Chapter 2. making it all MEAN something
Tải bản đầy đủ - 0trang
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com
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
Download at WoweBook.Com