|
PHY131 |
Math
Hints |
Prof.
Jason Harlow |
|
Introduction
to Physics I |
|
Physics
Department, |
The
language of science is math. Doing the calculations
involved in physical situations familiarizes you with
the concepts, develops your intuition and allows you to
discover things yourself. Here are a couple of hints
which you might find useful as the course progresses.
Units
Imagine
your instructor asks you for the height of the CN Tower.
The answer,"the height of the CN Tower is about 500"
does not make sense. A correct statement is: "The height
of the CN Tower is about 500 metres." In
this case, you need to specify the unit of
distance. Another unit of distance is the kilometre, or
1000 metres. So the statement could also be correctly
worded: "The height of the CN Tower is about half a
kilometre." Both are perfectly acceptable answers.
Almost every number has units. When we mark your problem
sets and tests, we will deduct points if we see
numerical final answers with units missing.
Calculators
Arithmetic can be a fun game, but I think
it's much better to just type the numbers into a
calculator and concentrate on the physics and math.
Don't you agree? That being said, you shouldn't just
blindly trust everything your calculator tells you. It's
easy to make a typing mistake and it's good to
double-check things. You should always think about your
numerical answers when you write them down and ask
yourself, "Does this make sense?"
If you don't already have one, please buy a
non-communicating pocket calculator for this course. It
doesn't have to be fancy or expensive, but it should
have an "EE" or "EXP" button on it at least. You cannot
bring a laptop or a phone into a test or exam.
Scientific
Notation
Sometimes, in this course, we
will deal with very large and very small numbers. It is
very tedious to write down numbers such as 100000000000
and 0.00000000000008, and also hard to type them into
your calculator. So in this course we will sometimes use
a short-form called "scientific notation" which uses
powers of ten (e.g. 1011 and 8 x 10−14).
For example, 187,000,000 in scientific notation is 1.87
x 108. Here are some powers of ten facts
which may help you:
|
1000 |
= |
103 |
= |
10 x 10 x 10 |
|
100 |
= |
102 |
= |
10 x 10 |
|
10 |
= |
101 |
= |
10 |
|
1 |
= |
100 |
|
|
|
0.1 |
= |
10−1 |
= |
|
|
0.01 |
= |
10−2 |
= |
|
|
0.001 |
= |
10−3 |
= |
|
Remember that raising a
number to a power just means multiplying that number by itself the number of
times in the exponent. For example,
24=2 x 2 x 2 x 2=16.
A BIG
HINT about typing numbers in scientific notation into
your calculator: The 
or 
key on
your calculator stands for "times ten to the power..."
So, for example, to type 6.1x109, you would type 
. To type a
negative power of ten, such as 3.4x10−4, on
most inexpensive calculators you would type 
.
For scientific notation on Excel or Google,
use "e" to stand for "times ten to the power". For example, 3.4x10−4
is 3.4e-4.
Practice
exercises: Use your
calculator to solve:
x = 1+1.5x10−4
y = 2.2x1015/(1.1x1012)
z = (9x10−25)
x (5x10−34)
(Answers:
x=1.00015, y=2000, z=4.5x10−58, if you got
them all right, then you are an expert on scientific
notation!!)