Transcript Scientific Methods

 The
base units we will use in this course:
Metric Prefixes are used on SI Units to
make it easier to describe the values.
Prefix:
Symbol:
Magnitude:
Meaning (multiply by):
Giga-
G
109
1 000 000 000
Mega-
M
106
1 000 000
kilo-
k
103
1000
100
1
Base
centi-
c
10-2
0.01
milli-
m
10-3
0.001
micro-
u (mu)
10-6
0.000 001
nano-
n
10-9
0.000 000 001

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
To convert between units we use a fun little process
called Dimensional Analysis.
All you need is a conversion factor to multiply your
number by.
Example:
• Let’s say I want to convert 5,000 seconds into minutes, because
having so many seconds laying around is impractical…
• First I need a conversion factor… 1 min = 60 secs
• And then I multiply by my conversion factor (remember you can
flip the factor to cancel the units!)
• So:
5,000 s x (1 min / 60 s) = 83.3 minutes

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

When we make measurements, each measurement only
has a certain degree of certainty.
Measurements can only be made to a certain decimal
place.
The last decimal place is always an approximation.
This is why we need to use Significant Figures.
Using ‘Sig Figs’ will let you know how precise a
number is.
Here are the rules:


•

The following are all Significant figures
1. ALL non-zero numbers (1-9)
2. ALL zero’s between non-zero numbers (302)
3. ALL zeros after a number that is to the right of a decimal
point (0.000200)
(also 2.0)
4. ALL zeros which are to the left of a written decimal point
(100. yes & 100 no)
Remember, exact numbers have an unlimited
number of Sig Figs.
Example: one dozen = 12
1.
2.
3.
4.
5.
6.
7.
23,450
6,345.8
0.034
0.0005670
567.00
90.01
100
4
5
2
4
5
4
1
 When
we are dealing with really BIG or really
small numbers, sometimes we need to describe
them using scientific notation.
 Example: 6.022x1023
 Just remember that the exponent on the 10 tells
you how many places the decimal is moved to
the right or left.
 Positive exponent->Right
Negative exponent->Left
 There will only be one integer to the left of the
decimal point.
Write in scientific
notation:
1. 1,900,000
2.
456,700,000
3.
0.0000230
4.
0.00000003009
1.9x106
4.567x108
2.3x10-5
3.009x10-8
A.
B.
C.
D.
1,257,000
.000001257
.0000001257
125,700
 We
will be using a lot of Algebra in Physics…
which is good because you’ve had 2 years of it,
right?
 And you will see plenty of fun equations like
these:
 Whenever
we are working problems with
equations we will need to solve for the variable
we are looking for before we substitute
numbers!

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
Solve this equation for G.
Our goal is to get G by itself on one side of the = sign.
Remember the golden rule of algebra: you have to do
the same thing to both sides in order to cancel units!
This means if you multiply by a variable on one side
you have to multiply it on the other side!





Solve this equation for G.
(r2)
(r2)
First, multiply each side by r2
to move it over to the left.
Divide by (m1m2) to get rid
of both variables
Flip it so that G is by
itself on the left side.
Wasn’t that easy?
(m1m2)
(m1m2)
A.
B.
C.
D.
𝑚=
𝑘𝑇𝑠2
2𝜋
𝑚=
𝑘𝑇𝑠
2𝜋
𝑚=
𝑘𝑇𝑠2
4𝜋2
𝑚=
𝑘𝑇𝑠
4𝜋2
A.
B.
C.
D.
36,000 m/hr
600 m/hr
.17 m/hr
.028 m/hr
A.
B.
C.
D.
2.8 km/hr
3.6 km/hr
28 km/hr
36 km/hr
Remember: This should all be a REVIEW!

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
Graphs have 2 axes: the horizontal (usually called ‘x’)
and the vertical (usually called ‘y’)
Graphs will be named according to what is plotted (it
goes by the general form “Y” vs. “X”
Each axis should always be labeled and include the
proper units.
 Lines
• The general equation for a line is:
y = mx + b
(where y is the dependent variable, x is the independent variable, m is
the slope, and b is the y-intercept)
• Slope
 The equation for slope is
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What is the slope of the line in the graph?
Slope (m) = (∆y / ∆x)
m = (y2 – y1) / (x2 – x1)
First, select two points that are
far apart
Plug values into the equation:
m = (30 – 10) / (14 – 4)
m=2
So, the slope is 2, but what are
the units, and what do they mean?
In this case, the units would be (smiley faces / puppies)
or /p
And this tells us that you would get 2 smiley faces for every puppy
you see!


What is the y-intercept of the graph and what does that
mean?
• The y-intercept is 2 and it means that even with 0
puppies you can have a happiness of 2
What is the mathematical representation (equation) for
our graph?
y = mx + b
• y = 2x + 2
or H = 2P + 2
A.
𝑦 = 2(𝑥 −
B.
𝑦 = 2(𝑥 +
C.
𝑦=
D.
𝑦=
1
(𝑥
2
1
(𝑥
2
3
)
2
3
)
2
− 6)
+ 6)
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Identifying relationships between variables is crucial in physics.
Two variables are said to be directly proportional when they are
each affected in the same way as the other when multiplied by a
constant.
• For instance, in the equation y = kx , y and x are directly
proportional because if you were to double y, x would have to
double as well.
Two variables are said to be indirectly proportional when one
variable is affected inversely when the other is multiplied by a
constant.
• For instance, in the equation y = 1/x , y and x are indirectly
proportional because if you were to double x, y would be
halved.


Two variables are said to be
directly related when one
variable increasing causes
the other to increase as well.
Two variables are indirectly
(inversely) related when one
variable increasing causes
the other to decrease.


Occasionally, you might run into a graph that is not
linear, like the one below.
This presents a problem, because we cannot do much
of an analysis with a curved line. This means we need to
linearize
the graph (turn it into a
straight line)


First, you need the equation for the line. For this one, it
is conveniently y = x2, or p = t2
To linearize the data and obtain a straight line, we will
need to plot a Position vs. Time2 graph instead.

The scientific method comes in many
different forms but always has these
basic steps:
1. Ask a question
2. Develop a hypothesis
(An if/then statement describing what you
think will answer the question)
3. Design an experiment
4. Analyze data and draw conclusions
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Let’s do a real world example:
Timmy is a geek and is having a hard time making
friends…
He just wants to be friends with the cool kids…

So Timmy decided to use the
scientific method:
1.
2.
3.
4.
First he asks his question:
“How can I be a cool kid?”
Then he develops a hypothesis –
an if/then statement that should answer his question or solve
his problem.
“If I take showers every day, then I can be friends with the
cool kids!”
He designs an experiment:
“I’ll take a shower every day and record how many words
the cool kids say to me each day.”
He performs his experiment for a certain amount of time
and records all his data.

So Timmy decided to use the
scientific method:
4.
He analyzes his data and draws
conclusions:


He made a graph to display his results:
There is a direct relationship between how many days he
showers and how much the cool kids talk to him!
Now he can draw a conclusion based on his data:

•
Timmy concluded that he is now cool and is friends with the
other cool kids!

In any experiment, it is important to identify the variables that are
being affected or kept the same. There are three types:
1. The Independent Variable
•
This is the what you change to see what will happen.
•
Example: For Timmy this was how many days in a row he took a
shower.
2.
The Dependent Variable
•
This is what you hope is affected by the Independent Variable.
•
Example: How many words a day the cool kids say to Timmy.
3.
Constants
•
This is everything that was not a part of the experiment but
needed to be kept constant.
•
Example: even though Timmy showered, he still never put on
deodorant or stopped playing video games for 12 hours a day.
Those variables were held constant.