# Graphing data

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10-Jan-2016Category

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LC Physics

Graphing data

Sometimes students think it is a straightforward matter of graphing one line of data against the other.

st30 40 50 60 70 80 90420409371342325291244In fact there are several major errors in this graph

How many can you spot?st30 40 50 60 70 80 90420409371342325291244Here are some hints..st30 40 50 60 70 80 90420409371342325291244So, 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

Lets have another quick look at the relevant wording of the questionThe 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 dataor maybe halve it or double it etc, before you try to graph itTo 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:

Graphing data

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

=> s = 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 calculatort2/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176Note: the units for t are also squaredNow you are ready to draw the graph.There are a few easy things you can do straight away:

Ask for graph paper (no marks otherwise!)Title the graphDecide what data will go on each axisTitle the axes (include units) Graphing dataAsk for graph paper (deducted most marks otherwise!) ..seriously!

Graphing dataTitle 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 Dont forget to convert to SI units!

t2/s2 0.0595 0.085 0.106 0.117 0.138 0.167 0.176To measure g, the acceleration due to gravity, by freefalls / cmSo far the graph looks like this..on graph paper..

naturally!Graphing dataFrom 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 /cmt2 / s2 Graphing dataThe next stage is VERY IMPORTANTLets 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 0.176Graphing dataThe values go from 30 up to 90...but you MUST start at zero

Use as much of your graph sheet as possiblebut make sure you go at least as far as 90ideally up to 100You must make equal sized intervals along your x axis

To measure g, the acceleration due to gravity, by freefalls /cm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0t2 / 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 0.176Try 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 freefalls /m18000016000014000012000010000080000600004000020000 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 itt2 / s2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0You must NEVER..join-the-dots!

Always pick a best-fit line. If the dots dont 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 freefalls /m18000016000014000012000010000080000600004000020000

t2 / ms2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

s /cm0.180.160.140.120.100.080.060.040.02

To measure g, the acceleration due to gravity, by freefallt2 / s2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0To 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 =

s /m(90, 0.176(0,0)To measure g, the acceleration due to gravity, by freefallt2 / s2 0.180.160.140.120.100.080.060.040.02

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

From the graph the units are:From the formula

Other suitable graphsA 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 1Boyles Law:You will be supplied with P and V measurements.

What will you plot against what?

ANS: P against 1/VP1/VSuitable graphs 2Measure g, using pendulumYou will be supplied with l and T measurements.

What will you plot against what?What is slope?

ANS: l against T2Slope = y/x = l /T2 = g/4lT2Suitable graphs 3Measure fundamental freq. against lengthYou 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) = (T/)f1/ lSuitable graphs 4Measure fundamental freq. against TensionYou 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)fTSuitable graphs 5Measure f of concave mirror or converging lensYou 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+y1/v1/u(1/u, 1/v)Suitable graphs 6Verify Snells LawYou will be supplied with

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