Graphing data
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Transcript of Graphing data
Graphing data
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
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
Here are some hints…..
s
t
30 40 50 60 70 80 90
420
409
371
342
325
291
244
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
Let’s have another quick look at the relevant wording of the question…
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 square the values of one line of data…or maybe halve it or double it etc, before you try to graph it
To decide how to manipulate the data, you must refer back to the formula that is relevant to that experiment
In the example above, the relevant formula is:
212
s ut at
Graphing data
212
s ut at when a body falls freely under gravity u = 0 and a = g
=> s = ½ gt2
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 line graph
Add a new line to the table and square the t values, using your calculator
t2/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176
Note: the units for ‘t’ are also squared
Now you are ready to draw the graph.There are a few easy things you can do straight away:
(i) Ask for graph paper (no marks otherwise!)
(ii) Title the graph
(iii) Decide what data will go on each axis
(iv) Title the axes (include units)
Graphing data
(i) Ask for graph paper (deducted
most marks otherwise!)
…..seriously!
Graphing data
(ii) Title the graphYou can find a very suitable one in the question
Graphing data
(iii) Decide what data will go on each axisAs a rule, “their top line is your bottom line” – so ‘s’ will go on the x axis
Don’t forget to convert to SI units!
t2/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176
To measure g, the acceleration due to gravity, by freefall
s / cm
So far the graph looks like this….….on graph paper…..
naturally!
Graphing data From the formula, we know we need
‘s’ and ‘t2’, so the middle line of data is not used in the graph.
The y axis will hold the ‘t2’ values. Also quote the correct units (s2)
t2/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176
To measure g, the acceleration due to gravity, by freefall
….….on graph paper…..
naturally!
s /cm
t2 / s2
Graphing data
The next stage is VERY IMPORTANTLet’s have another look at the data we now want to plot….start with ‘s’
t2/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176
Graphing data
The values go from 30 up to 90….…..but you MUST start 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 sized intervals along your x axis
To measure g, the acceleration due to gravity, by freefall
s /cm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
t2 / s2
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!!!!!!!!!
t2/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176
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 exactly at the point, and draw a small circle around it to highlight it
t2 / s2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
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 each side of the line.
To measure g, the acceleration due to gravity, by freefall
s /m
180000
160000
140000
120000
100000
80000
60000
40000
20000
t2 / ms2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
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
t2 / s2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
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 = 2 1
2 1
y yx x
s /m
(90, 0.176
(0,0)
To measure g, the acceleration due to gravity, by freefall
t2 / s2 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
2 1
2 1
0.176 00.9 00.196
y ySlope
x x
2y sx m
2
2
2
121
02
12
s ut at
s gt
s gt
From the graph the units are:
From the formula
2
2
2slope
2 210.2 m/s
slope 0.196
y tx s g
g
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 y and x axes. Also determine how to get slope
Study how many graphs are straight lines
“Suitable graphs 1” Boyles Law:
You will be supplied with P and V measurements.
What will you plot against what?
ANS: P against 1/V
P
1/V
“Suitable graphs 2” Measure g, using pendulum
You will be supplied with l and T measurements.
What will you plot against what? What is slope?
ANS: l against T2 Slope = y/x = l /T2 = g/4∏
l
T2
“Suitable graphs 3” Measure fundamental freq. against length
You will be supplied with f and l measurements
What will you plot against what? What is slope?
ANS: f against 1/ l Slope = y/x = f/(1/l) = ½√(T/µ)
f
1/ l
“Suitable graphs 4” Measure fundamental freq. against Tension
You will be supplied with f and T measurements.
What will you plot against what? What is slope?
ANS: f against √T Slope = y/x = f/√T = 1/(2L√µ)
f
√T
“Suitable graphs 5” Measure f of concave mirror or converging lens
You will be supplied with u and v measurements.
What will you plot against what?
ANS: 1/v against 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)
“Suitable graphs 6” Verify Snell’s Law
You will be supplied with <i and <r measurements.(or possibly Real depth and Apparent depth)
What will you plot against what? What is slope?
ANS: Sin i against Sin r (or real against apparent) Slope = y/x = Sin i/Sin r = n = refractive index
Sin i
Sin r
“Suitable graphs 7” Joules Law:
You will be supplied with ∆θ and I measurements
What will you plot against what? What is slope?
ANS: ∆θ against I2 Slope: y/x = ∆θ/I2 = Rt/mc
∆θ
I2
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)
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