How to Graph HL Physics

7/30/2019 How to Graph HL Physics

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How to Graph Data LC

Higher Physics

Copyright © Dee Magui re

CBS,

Kilkenny

For non-commercial purposes only….. Enjoy!

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Graphing data



Sometimesstudents think

it is astraightforwardmatter of

graphing oneline of dataagainst the

other…….

s

t

30 40 50 60 70 80 90

420

409

371

342

325

291

244



In fact thereare several

major errors inthis graph

How many canyou spot?

s

t

30 40 50 60 70 80 90

420

409

371

342

325

291

244



Here are somehints…..

s

t

30 40 50 60 70 80 90

420

409

371

342

325

291

244



So, it may not be as simple asgraphing the exact data that is in theexam question

…………..but there are a number of guidelines to help you



Let‟s have another quick look at therelevant wording of the question…



The word “ suitable” is important.

This is usually a strong hint that thedata in the table needs to bemanipulated a bit before you graph it

That means that you may have tosquare 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 theformula that is relevant to thatexperiment

In the example above, the

relevant formula is:2

1

2 s ut at



Graphing data

212

s ut at

when a body falls freely under gravity u = 0 and a = g

=> s = ½ gt 2

Here, we have the link between „s‟ and „t ‟

Note: the „t ‟ is squared

This means we also need to square the „t ‟ valuesto ensure we get a straight line graph



Add a new line to the table and squarethe t values, using your calculator

t 2/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 cando 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!

t 2/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 farthe graphlooks like

this…. ….ongraphpaper…..

naturally!



Graphing data

From the formula, we know we need „s‟ and „t 2‟, so the middle line of datais not used in the graph.

The y axis will hold the „t 2

‟ values. Also quotethe correct units s2

t 2/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 VERYIMPORTANT Let‟s have another look at the data

we now want to plot….start with „s‟

t 2/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




freefall

s /cm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

t 2 / s2

N d id h i ill b



Now decide on how your y axis will bedivided….

The values go from approx 0.06 to 0.17…..but youMUST 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/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176




freefall

s /m

180000

160000

140000

120000

100000

80000

60000

40000

20000

0

Now, start plotting yourpoints

Identify a point by placinga dot exactly at the point,and draw a small circlearound it to highlight it

t 2 / 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 thedots don‟t form an EXACT straightline, make sure there is the same

number of dots on each side of theline.




freefall

s /m

180000

160000

140000

120000

100000

80000

60000

40000

20000

2 / 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

t 2 / 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, taketwo points ON THE LINE, (not fromthe 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 y x x



s /m

(90, 0.176

(0,0)

To measure g , the acceleration due to gravity, by freefall

t 2 / 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 0

0.9 0

0.196

y ySlope

x x



2 y s

x m

2

2

2

1

2

10

2

1

2

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 t

x s g

g



Other “suitable” graphs

A number of other data experiments will requireyou to plot a “suitable” graph

Make sure to consider carefully what you will plot

Study the next few examples and decide whatshould 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




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 T 2 Slope = y / x = l /T 2 = g /4∏

l

T 2




Measure fundamental freq. against length

You will be supplied with f and l measurements


ANS: f against 1/ l

Slope = y / x = f /(1/l ) = ½√(T / µ)

f

1/ l




Measure fundamental freq. against Tension You will be supplied with f and T measurements.


ANS: f against √ T Slope = y / x = f /√ T = 1/(2L√µ)

f

√ T




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 online (1/u,1/v ) = ( x ,y ), then 1/f = 1/u + 1/v = x +y

1/v

1/u

(1/u, 1/v )




Verify Snell’s Law You will be supplied with <i and <r measurements.(or possibly Real depth and Apparent depth)


ANS: Sin i against Sin r (or real against apparent)Slope = y / x = Sin i /Sin r = n = refractive index

Sin i

Sin r




Joules Law: You will be supplied with ∆θ and I measurements


ANS: ∆θ against I 2 Slope: y / x = ∆θ /I 2 = Rt /mc

∆θ

I 2

I



In summary…. Do it on graph paper

Title the graph and the axesInclude units on the axes

Divide your axes correctly

Use slope formula to getrequired information

And finally………..

Plot your points

Use a formula to help you decide what goeswhere (Their top line is your bottom line)



If you make a mistake on yourdivision of axes etc, it is oftenquicker and neater to start again

….Ask for more graph paper

Documents

How to Graph HL Physics