Honors Physics

Linearisation of Data

The purpose of most physics experiments is to determine relationships between physical variables in an observed phenomenon. Reliable relationships expressed in a formula involving the variables allows one to predict a physical outcome when there is a change in another physical variable.

Linearisation of Experimential Data

Given the following Data we wish to understand the relationship between Distance and Time

Time (s) Distance (m)
0.01 0.00
0.10 0.05
0.20 0.11
0.30 0.43
0.40 0.75
0.50 1.14
0.60 1.84
0.70 2.53
0.80 3.45
0.90 3.67
1.00 4.87

Step 1) Plot the data

Plot the Data Using Computer Software

Step 2) Identify the General Relationship

Given Our Data Plot and the Plots of our Basic Relationships We need to choose the one that is the best match when compared to our data

Plot Basic Relationship Our Data Plot

In Our Case our data is best matched by the Quadratic Plot y = k x2

Step 3) Linearise the Data

So as we can see we will need to square the time and then create a new plot

Step 4) Plot the Linearised Data

Data after Modification

Time (s) Time2 (s2) Distance (m)
0.01 0.0001 0.00
0.10 0.010 0.05
0.20 0.04 0.11
0.30 0.09 0.43
0.40 0.16 0.75
0.50 0.25 1.14
0.60 0.36 1.84
0.70 0.49 2.53
0.80 0.64 3.45
0.90 0.81 3.67
1.00 1.00 4.87

Distance = (1/2)ag time2

This means that our slope is equal to (1/2) ag, where ag is the acceleration due to gravity

ag = 9.79 m/s2 Which is our measured acceleration due to gravity

The accepted value for the acceleration due to gravity on Earth is 9.81 m/s2 so we
are in very good aggrement.