Reducing to linear form using a graphWatch

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#1
Does anyone know why it is important to reduce data to linear form to get a straight line on a graph+ evidence please?
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2 years ago
#2
Let's start at the start. Why do we do experiments? To test a hypothesis. How do we do it? By changing one variable and measuring the other.

Once we have a set of data, we plot it on a graph to obtain a straight line or curve. It is better to manipulate data to get a straight line graph because straight line are easy to model with a basic equation y = mx + c.

Also, a straight line has a very clear meaning - directly proportional. A curve could be an exponential or a simple x^n graph. Quite often the gradient of straight line is used to obtain a value. Take for example the determination of g by pendulum.

T = 2pi x sqrt(L/g)
Plotting a graph of T against L would give you a curve from which you couldn't use to find the value of g. But squaring both sides:

T^2 = 4pi^2 x L/g = (4pi^2/g) x L

Plotting a graph of T^2 against L will give a straight line of constant gradient where m = 4pi^2/g. A numerical value of m can be determined from the graph and the equation g = 4pi^2/m can be used to calculate g.

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