix

is for - it’s a point of reference that you can turn to at any time.

Learn

Practice Practice Practice Practice

Trigonometry

Pythagoras hyp 2 = opp 2 + adj 2

Sine sin (θ) = opphyp

Cosine cos (θ) = adjhyp

Tangent tan (θ) = oppadj

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Intro

In this section we answer the burning question:

“So why DID they put that in a physics book?”

I can’t believe they put that in a physics book?”

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xxxiv intro

how to use this book

Who is this book for?

Who should probably back away from this book?

If you can answer “yes” to all of these:

Don’t worry if you’re missing the calculator - they only cost a few dollars.

If you can answer “yes” to any of these:

this book is for you

this book is not for you

[Note from marketing: this book is

for anyone with the cash to buy it.]

Do you have access to a pen and a scientific calculator?

1

Do you want to learn and understand physics by doing, rather than by reading, whether you need to pass an exam at the end or not?

2

Do you prefer chatting with friends about interesting things to dry, dull, academic lectures?

3

Are you someone who’s never studied basic algebra?

(You don’t need to be advanced, but you should be able to add, subtract, multiply and divide We’ll cover everything else you need to know about math and physics.)

1

Are you a physics ninja looking for a reference book?

2

Are you afraid to try something different? Would you

rather have a root canal than mix stripes with plaid?

Do you believe that a physics book can’t be serious

if it involves implementing a training schedule for thoroughbred hamster racing?

3

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you are here 4 xxxv

the intro

“How can this be a serious physics book?”

“What’s with all the graphics?”

“Can I actually learn it this way?”

Your brain craves novelty It’s always searching, scanning, waiting for something

unusual It was built that way, and it helps you stay alive

So what does your brain do with all the routine, ordinary, normal things you

encounter? Everything it can to stop them from interfering with the brain’s

real job—recording things that matter It doesn’t bother saving the boring

things; they never make it past the “this is obviously not important” filter

How does your brain know what’s important? Suppose you’re out for a

day hike and a tiger jumps in front of you, what happens inside your head

and body?

Neurons fire Emotions crank up Chemicals surge

And that’s how your brain knows

This must be important! Don’t forget it!

But imagine you’re at home, or in a library It’s a safe, warm, tiger-free zone

You’re studying Getting ready for an exam Or trying to learn some tough

technical topic your boss thinks will take a week, ten days at the most

Just one problem Your brain’s trying to do you a big favor It’s trying

to make sure that this obviously non-important content doesn’t clutter

up scarce resources Resources that are better spent storing the really

big things Like tigers Like the danger of fire Like how you should

never have posted those photos on your Facebook page

And there’s no simple way to tell your brain, “Hey brain, thank you

very much, but no matter how dull this book is, and how little I’m

registering on the emotional Richter scale right now, I really do want

you to keep this stuff around.”

We know what you’re thinking

We know what your brain is thinking

Your brain think

s THIS is important.

saving.

Great Only 880 more dull, dry, boring pages.

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xxxvi intro

Weight

Normal force

θ

So what does it take to learn something? First, y

ou have to get it, then mak e sure you don’t forget it It’s not a bout pushing facts into y

our head Based on th e latest research in cognitiv e science, neurobiology

, and educational psyc hology,

learning takes a lot mor e than text on a page W

e know what turns your br ain on.

Some of the Head First lear ning principles:

Make it visual. Images are far more memorable than words alone, and

make learning much more effective (up to 89% imp

rovement in recall and transfer studies). It also makes things more understandable. Put the

words within or near t he graphics they relate

to, rather than on the bottom or on another page, and learners will be up to twice as likely to solve problems related to the content.

Use a conversational and personalized style . In recent studies,

students performed up to 40% better on post-learning tests if the content sp

oke directly

to the reader, using a first-person, conversational style rather than taking a fo

rmal tone. Tell stories instead of lecturing. Use casual language. Don’t take yoursel

to solve problems, draw conclusions, and generate new knowledge. And for that, you need challenge

s, exercises, and thought-provoking questions, and activities that involve both

sides of the brain and multiple senses.

Get—and keep—the re ader’s attention. We’ve all had the “I really want

to learn this but

I can’t stay awake past page one” experience. Your brain pays attention to th

ings that are out of the ordinary, interesting, strange, eye-catching, unexpected. Learning a new, to

ugh, technical topic doesn’t have to be boring. Your brain will learn

ing stories about a boy and his dog. We’re talking emotions like surprise, curiosi

ty,

fun, “what the ?” , and the feeling of “I Rule!” that comes when you solve

a puzzle, learn something everybody else thinks is hard, or realize you know something that “I’m more technical than thou” Bob from engineering doesn’t

.

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you are here 4 xxxvii

If you really want to learn, and you want to learn more quickly and more

deeply, pay attention to how you pay attention Think about how you think

Learn how you learn

Most of us did not take courses on metacognition or learning theory when we

were growing up We were expected to learn, but rarely taught to learn.

But we assume that if you’re holding this book, you really want to learn how

to do physics And you probably don’t want to spend a lot of time If you want

to use what you read in this book, you need to remember what you read And

for that, you’ve got to understand it To get the most from this book, or any book

or learning experience, take responsibility for your brain Your brain on this

content

The trick is to get your brain to see the new material you’re learning as

Really Important Crucial to your well-being As important as a tiger

Otherwise, you’re in for a constant battle, with your brain doing its best to

keep the new content from sticking

So just how DO you get your brain to treat physics

like it was a hungry tiger?

There’s the slow, tedious way, or the faster, more effective way The

slow way is about sheer repetition You obviously know that you are able to learn

and remember even the dullest of topics if you keep pounding the same thing into your

brain With enough repetition, your brain says, “This doesn’t feel important to him, but he

keeps looking at the same thing over and over and over, so I suppose it must be.”

The faster way is to do anything that increases brain activity, especially different

types of brain activity The things on the previous page are a big part of the solution,

and they’re all things that have been proven to help your brain work in your favor For

example, studies show that putting words within the pictures they describe (as opposed to

somewhere else in the page, like a caption or in the body text) causes your brain to try to

makes sense of how the words and picture relate, and this causes more neurons to fire

More neurons firing = more chances for your brain to get that this is something worth

paying attention to, and possibly recording

A conversational style helps because people tend to pay more attention when they

perceive that they’re in a conversation, since they’re expected to follow along and hold up

their end The amazing thing is, your brain doesn’t necessarily care that the “conversation”

is between you and a book! On the other hand, if the writing style is formal and dry, your

brain perceives it the same way you experience being lectured to while sitting in a roomful

of passive attendees No need to stay awake

But pictures and conversational style are just the beginning…

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xxxviii intro

Here’s what WE did:

We used pictures, because your brain is tuned for visuals, not text As far as your brain’s

concerned, a picture really is worth a thousand words And when text and pictures work

together, we embedded the text in the pictures because your brain works more effectively

when the text is within the thing the text refers to, as opposed to in a caption or buried in the

text somewhere

We used redundancy, saying the same thing in different ways and with different media types,

and multiple senses, to increase the chance that the content gets coded into more than one area

of your brain

We used concepts and pictures in unexpected ways because your brain is tuned for novelty,

and we used pictures and ideas with at least some emotional content, because your brain

is tuned to pay attention to the biochemistry of emotions That which causes you to feel

something is more likely to be remembered, even if that feeling is nothing more than a little

humor , surprise, or interest.

We used a personalized, conversational style, because your brain is tuned to pay more

attention when it believes you’re in a conversation than if it thinks you’re passively listening

to a presentation Your brain does this even when you’re reading.

We included more than 80 activities, because your brain is tuned to learn and remember

more when you do things than when you read about things And we made the exercises

challenging-yet-do-able, because that’s what most people prefer.

We used multiple learning styles, because you might prefer step-by-step procedures, while

someone else wants to understand the big picture first, and someone else just wants to see

an example But regardless of your own learning preference, everyone benefits from seeing the

same content represented in multiple ways

We include content for both sides of your brain, because the more of your brain you

engage, the more likely you are to learn and remember, and the longer you can stay focused

Since working one side of the brain often means giving the other side a chance to rest, you

can be more productive at learning for a longer period of time

And we included stories and exercises that present more than one point of view,

because your brain is tuned to learn more deeply when it’s forced to make evaluations and

judgments

We included challenges, with exercises, and by asking questions that don’t always have

a straight answer, because your brain is tuned to learn and remember when it has to work at

something Think about it—you can’t get your body in shape just by watching people at the

gym But we did our best to make sure that when you’re working hard, it’s on the right things

That you’re not spending one extra dendrite processing a hard-to-understand example,

or parsing difficult, jargon-laden, or overly terse text

We used people In stories, examples, pictures, etc., because, well, because you’re a person

And your brain pays more attention to people than it does to things

If the restoring force

is proportional to the displacement, you have simple harmonic motion (abbreviated to SHM) SHM looks like circular motion from side on, and the equations for the displacement, velocity and acceleration are all sinusoidal (shaped like a sine or cosine graph).

For a spring, the period depends on the mass

a point where you require calculus So use energy to solve SHM problems where you can.

The kinetic energy in the equilibrium position (where the force and displacement are



Kinetic Potential

Potential

Your Physics Toolbox

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