Graphing and Analysis Skills in Physics.ppt

Graphing and Analysis skills used in Physics

1. Graphingand
Analysisin Physics

2. Graphing data

3. Sometimes
students think
it is a
straightforward
matter of
graphing one
line of data
against the
other…….
s
t
30 40 50 60 70 80 90
420
409
371
342
325
291
244

4. In fact there
are several
major errors in
this graph
How many can
you spot?
s
t
30 40 50 60 70 80 90
420
409
371
342
325
291
244

5. Here are some
hints…..
s
t
30 40 50 60 70 80 90
420
409
371
342
325
291
244

6. So, it may not be as simple as
graphing the exact data that is in the
exam question
…………..but there are a number of
guidelines to help you

7. Let’s have another quick look at the
relevant wording of the question…

8. The word “suitable” is important.
This is usually a strong hint that the
data in the table needs to be
manipulated a bit before you graph it
That means that you may have to
squarethe values of one line of
data…or maybe halveit or double
it etc, before you try to graph it

9. To decide howto manipulate the
data, you must refer back to the
formula that is relevant to that
experiment
In the example above, the
relevant formula is: 21
2
s ut at

10. Graphing data21
2
s ut at
when a body falls freely under gravityu= 0 and a= g
=> s= ½gt
2
Here, we have the link between ‘s’ and ‘t’
Note: the ‘t’ is squared
This means we also need to square the ‘t’ values
to ensure we get a straight linegraph

11. Add a new line to the table and square
the tvalues, using your calculator
t
2
/s
2
0.0595 0.085 0.106 0.117 0.138 0.167 0.176
Note: the units for ‘t’ are also squared

12. Now you are ready to draw the graph.
There are a few easy things you can
do straight away:
(i)Title the graph
(ii)Decide what data will go on each axis
(iii)Title the axes (include units)

13. Graphing data
Title the graph
You can find a very suitable one in the question

14. Graphing data
Decide what data will go on each axis
As a rule, “their top line is your bottom
line” –so ‘s’ will go on the xaxis
Don’t forget to convert to SI units!
t
2
/s
2
0.0595 0.085 0.106 0.117 0.138 0.167 0.176

15. Independent and Dependent
Variables
In an experiment, it is good practice
to put the variable that was
deliberately altered (the Independent
variable) on the X AXIS
The variable that was
observed/measured as the result
(the Dependent variable) on the Y
AXIS

16. To measure g, the acceleration due to gravity, by
freefall
s/ cm
So far
the graph
looks like
this….
….on
graph
paper…..
naturally!

17. Graphing data
From the formula, we know we need
‘s’ and ‘t
2
’, so the middle line of data
is not used in the graph.
The y axis will hold the ‘t
2
’ values. Also quote
the correct units (s
2
)
t
2
/s
2
0.0595 0.085 0.106 0.117 0.138 0.167 0.176

18. To measure g, the acceleration due to gravity, by
freefall
….
….on graph
paper…..
naturally!
s/cm
t
2
/ s
2

19. Graphing data
The next stage is VERY
IMPORTANT
Let’s have another look at the data
we now want to plot….start with ‘s’
t
2
/s
2
0.0595 0.085 0.106 0.117 0.138 0.167 0.176

20. Graphing data
The values go from 30 up to 90….
…..but you MUSTstart at zero
Use as much of your graph sheet as possible…
…but make sure you go at least as far as
90…ideally up to 100
You must make equal sizedintervals along your xaxis

21. To measure g, the acceleration due to gravity, by
freefall
s/cm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
t
2
/ s
2

22. Now decide on how your y axis will be
divided….
The values go from approx 0.06 to 0.17…..but you
MUST start at zero
You must go AT LEAST AS FAR as 0.176
Try to use as much of the page as possible, using
EQUAL sized divisions
Do NOT write the above readings on your
graph!!!!!!!!!
t
2
/s
2
0.0595 0.085 0.106 0.117 0.138 0.167 0.176

23. To measure g, the acceleration due to gravity, by
freefall
s /m
180000
160000
140000
120000
100000
80000
60000
40000
20000
0
Now, start plotting your
points
Identify a point by placing
a dot exactlyat the point,
and draw a small circle
around it to highlight it
t
2
/ s
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

24. You must NEVER…..join-the-dots!
Always pick a “best-fit” line. If the
dots don’t form an EXACT straight
line, make sure there is the same
number of dots on eachside of the
line.

25. To measure g, the acceleration due to gravity, by
freefall
s /m
180000
160000
140000
120000
100000
80000
60000
40000
20000
t
2
/ ms
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

26. s /cm
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
To measure g, the acceleration due to gravity, by freefall
t
2
/ s
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

27. To read a slope from the graph, take
two points ON THE LINE, (not from
the table) that are far apart
Usually we can use the origin as one
of these points
Then use the formula:
slope =21
21
yy
xx



28. s /m
(90, 0.176
(0,0)
To measure g, the acceleration due to gravity, by freefall
t
2
/ s
2
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

29. 21
21
0.176 0
0.9 0
0.196
yy
Slope
xx








30. 2
ys
xm
 2
2
2
1
2
1
0
2
1
2
s ut at
s gt
s gt


 From the graph the units are:
From the formula2
2
2
slope
22
10.2m/s
slope 0.196
yt
x s g
g
   
   

31. Other “suitable” graphs
A number of other data experiments will require
you to plot a “suitable” graph
Make sure to consider carefully what you will plot
Study the next few examples and decide what
should be plotted on yand xaxes. Also determine
how to get slope
Study how many graphs are straight lines

32. “Suitable graphs 1”
To Prove Boyles Law: (P
1V
1= P
2V
2= P
3V
3= ….)
You will be supplied with Pand Vmeasurements.
What will you plot against what?
ANS: Pagainst 1/V
P
1/V

33. “Suitable graphs 2”
Measure g, using pendulum
You will be supplied with land Tmeasurements.
What will you plot against what? What is slope?
ANS: lagainst T
2
Slope= y/x= l/T
2
= g/4∏
2
l
T
2

34. “Suitable graphs 3”
Measure fundamental freq .against lengthof string.
You will be supplied with f and lmeasurements
What will you plot against what? What is slope?
ANS: fagainst 1/ l
Slope= y/x= f/(1/l)
=
½√(T/µ)
f
1/ l

35. “Suitable graphs 4”
Measure fundamental freq .against Tension
You will be supplied with fand Tmeasurements.
What will you plot against what? What is slope?
ANS: fagainst √T
Slope= y/x= f/√T
=
1/(2Lõ)
f
√T

36. “Suitable graphs 5”
Measure f of concave mirror or converging lens
You will be supplied with uand vmeasurements.
What will you plot against what?
ANS: 1/vagainst 1/u
To get f: Rather than use slope, take any point on
line (1/u,1/v) = (x,y), then 1/f= 1/u+ 1/v= x+y
1/v
1/u
(1/u, 1/v)

37. “Suitable graphs 6”
Verify Snell’s Law
You will be supplied with <iand <rmeasurements.
(or possibly Real depth and Apparent depth)
What will you plot against what? What is slope?
ANS: Sin iagainst Sin r(or real against apparent)
Slope= y/x = Sin i/Sin r= n= refractive index
Sini
Sin r

38. “Suitable graphs 7”
Joules Law:
You will be supplied with ∆θand I measurements
What will you plot against what? What is slope?
ANS: ∆θagainst I
2
Slope: y/x= ∆θ/I
2
= Rt/mc
∆θ
I
2

39. In summary….
Do it on graph paper
Title the graph and the axes
Include units on the axes
Divide your axes correctly
Use slope formula to get
required information
And finally………..
Plot your points
Use a formula to help you decide what goes
where (Their top line is your bottom line)

40. If you make a mistake on your
division of axes etc, it is often
quicker and neater to start again
….Ask for more graph paper