Head First Physics. A learner's companion to mechanics and practical physics (AP Physics B - Advanced Placement) Heather Lang

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• Head First Physics: A learners companion to mechanics and practical physics
• Dedication
• A Note Regarding Supplemental Files
• Advance Praise for Head First Physics
• Praise for other Head First academic titles
• Praise for the Head First Approach
•  
• Author of Head First Physics
• How to Use this Book: Intro
  • Who is this book for?
    • Who should probably back away from this book?
  • We know what youre thinking
  • We know what your brain is thinking
  • Metacognition: thinking about thinking
  • Heres what WE did:
  • Heres what YOU can do to bend your brain into submission
  • Read Me
  • The technical review team
• Acknowledgments
  • Safari Books Online
• 1. Think Like a Physicist: In the beginning ...
  • Physics is the world around you
  • You can get a feel for whats happening by being a part of it
    • So - could you ever escape from the bottomless pit?
  • Use your intuition to look for special points
  • The center of the earth is a special point
  • Ask yourself What am I ALREADY doing as I reach the special point?
  • Where youre at - and what happens next?
  • Now put it all together
  • Your Physics Toolbox
• 2. Making it all MEAN Something: Units and measurements
  • Its the best music player ever, and youre part of the team!
  • So you get on with measuring the myPod case
  • When the myPod case comes back from the factory...
  • ...its waaay too big!
  • There arent any UNITS on the blueprint
  • Youll use SI units in this book (and in your class)
  • You use conversion factors to change units
  • You can write a conversion factor as a fraction
  • Now you can use the conversion factor to update the blueprint
  • You just converted the units for the entire blueprint!
  • But theres STILL a problem ...
  • What to do with numbers that have waaaay too many digits to be usable
  • How many digits of your measurements look significant?
  • Generally, you should round your answers to three significant digits
    • You need to follow certain rules when youre rounding answers
  • Is it OK to round the myPod blueprint to three significant digits?
  • You ALREADY intuitively rounded your original myPod measurements!
  • Any measurement you make has an error (or uncertainty) associated with it
  • The error on your original measurements should propagate through to your converted blueprint
  • Right! Time to attack the blueprint again!
  • STOP!! Before you hit send, do your answers SUCK?!
  • You nailed it!
  • When you write down a measurement, you need the right number of significant digits
  • Your Physics Toolbox
• 3. Scientific Notation, Area, and Volume: All numbers great and small
  • A messy college dorm room
  • So how long before things go really bad?
  • Power notation helps you multiply by the same number over and over
    • Your calculators power button gives you superpowers
  • Your calculator displays big numbers using scientific notation
  • Scientific notation uses powers of 10 to write down long numbers
  • Scientific notation helps you with small numbers as well
  • Youll often need to work with area or volume
  • Look up facts in a book (or table of information)
  • Prefixes help with numbers outside your comfort zone
  • Scientific notation helps you to do calculations with large and small numbers
  • The guys have it all worked out
  • 200,000,000 meters cubed bugs after only 16 hours is totally the wrong size of answer!
  • Be careful converting units of area or volume
  • So the bugs wont take over ... unless the guys sleep in!
  • Question Clinic: The Converting units of area or volume Question
  • Your Physics Toolbox
• 4. Equations and Graphs: Learning the lingo
  • The new version of the Break Neck Pizza website is nearly ready to go live ...
  • ...but you need to work out how to give the customer their delivery time
  • If you write the delivery time as an equation, you can see whats going on
  • Use variables to keep your equation general
  • You need to work out Alexs cycling time
  • When you design an experiment, think about what might go wrong!
  • OK - time to recap where youre at...
  • Conduct an experiment to find out Alexs speed
    • Heres what happens:
  • Write down your results... in a table
  • Use the table of distances and times to work out Alexs speed
  • Random errors mean that results will be spread out
  • A graph is the best way of taking an average of ALL your results
  • Use a graph to show Alexs time for ANY distance
  • The line on the graph is your best estimate for how long Alex takes to cycle ANY distance
  • You can see Alexs speed from the steepness of the distance-time graph
  • Alexs speed is the slope of the distance-time graph
  • Now work out Alexs average speed from your graph
  • You need an equation for Alexs time to give to the web guys
  • Rearrange the equation to say time = something
  • Use your equation to work out the time it takes Alex to reach each house
  • So you do a test run with the website ...
  • So just convert the units, and youre all set...right?
  • Include the cooking time in your equation
  • The Break Neck website goes live, and the customers love it!
  • A few weeks later, you hear from Break Neck again
  • A graph lets you see the difference the stop lights made
  • The stop lights change Alexs average speed
  • Add on two minutes per stop light to give the customer a maximum delivery time ...
  • ...the customers are extremely happy ...
  • ...and youre invited to the Pizza Party
  • Question Clinic: The Did you do what they asked you Question
  • Your Physics Toolbox
• 5. Dealing with Directions: Vectors
  • The treasure hunt
  • Displacement is different from distance
  • Distance is a scalar; displacement is a vector
  • You can represent vectors using arrows
  • You found the next clue...
    • But theres a problem ...
  • You can add vectors in any order
  • Well done - youve found the third clue!
  • Question Clinic: The Wheat from the chaff Question
  • Angles measure rotations
  • Now you can get on with clue 3!
  • If you cant deal with something big, break it down into smaller parts
  • You move onto the fourth clue...
  • Velocity is the vector version of speed
  • Write units using shorthand
  • So, on to clue 4 ...
  • You need to allow for the streams velocity too!
  • If you can find the streams velocity, you can figure out the velocity for the boat
  • It takes the boat time to accelerate from a standing start
  • How do you deal with acceleration?
  • So its back to the boat ...
  • Vector, Angle, Velocity, Acceleration = WINNER!!!
  • Your Physics Toolbox
  • Question Clinic: The Design an experiment Question
• 6. Displacement, Velocity, and Acceleration: Whats going on?
  • Just another day in the desert ...
  • ...and another Dingo-Emu moment!
  • How can you use what you know?
  • The cage accelerates as it falls
  • Vectorize your equation
  • You want an instantaneous velocity, not an average velocity
  • You already know how to calculate the slope of a straight line...
  • A point on a curved line has the same slope as its tangent
  • The slope of somethings velocity-time graph lets you work out its acceleration
  • Work out the units of acceleration
  • Success! You worked out the velocity after 2.0 s - and the cage wont break!
  • Now onto solve for the displacement!
  • Your Physics Toolbox
• 7. Equations of motion (part 1): Playing With Equations
  • How high should the crane be?
  • Graphs and equations both represent the real world
  • Youre interested in the start and end points
  • You have an equation for the velocity - but what about the displacement?
  • See the average velocity on your velocity-time graph
  • Test your equations by imagining them with different numbers
  • Calculate the cages displacement!
  • You know how high the crane should be!
  • But now the Dingo needs something more general
  • A substitution will help
  • Get rid of the variables you dont want by making substitutions
  • Continue making substitutions ...
  • You did it - you derived a useful equation for the cages displacement!
  • Check your equation using Units
  • Check your equation by trying out some extreme values
  • Your equation checks out!
  • Question Clinic: The Substitution Question
  • Question Clinic: The Units or Dimensional analysis Question
  • Think like a physicist!
  • Your Physics Toolbox
• 8. Equations of Motion (Part 2): Up, up, and... back down
  • Previously ...
  • Now ACME has an amazing new cage launcher
  • The acceleration due to gravity is constant
  • Velocity and acceleration are in opposite directions, so they have opposite signs
  • You can use one graph to work out the shapes of the others
  • Is a graph of your equation the same shape as the graph you sketched?
  • Ready to launch the cage!
    • Your launch velocity of 5.0 m/s is definitely right!
  • Fortunately, ACME has a rocket-powered hovercraft!
  • You can work out a new equation by making a substitution for t
  • Multiply out the parentheses in your equation
    • You can sort out one of the terms on the right hand side like this
  • You have two sets of parentheses multiplied together
    • Then you can figure out your second term on the right hand side
  • Where youre at with your new equation
  • You need to simplify your equation by grouping the terms
  • You can use your new equation to work out the stopping distance
  • There are THREE key equations you can use when theres constant acceleration
  • You need to work out the launch velocity that gets the Dingo out of the Grand Canyon!
  • The launch velocitys right!
  • You need to find another way of doing this problem
  • Question Clinic: The Sketch a graph or Match a graph Question
  • Question Clinic: The Symmetry and Special points Questions
  • Your Physics Toolbox
• 9. Triangles, Trig and Trajectories: Going two-dimensional
  • Camelot - we have a problem!
  • How wide should you make the moat?
  • Looks like a triangle, yeah?
  • A scale drawing can solve problems
  • Pythagoras Theorem lets you figure out the sides quickly
  • Sketch + shape + equation = Problem solved!
  • You kept them out!
  • But the attackers get smarter!
  • Camelot ... we have ANOTHER problem!
  • Relate your angle to an angle inside the triangle
  • Classify similar triangles by the ratios of their side lengths
  • Sine, cosine and tangent connect the sides and angles of a right-angled triangle
  • How to remember which ratio is which??
  • Calculators have sin(), cos() and tan() tables built in
  • Back at the castle, everyones depending on you!
  • You can know everything! *
  • Does your answer SUCK?
  • Uh oh. Gravity...
  • The cannonballs velocity and acceleration vectors point in different directions
  • Gravity accelerates everything downwards at 9.8 m/s2
  • The horizontal component of the velocity cant change once youve let go
  • The horizontal component of a projectiles velocity is constant
  • The same method solves both problems
  • Question Clinic: The Projectile Question
  • And so they ran away ...
  • Question Clinic: The Missing steps Question
  • Your Physics Toolbox
• 10. Momentum Conservation: What Newton Did
  • The pirates be havin a spot o bother with a ghost ship ...
  • What does the maximum range depend on?
  • Firing at 45° maximizes your range
  • You cant do everything thats theoretically possible - you need to be practical too
  • Sieges-R-Us has a new stone cannonball, which they claim will increase the range!
  • Massive things are more difficult to start off
  • Massive things are more difficult to stop
  • Newtons First Law
  • Mass matters
  • A stone cannonball has a smaller mass - so it has a larger velocity. But how much larger?
  • Heres your lab equipment
  • How are force, mass and velocity related?
  • Vary only one thing at a time in your experiment
  • Mass x velocity - momentum - is conserved
  • A greater force acting over the same amount of time gives a greater change in momentum
  • Write momentum conservation as an equation
  • Momentum conservation and Newtons Third Law are equivalent
  • Youve calculated the stone cannonballs velocity...
  • ...but you want the new range!
  • Use proportion to work out the new range
  • You solved the pirates problem!
  • Question Clinic: The Proportion Question (often multiple choice)
  • Your Physics Toolbox
• 11. Weight and the normal force: Forces for courses
  • WeightBotchers are at it again!
  • Is it really possible to lose weight instantly?!
  • Scales work by compressing or stretching a spring
  • Mass is a measurement of stuff
  • Weight is a force
  • The relationship between force and mass involves momentum
  • If the objects mass is constant, Fnet = ma
  • The scales measure the support force
  • Now you can debunk the machine!
  • The machine reduces the support force
  • Force pairs help you check your work
  • You debunked WeightBotchers!
  • But WeightBotchers are back!
  • A surface can only exert a force perpendicular (or normal) to it
  • When you slide downhill, theres zero perpendicular acceleration
  • Use parallel and perpendicular force components to deal with a slope
  • Another fake busted!
  • Question Clinic: The Free body diagram Question
  • Question Clinic: The Free body diagram Question
  • Your Physics Toolbox
• 12. Using forces, momentum, friction and impulse: Getting on with it
  • Its ... SimFootball!
  • Momentum is conserved in a collision
  • But the collision might be at an angle
  • A triangle with no right angles is awkward
  • Use component vectors to create some right-angled triangles
  • The programmer includes 2D momentum conservation ...
  • ...but the players keep on sliding for ever!
  • In real life, the force of friction is present
  • Friction depends on the types of surfaces that are interacting
  • Friction depends on the normal force
  • Be careful when you calculate the normal force
  • Youre ready to use friction in the game!
  • Including friction stops the players from sliding forever!
  • The sliding players are fine - but the tire drag is causing problems
  • Using components for the tire drag works!
  • Question Clinic: The Friction Question
  • How does kicking a football work?
  • Ft is called impulse
  • The games great - but theres just been a spec change!
  • The strength of the moons gravitational field is lower then the Earths
  • For added realism, sometimes the players should slip
  • You can change only direction horizontally on a flat surface because of friction
  • The game is brilliant, and going to X-Force rocks!
  • Newtons Laws give you awesome powers
  • Your Physics Toolbox
• 13. Torque and Work: Getting a lift
  • Half the kingdom to anyone who can lift the sword in the stone ...
  • Can physics help you to lift a heavy object?
  • Use a lever to turn a small force into a larger force
  • Do an experiment to determine where to position the fulcrum
  • Zero net torque causes the lever to balance
  • Use torque to lift the sword and the stone!
  • Question Clinic: The Two equations, two unknowns Question
  • So you lift the sword and stone with the lever ...
  • ...but they dont go high enough!
  • You cant get something for nothing
  • When you move an object against a force, youre doing work
  • The work you need to do a job = force x displacement
  • Which method involves the least amount of work?
  • Work has units of Joules
  • Energy is the capacity that something has to do work
  • Lifting stones is like transferring energy from one store to another
  • Energy conservation helps you to solve problems with differences in height
  • One of our stackable stones is missing ...
  • Will energy conservation save the day?
  • You need to do work against friction as well as against gravity
  • Doing work against friction increases internal energy
  • Heating increases internal energy
  • Its impossible to be 100% efficient
  • Your Physics Toolbox
• 14. Energy Conservation: Making your life easier
  • The ultimate bobsled experience
  • Forces and component vectors solve the first part ...
  • ...but the second part doesnt have a uniform slope
  • A moving object has kinetic energy
  • The kinetic energy is related to the velocity
  • Calculate the velocity using energy conservation and the change in height
  • Youve used energy conservation to solve the second part
  • In the third part, you have to apply a force to stop a moving object
  • Putting on the brake does work on the track
  • Doing work against friction increases the internal energy
  • Energy conservation helps you to do complicated problems in a simpler way
  • Theres a practical difference between momentum and kinetic energy
  • Question Clinic: The Show that Question
  • Question Clinic: The Energy transfer Question
  • After the roaring success of SimFootball, its time for SimPool
    • Reusing the old code makes the pool balls stick together!
  • Momentum conservation will solve an inelastic collision problem
  • You need a second equation for an elastic collision
  • Energy conservation gives you the second equation that you need!
  • Factoring involves putting in parentheses
  • You can deal with elastic collisions now
  • In an elastic collision, the relative velocity reverses
  • The pool ball collisions work!
  • Theres a gravity-defying trick shot to sort out ...
  • Where is the problem with the programmers reasoning?
  • The initial collision is inelastic - so mechanical energy isnt conserved
  • Use momentum conservation for the inelastic part
  • Question Clinic: The Ballistic pendulum Question
  • Your Physics Toolbox
• 15. Tension, Pulleys and Problem Solving: Changing direction
  • Its a bird... its plane...
  • ...no, its... a guy on a skateboard?!
  • Always look for something familiar
  • Michael and the stack accelerate at the same rate
  • Use tension to tackle the problem
  • Look at the big picture as well as the parts
  • But the day before the competition ...
  • Using energy conservation is simpler than using forces
  • There goes that skateboard...
  • Your Physics Toolbox
• 16. Circular Motion (Part 1): From to
  • Limber up for the Kentucky Hamster Derby
  • You can revolutionize the hamsters training
  • Thinking through different approaches helps
  • A circles radius and circumference are linked by
  • Convert from linear distance to revolutions
  • Convert the linear speeds into Hertz
  • So you set up the machine ...
  • ...but the wheel turns too slowly!
  • Try some numbers to work out how things relate to each other
    • What if you set the motor to 1.0?
    • What if the wheel goes at 1.0 Hz?
  • The units on the motor are radians per second
  • Convert frequency to angular frequency
  • The hamster trainer is complete!
  • A couple of weeks later ...
  • You can increase the (linear) speed by increasing the wheels radius
  • Question Clinic: The Angular quantities Question
  • Your Physics Toolbox
• 17. Circular Motion (Part 2) Staying on track
  • Houston ... we have a problem
  • When youre in freefall, objects appear to float beside you
  • Whats the astronaut missing, compared to when hes on Earth?
  • Can you mimic the contact force you feel on Earth?
  • Accelerating the space station allows you to experience a contact force
  • You can only go in a circle because of a centripetal force
  • Centripetal force acts towards the center of the circle
  • The astronaut experiences a contact force when you rotate the space station
  • What affects the size of centripetal force?
  • Spot the equation for the centripetal acceleration
  • Give the astronauts a centripetal force
  • The astronauts want as much floor space as possible
  • Here, the floor space is the area of a cylinders curved surface
  • If you work out the volume, you can calculate the astronauts floor space
  • Lets test the space station...
    • Cant cope with rotation
    • Apple falls straight while space station rotates
    • Head and feet at different radii
  • Fewer uncomfortable things happen with the 100 m radius space station
  • Youve sorted out the space station design!
  • Question Clinic: The Centripetal force Question
  • Back to the track!
  • The bobsled needs to turn a corner
  • Angling the track gives the normal force a horizontal component
  • When you slide downhill, theres no perpendicular acceleration
  • When you turn a corner, theres no vertical acceleration
  • How to deal with an object on a slope
  • Banking the track works ...
  • ...but now they want it to loop-the-loop!
  • The support force (normal force or tension force) required for a vertical circle varies
  • Any force that acts towards the center of the circle can provide a centripetal force
  • How fast does the bobsled need to go?
  • Question Clinic: The Banked curve Question
  • Question Clinic: The Vertical circle Question
  • Your Physics Toolbox
• 18. Gravitation and Orbits: Getting away from it all
  • Party planners, a big event, and lots of cheese
  • What length should the cocktail sticks be?
  • The cheese globe is a sphere
  • The surface area of the sphere is the same as the surface area of the cheese
  • Let there be cheese...
  • ...but there are gaps in the globe!
  • The partys on!
  • To infinity - and beyond!
  • Earths gravitational force on you becomes weaker as you go further away
  • Gravitation is an inverse square law
  • Now you can calculate the force on the spaceship at any distance from the Earth
  • The potential energy is the area under the force-displacement graph
  • If U = 0 at infinity, the equation works for any star or planet
  • Use energy conservation to calculate the astronauts escape velocity
  • We need to keep up with our astronaut
  • The centripetal force is provided by gravity
  • With the comms satellites in place, its Pluto (and beyond)
  • Question Clinic: The gravitational force = centripetal force Question
  • Your Physics Toolbox
• 19. Oscillations (Part 1): Round and round
  • Welcome to the fair!
  • Reproduce the duck on the display
  • The screen for the game is TWO-DIMENSIONAL
  • So we know what the duck does...
  • ...but where exactly is the duck?
  • Any time youre dealing with a component vector, try to spot a right-angled triangle
  • Lets show Jane the display
  • The second player sees the x-component of the ducks displacement
  • We need a wider definition of cosine, too
  • sine and cosine are related to each other
  • Let the games begin!
  • Janes got another request: Whats the ducks velocity from each players point of view?
  • Get the shape of the velocity-time graph from the slope of the displacement-time graph
  • The game is complete!
  • Your Physics Toolbox
• 20. Oscillations (Part 2): Springs n swings
  • Get rocking, not talking
  • The plant rocker needs to work for three different masses of plant
  • A spring will produce regular oscillations
  • Displacement from equilibrium and strength of spring affect the force
  • A mass on a spring moves like a side-on view of circular motion
  • A mass on a spring moves with simple harmonic motion
  • Simple harmonic motion is sinusoidal
  • Work out constants by comparing a situation-specific equation with a standard equation
    • Look at the amplitude
    • Look at the argument of the cosine
  • Question Clinic: The This equation is like that one Question
  • You rock! Or at least Annes plants do
  • But Anne forgot to mention someting ...
  • The plants rock - and you rule!
  • But now the plant rockers frequency has changed ...
  • The frequency of a horizontal spring depends on the mass
  • Will using a vertical spring make a difference?
  • A pendulum swings with simple harmonic motion
  • What does the frequency of a pendulum depend on?
  • The pendulum design works!
  • Question Clinic: The Vertical spring Question
  • Question Clinic: The How does this depend on that Question
  • Your Physics Toolbox
• 21. Think Like a Physicist: Its the final chapter
  • Youve come a long way!
  • Now you can finish off the globe
  • The round-trip looks like simple harmonic motion
  • But what time does the round-trip take?
  • You can treat the Earth like a sphere and a shell
  • The net force from the shell is zero
  • The force is proportional to the displacement, so your trip is SHM
  • Question Clinic: The Equation youve never seen before Question
  • You know your average speed - but whats your top speed?
  • Circular motion from side on looks like simple harmonic motion
  • You can do (just about) anything!
• A. Leftovers: The top 6 things (that we didnt cover before, but are covering now)
  • #1 Equation of a straight line graph, y = mx + c
  • #2 Displacement is the area under the velocity-time graph
  • #3 Torque on a bridge
  • #4 Power
  • #5 Lots of practice questions
  • #6 Exam tips
• B. Equation Table: Point of Reference
  • Mechanics equation table
• Index
• About the Author
• Copyright

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