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Chapter 2. making it all MEAN something

Chapter 2. making it all MEAN something

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myPod rocks



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

Introducing the myPod - a revolution in portable music players!

Your design team has just finished the final case prototype. Now

you need to draw up the blueprints to be sent to the factory that’s

manufacturing the cases.



MEMO

sign Team

From: myPod Case De

fully

the latest, and hope

We’ve just sent over

case design.

final, model myPod



e plans and send

Could you draw up th

e the cases are being

them to factory wher

Pod

send us back the my

manufactured? And

done.

model when you’re



Just send us the

case plans, and we’ll

send you a prototype

ASAP!



ited

receive one of the lim

You will, of course,

if

Pods for your troubles

edition numbered my

this around quickly!

you manage to turn



The factory



18   Chapter 2

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making it all mean something



So you get on with measuring the myPod case

The quicker the factory gets the plans, the better.



Here’s the myPod case with various lengths marked out that you’ll need to

measure. Cut out the ruler (or just use your own that looks similar to ours)

and write in the lengths. (The myPod design team already started writing

them on for you.)



5



100



3

1

31



you are here 4   19

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size matters



When the myPod case comes back from the factory...

After a lightning-quick turnaround, the myPod case comes back from

the factory. But there’s a problem.



Here’s the myPod case with various lengths marked out that you’ll need to

measure. Cut out the ruler (or just use your own that looks similar to ours)

and write in the lengths. (The myPod design team already started writing

them on for you.)



42



Uhh ... it was

supposed to fit

in my pocket.



8



38



5

3



100



10



1

31

8

60



20   Chapter 2

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making it all mean something



... it’s waaay too big!

The myPod case is huge. Massive. Rocket-sized, not pocket-sized.

But when you give the factory a call, they say they followed your

instructions exactly.

Not our fault.

We followed the

blueprints EXACTLY!



Something’s obviously gone very wrong. But what?!

Have another look at your blueprint, and see if it

could be interpreted differently.



you are here 4   21

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units are useful



The numbers on

the blueprint

don’t have UNITS.



There aren’t any UNITS on the blueprint

The ruler you used is marked off in millimeters (mm)- but there

aren’t any notes on the blueprint that say this. The factory is used

to working in inches and assumed it was a giant promotional item.

Inches are around 25 times bigger than millimeters, so the myPod

has come back MUCH bigger than expected!

In physics, it’s really important to say what the units

are any time you write down a number.

Units give numbers meaning, so

you know whether the number

represents millimeters or inches,

or something else entirely.



42



This measurement

was supposed to

mean 100 mm

but ended up as

100 inches-taller

than a person!



8



The design team set

up the mistake by not

including units on the

measurements they’d

already made.



38



5



100



10

3



1

31

8



Your ruler’s marked off

in mm - but there’s no

note of this anywhere

on the blueprint.



60



A number without any units is meaningless.



22   Chapter 2

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making it all mean something



Units Magnets



Throughout the book, you’ll be attaching lots of different units to

numbers to give them meaning. Your job is to match the units with

the kind of quantity they measure. You might not have heard of all of

these, but give it a shot.



Length



Time



Mass



Use these spaces to draw the

magnets in the right columns.

inches

yards



milliseconds



years



milligrams



meters



feet

minutes



tonnes



millimeters



kilometers



hours



seconds



grams

kilograms



days



you are here 4   23

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unit magnets solution



Units Magnets Solution



Check your work; were you able to match these up correctly?



Length



Time



Mass



millimeters



milliseconds



milligrams



inches



seconds



grams



feet



minutes



kilograms



yards



hours



tonnes



meters



days



kilometers



years







Don’t worry if you’re not familiar

with all of these units just quite yet.

You won’t have to work with all of these unfamiliar

units throughout the book! Instead, you’ll be sticking

with the system used worldwide, which is what the

next couple of pages are all about!



Plus you can always look up

unfamiliar units.



24   Chapter 2

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making it all mean something



You’ll use SI units in this book (and in your class)

The system of units used in physics worldwide is called SI (short for Système Internationale).

They’re much easier to use since they go up in multiples of 1000 for each ‘step.’



AP Physics B

or UK A Level



If you’re working with lengths, instead of having to do calculations using 12 inches in a

foot, 3 feet in a yard, and 1760 yards in a mile, you have 1000 millimeters in a meter, 1000

meters in a kilometer, and so on and so forth.



Working with lengths

is much easier in SI.



And with masses, instead of having to remember that there are 16 ounces in a pound

and 2000 pounds in a ton, you have 1000 milligrams in a gram, 1000 grams in a kilogram

(about the equivalent of three cans of soda), and so on. The only SI unit which doesn’t

follow this convention is time.



And working with

masses is easier too.



Multiplying and dividing by 1000 is more straightforward mental arithmetic, so calculations

involving SI units are quicker and easier than calculations with other unit systems. If you’re

converting meters to kilometers, you divide by 1000 (easier), but going from yards to miles

involves dividing by 1760 (not straightforward, and definitely not mental arithmetic!).



inch



It’s easy to multiply

and divide by 10’s using

mental arithmetic.



But time is so widely agreed

on; it’d be silly to reinvent it!



millimeter

× 1000



× 12

foot

×3

yard



It’s harder to

do the non-SI

multiplications

and divisions.



The multipliers are different at

each stage with non-SI units.



× 1000



kilometer



× 1760

mile



meter



SI units go up in multiples of 1000,

which makes the math a whole lot easier!



you are here 4   25

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ask away



Q:



Run it past me again - why am I

being forced to use SI units when I’m

more used to yards and miles? I really

have no idea how much a kilogram is!



A:



SI units have been used throughout

the world as the basic standard in physics

since 1960. SI units are an agreed worldwide

standard and make sure that everyone is

using the same words and definitions when

they make measurements.



Q:



But I don’t see why I can’t just use

the units I’m more familiar with. Surely

I’m less likely to make mistakes in

calculations if I use units I’m used to?



A:



SI units actually make calculations

easier. Instead of having to use all sorts

of weird ratios to move between units (like

inches, feet, yards, miles), you’ll use tens.

So even if they’re less familiar at first, they’ll

be quicker and easier in the long run.



Q:



But I’m not at all familiar with SI

units at the moment. What kinds of units

am I going to come across?



A:



It’s funny you should ask ...



Here are the SI units you’ll use the most

Length



The SI unit of length is the meter.

Other related units are the millimeter (1000th of a meter),

centimeter (100th of a meter), and kilometer (1000 meters).



Time



The SI unit of time is the second.

To work with time units, you’ll just use common sense. There are

60 seconds in a minute, 60 minutes in an hour, 24 hours in a day,

and 365 days in a year.



Mass



The SI unit of mass is the kilogram.

Other related units are the gram (1000th of a kilogram) and the

milligram (1000th of a gram).



If you use SI units, people all over the world will

understand your measurements.

26   Chapter 2

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making it all mean something



Q:



It’s a real pain to have to write

out ‘millimeters’ or whatever every

time. At least the units I’m used to have

abbreviations - like lb for pounds.



A:



SI units have abbreviations too!

Generally, you just use the first letter of the

unit - m for meters, s for seconds, and so on.



Q:



OK, but what about things that

start with the same letter - meters and

minutes, for example?



A:



The main SI unit takes precedence.

The main unit for length is the meter, so it

gets abbreviated to ‘m’. The main SI unit for

time is the second - the minute is defined

as 60 seconds, so it isn’t as important and

usually gets abbreviated as ‘min’.



Q:



OK, so what about kilometers and

kilograms. They start with the same

FOUR letters!



A:



The ‘kilo’ is a prefix that goes in front

of the unit. A kilogram is 1000 times more

than a gram; a kilometer is 1000 times

further than a meter. The abbreviation

includes the prefix as well, so kilograms are

‘kg’ and kilometers are ‘km’.



It’s easier when

everyone uses

SI units.



Q:



So “kilo” means 1000, right? But

what does ‘milli’ mean, then? It sure

meant 1000 when the millennium came

around, but a millimeter and kilometer are

different things, right?!



A:



Great observation! Kilo is Greek for

1000, and milli is Latin for 1000. In the SI

system, ‘kilo’ in front of a unit means it’s

1000 times as big - so a kilogram is 1000

grams. And ‘milli’ in front of a unit means

it’s 1000 times smaller - so a millimeter is

1/1000th of a meter.



Q:



I was kind of wondering something.

The meter is the main SI unit, and it

doesn’t have a prefix before the unit. So

why is the kilogram the main SI unit and

not the gram? That’s plain weird!



A:

Hey, you gotta help me out - I

want this job to build the cases.

Could you change the millimeters

into inches on the plan?



Most everyday physics things like cars,

people, and such have masses that are a

nice manageable number of kilograms, but

thousands, or even millions, of grams. It

was a convention that everyone ended up

using from 1960 onwards. It’s easier when

everyone does the same thing!



How would you convert the

measurements you’ve already made

into inches without remeasuring?



you are here 4   27

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converting units



So we need to redo the

blueprint using inches

instead of mm.



Joe: Yeah. I guess we can remeasure the myPod using a ruler marked off

in inches and make a new blueprint.

Frank: That sounds like an awful lot of work. It took ages to measure

all the lengths in the first place, and I can’t face having to do it all over

again with inches instead of mm.

Joe: Do we definitely have to remeasure though? Can we do something

with the measurements we already made instead?

Jim: It would be nice if they wanted the blueprint in centimeters instead.

Then we’d just have to multiply each measurement by 0.1 to convert it

from mm to cm.

Frank: How does that work?

Jim: We already know that there are 10 mm in 1 cm, which means that

1 mm = 0.1 cm. For every mm, you have 0.1 cm. So if you multiply the

number of mm by 0.1, you get the number of cm.

Frank: You mean if the measurement is 23 mm, you multiply the

number of mm in the measurement by the number of cm that’s

equivalent to 1 mm. So 23 × 0.1 = 2.3 cm. But what about the

blueprint? That needs to be in inches, not cm, right?

Joe: What if we find out how may inches 1 mm is? Can’t we do

exactly the same thing we just did going from mm to cm?



If you know how

many inches 1 mm is,

you can CONVERT

your measurements

from mm to inches.



Jim: Hmm ... Yes, I think we could.

Frank: So we’d multiply the length in mm by the number of inches

that’s equivalent to 1 mm. It’s the same thing that we did to convert

a measurement from mm to cm, but it’s more useful, as it’s what we’re

actually supposed to be doing!

Joe: So we can just use a calculator to do the new plans without

remeasuring. That rocks!

Jim: Let’s get to it!



28   Chapter 2

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