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Chapter 1. think like a physicist

Chapter 1. think like a physicist

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welcome to the world of physics



Physics is the world around you

Physics is about the world around you and how stuff in the world actually

works. How do you aim a cannon with no direct line of sight? How can

a satellite orbit the earth without falling back down? Will you win a prize

shooting ducks at the fairground? Will the Dingo catch the Emu...

All of this should be really interesting... except that opening a normal physics

textbook can make you feel rather like you’ve just fallen into a bottomless pit....



...and fall right on in!



...

Open a normal physics textbook



(not a word that

can be used for

Head First Physics!)



Units



Falling



Energy Conservation

Scalar



Inelastic collision



Special points



Frequency



Centripetal force

Angular frequency

Component



Weight

Spring



Gravitational field



Momentum conservation

Impulse

Equation



I don’t

get it!



Torque



Elastic potential energy

Constant acceleration

Distance



Scientific notation

Displacement

Friction



Trigonometry

Angular velocity



Kinetic energy

Symmetry



Freefall

Slope



Internal energy

Area



But there’s hope, because...



Circumference

Inverse square law

Acceleration



Graph



Experiment



Period



Force



Elastic collision



Pendulum



Simple Harmonic Motion

Pythagoras

Substitution

Pulley



Time



Tension



Energy



Equations of motion



Radians



Normal force



Be part of it



Vector



Speed



Gravitational potential energy

Mechanical energy

Velocity

Radius

Work



Volume



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Power



Free body diagram

Newton’s Laws



Does it SUCK?

Mass



Amplitude



think like a physicist



You already know more

than you think you do!

Honest!

I sure hope so

- feeling like I’m

stuck really stinks!



Imagine you’re part of a physics problem.

What would you feel?

You can get a feel for what’s going on by being a part of it.



Places where important or interesting things happen.

You can use your intuition to spot special points.



Where have you seen or experienced something like this before?

You can use your life experience to spot what things are like.



You don’t pass physics by memorizing things.

You pass physics by learning how to think about it.



This book is all about learning to think like a physicist.

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can you feel it?



You can get a feel for what’s happening by being a part of it

The best way to get started with any kind of physics is to imagine

that you’re there, in the middle of it. Maybe you’re a block, or a

car, or a racing driver. Then ask yourself, “What would I feel?”

Which direction am I moving in?

Am I speeding up or slowing down?

Is there anything pushing or pulling me?





Go to the start of

the problem then

BE a part of it!



(and so on...)



Be a part of it!



So - could you ever escape from the bottomless pit?

Suppose you really are falling into a bottomless pit that runs from

one side of the world to the other. What do you think would happen

(assuming that the earth isn’t hot and molten inside)?

Not sure where to start? That’s okay ... break it down and go right

back to the beginning. Be a part of the problem! Ask yourself,

“What would I feel just after I step into the tunnel?”



BE part of it



Your job is to imagine you just stepped

out over a bottomless pit. What would

you feel if you were part of the scenario?

Which direction are you moving

in? Are you speeding up or

slowing down?

WHY are you feeling that?



You’ve just

stepped over

the edge.



DIRECTION:

SPEED:



WHY:



Ask yourself, “What would I FEEL if I was part of the scenario?”

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think like a physicist



BE part of it - Solution



Your job is to imagine you just stepped

out over a bottomless pit. What would

you feel if you were part of the scenario?

Which direction are you moving

in? Are you speeding up or

slowing down?

WHY are you feeling that?



Normally the solutions are

visible when you’re working n’t

the problem... but we’re juston

getting started.



SPEED: I get faster as I fall.

WHY: Gravity attracts me into the earth.







Q:



But all I’ve done is write down what I already

knew and what was really obvious! I haven’t worked

out what happens inside the earth at all!



A:



Physics is about being able to put yourself into a

problem and asking “What would I feel?” When you’re

doing this, you need to start at the start - with what’s

initially going on.



Q:

A:



DIRECTION: I fall down, into the tunnel.



Why? It hasn’t helped me get a final answer!



Starting off a question with ‘obvious’ things gives

your brain time to calm down and settle. It’s the first step

towards solving a more complicated problem. Once you’ve

made a start, you can build on it by using your intuition

and experience to spot ‘special points’ (where important

or interesting things happen) and similarities to problems

you’ve seen before.



Don’t worry if you wrote down

something a bit different.

This is what we wrote. Your answers should be

similar, but maybe not identical.



Q:



What if I start out OK then get stuck or make a

mistake? Surely I’ve completely failed if I don’t get the

right answer at the end?



A:



Usually people grading exams are more interested

in whether you understand the physics, even though the

math part is important too. So, if you’re able to start off

in the right direction and show that you understand the

important physics principles, you’ll get credit for it even if

you get stuck or make a mistake later on.



Q:

A:



But I still have no idea what happens next here!



You’ve already realized that gravity is important.

And that you’ll fall faster as you fall into the tunnel. That’s

a great start for you to build on.



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isn’t that special



Use your intuition to look for ‘special points’

You’ve just started off the bottomless pit problem by being a part

of it. You started at the start, imagined you’d just stepped over the

edge, and asked yourself “What would I feel?” And you know that

you’ll fall into the tunnel, getting faster as you go.



You fall into the

tunnel, getting faster

and faster as you go.



But what happens next?

The key is to use your intuition to look for ‘special points’

– places where important or interesting things happen.

For example, the edge of a cliff is a special point because

that’s where you change from being supported by the ground

to being unsupported. And the center of a seesaw is a

‘special point’ because it’s the only place on the seesaw that

one person can stand without either side going up or down.



The EDGE is the

special point that makes

the difference between

being supported and

unsupported.



You’ve already worked

out what happens at one

special point - the EDGE

of the tunnel.



The CENTER is the special

point that makes the

difference between being

balanced and unbalanced.



Spotting special points then asking “What would I feel if I was

there?” helps you to understand what’s going on.

You already did that for one special point - at the edge of the tunnel.

Now it’s time to look out for more special points in this problem, so

you can think about what’s going on there.



In physics, the

‘special points’ where

things happen are

usually at the EDGES

and in the CENTER.



Once you know what’s happening at each special point you can play

connect the dots and work out what’s happening in between too.



The edge of the tunnel is a special

point. Can you spot any other

special points in this problem?



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think like a physicist

So we just worked out that you fall into the

tunnel from one special point - the edge. And now

we’re supposed to look for other special points.



Jill: I have a hunch that the center of the earth must be important

- it just looks like it must be!

Frank: Yeah. Even though we’re assuming the center of the earth

isn’t hot (because we’re dealing with an Earth which has lots of

physics words written on it), the center still looks really important!

Jill: But what’s gonna happen there?

Frank: I’m not sure. I guess that either you stop, or you keep on

falling. But that’s not narrowing it down all that much!

Jill: Maybe we can use what we already figured out? Didn’t

we say that when you’re at the surface and step over the edge of the

tunnel, you fall down into the tunnel because of gravity?

Frank: Yeah, that’s right. I guess that the earth attracts you because

it’s so big. Gravity is the stuff the earth’s made of and the stuff

you’re made of attracting each other, right?

Jill: And when you’re at the surface - at the edge of the tunnel - the

whole of the earth is under you. So gravity attracts you downwards.

Frank: Yeah, that makes sense. So what’s going on in the center?

The whole Earth isn’t under you any more - it’s kinda all around

you. There’s the same amount of Earth around you in all directions!



Once you’ve found

a special point, ask

yourself:

“What would I FEEL

there?” and “What is

being there LIKE?”

What’s it

SIMILAR to?



Jill: Then you must get pulled in all directions at once. Ouch!

Sounds like you’d get torn apart or something!

Frank: Hmm. The Earth’s gravity isn’t strong enough to pull my

atoms apart when I’m standing on the surface. I have a feeling it’ll

be more like standing in the exact center of a seesaw.

Jill: You mean, kinda like a balance point? I guess if you were

at either end of the seesaw - or at either end of the tunnel - you’d

move. But if you’re in the center of the seesaw - or the center of the

earth, you’re balanced.

Frank: Yeah. With the seesaw, it’s like you have one foot ‘pulling’

you an equal amount each way, so you stay balanced. And in the

center of the earth, you have half the earth on one side and half the

earth on the other side. That’s balanced too.

Jill: So you must stop when you reach the center of the earth if you

balance there. We solved the problem - you never get out!

Frank: Hmm... but didn’t we say before that you’re already

moving very fast by the time you reach the center?

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journey to the center of the earth



The center of the earth is a special point

As Frank and Jill have worked out, the center of the earth is a special

point where important or interesting things might happen. Maybe

your eye was drawn to the center because of the symmetry, as

there’s the same amount of Earth around you in all directions.

So - be a part of it! Imagine yourself at the center of the earth. What

would I feel there? What is being there like?



The white arrows show you

the direction that gravity

is attracting you in.



You’re attracted

downwards.



At the first special

point—the edge of the

tunnel—you’re pulled

downwards into the tunnel

by gravity. This is because

of the attraction between

the “stuff ” the earth’s made

of and the “stuff ” you’re

made of.



There’s lots of

‘stuff’ under you.



(Stuff isn’t a particularly

technical term - we’re

basically using it to mean all

of your atoms.)



You’re equally

attracted in all

directions.



At the second special

point, in the center of the

earth, all of your atoms are

pulled equally in all directions.

You aren’t attracted in any

direction more strongly that

you are in any other direction.

Being attracted in all directions

at once may not sound like fun

- but you’re made of stronger

stuff. The Earth’s gravity isn’t

strong enough to pull your

atoms apart. This means that

all of the attractions balance

each other out.



This time, there’s

‘stuff’ all around you.



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At the center,

you’re equally

attracted in

all directions

- so all the

gravitational

attractions

balance out.



think like a physicist



You’re pulled

downwards.



Ask yourself “What am I ALREADY

doing as I reach the special point?”

But Frank and Jill nearly made a big mistake when they were

thinking about out what it would feel like in the center of the

earth. At first, they thought that if all the gravitational attractions

balance out, then you’ll be stationary in the center of the earth,

like you are when you balance yourself on the center of a seesaw.



You get faster

as you fall.



But is that really true? You’re already going very fast when

you reach the center of the earth. You’ve fallen a very long way

to get there, moving faster and faster all the time. If all the

attractions balance out, what is there to slow you down?

What is it like to be already going fast when there’s nothing

pulling or pushing you?



When you put yourself in a

problem, try to imagine what you’re

ALREADY doing when you reach

the special point before going on to

think about what happens next.



BE part of it



You’re pulled equally

in all directions.



The black arrows

show your SPEED.



You’re ALREADY

going fast when you

reach the center.



Your job is to imagine that you’re going

very fast. Maybe you’re a car or a speed

skater. What it is LIKE to be going very

fast when nothing can pull or push

you, and you can’t pull or push

on anything either? That means

no brakes and no grabbing on to

something to slow down. Does this give

you any clues about what it will be LIKE

at the center of the earth when all the

attractions balance out?

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be the solution



BE part of it - Solution



Your job is to imagine that you’re going

very fast. Maybe you’re a car or a speed

skater. What it is LIKE to be going very

fast when nothing can pull or push

you, and you can’t pull or push

on anything either? That means

no brakes and no grabbing on to

something to slow down. Does this give

you any clues about what it will be LIKE

at the center of the earth when all the

attractions balance out?



If I can’t brake or grab onto anything,

then I can’t slow down. I’ll just keep on

going really fast.

I think the same thing will happen in

the center of the earth. None of the

directions of attraction will “win”, and I’ll

just keep on going at the same speed.



Isn’t this all a bit ridiculous? You wouldn’t go at

the same speed-you’d slow down from air resistance

or bumping into the sides of the tunnel...or something

like that... especially as the earth turns!



That’s right - we’ve made some assumptions

to turn the problem into a simpler version

We already made an assumption back on page  that

(for this problem) the earth is solid and isn’t hot in the middle,

as getting fried isn’t helpful.

And quite right - we’re also assuming that air resistance doesn’t

slow you down and that the pit goes between the North and

South poles, so you don’t hit the sides as the earth turns.

In physics, the way of solving a complex problem is often to

make approximations or assumptions to turn it into a simpler

problem. That’s OK, as you can ask yourself later on what the

difference would be if you hadn’t made the assumption. But

only once you’ve got to come to grips with the simpler version.



You might have said

that it was LIKE

something else. That’s

OK. The main thing

is that you keep on

going at the SAME

SPEED if there’s

nothing pushing or

pulling on you.



Sometimes, including

all the hard stuff

right from the start

makes the problem

impossible to solve.



In physics, you sometimes make approximations or assumptions to turn

a complex problem into a simpler version.

Understanding the simpler version helps you with the complex version.

10   Chapter 1

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think like a physicist



You’re pulled

downwards.



Where you’re at - and what happens next?



You get faster

as you fall.



You’ve learned to step into the problem, so you can be a part

of it and ask “What would I feel” and “What’s it like.”

This is a good way to start off and helps you see what the

important things in the problem are. Here, you realized that

gravity is important, and that you fall towards the center of the

earth, getting faster and faster as you go.

You’ve also used your intuition to spot ‘special points.’ You’ve

spotted that the center of the earth is a place where the

gravitational attraction between the stuff you’re made of and the

stuff the earth’s made of is the same in all directions.

And you worked out that this means you just keep on going at

the same speed you were already going at as you pass through

the center because there’s nothing to slow you down! So you’re

You’re pulled equally

going quickly, but you aren’t getting faster and faster anymore.

directions.



in all



“Stuff” is

all or mostly

below you.



But now you’re through the center, what happens

next? What would you feel? What’s it like? You

already know that gravity is important and that its

influence depends on where you and the earth are

compared to each other. So - what happens next?



You continue at

the same speed.



What do you think happens after you pass through the center

of the earth? Do you continue at the same speed? Do you start

falling faster? Do you slow down? How far do you think you

keep falling? Or do you think something else happens?



“Stuff” is all

around you.



Write things on your

sketch to help explain!



Draw a picture then write down any ideas you have.



Hint: Think about where the majority

of the earth’s “stuff” is when you’re

at various points in the tunnel.

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a land down under



Center of the earth.



More ‘stuff’ above

you than below you.



What do you think happens after you pass through the center of the

earth? Do you continue at the same speed? Do you start falling faster? Do

you slow down? How far do you think you keep falling? Or do you think

something else happens?

Draw a picture then write down any ideas you have.



I think that after passing through the center there starts to be

more Earth above you than there is below you.

This acts a bit like brakes - you’re moving away from the center

but gravity’s attracting you back in. The further from the center

you are, the more Earth’s above you, so the more you slow down.

I think you’ll be moving slower and slower until you reach the other

side of the tunnel.



I thought that gravity always

speeds you up when you fall. Now

you’re saying it can slow you down?



A:



Things are always attracted towards

each other by gravity. Whether you’re

already moving away from the earth

or moving towards it, you’ll always be

attracted towards the center of the earth.



Q:



But that doesn’t say anything

about speeding up or slowing down!



A:



You need to think about the speed

and direction you’re already traveling in.

If you throw a ball up, it’s moving away

from the center of the earth, and it gets

slower. When it comes back down again,

it’s moving towards the center of the earth,

and it gets faster.



Slowing down

even more.



This is an EXTREME,

another ‘special point!’



You should never be

afraid to ask questions!



Q:



Slowing down.



It looks like you’re always

attracted towards the center, right?



You’re always attracted towards

the center unless you’re already

in the center.

Right. When you’re on the surface at the

start, there’s a lot more Earth under you

than there is on top of you, and you’re

attracted towards the center. This makes you

speed up.

When you’re in the center, the attractions all

cancel each other out, and you keep going at

the same speed.

As you move through the center towards

the other side, there’s more and more Earth

above you than there is below you. So you

start being attracted back towards the center,

which slows you down.



12   Chapter 1

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