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Data Analysis Exercises

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Exercise 1
In an experiment, two variable quantities, x and y were measured. The relation between x and y is thought to be:

y = ax½
Results

x /m
±0·01m

y /s
±0·05
0·10 0·64
0·20 0·90
0·40 1·27
0·80 1·80
1·00 1·90
a) Plot a graph which could be used to verify the relation between x and y.
b) From the graph find the value of the constant, a.
c) Add to the graph "error bars" for the first and last results.

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Exercise 2
In an experiment, two variable quantities, x and y were measured. The relation between x and y is thought to be:

y = bx3
Results

x /cm
±0·02cm

y /g
±0·25g
0·67 2·25
0·80 4·00
0·90 5·52
0·95 6·60
a) Plot a graph which could be used to verify the relation between x and y.

b) Add "error bars" to the points on the graph.

c) Use the graph to estimate the maximum and minimum values of the constant, b. Give your final answer for b in the usual form:
b = (value) ± (indeterminacy)
d) What physical quantity might b represent ?

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Exercise 3
A point source of light was placed at different distances, r from a photo-electric cell. The current, I, generated by the cell was measured.
It is thought that the relation between I and r is of the form:
I = krn where k and n are constants
Now (as every ten year old child knows), taking logs of both sides of this equation gives us:

log I  = log k + n.log r
Results

r /cm
±0·5cm

I /mA
±2mA
15 108
20 _61
25 _39
30 _27
35 _24
40 _15
45 _12
a) Plot a graph which could be used to verify the relation between I and r
b) Use the graph to find the values of the constant n
c) Find the value of the constant k
d) A significant error was made in one of the measurements. Suggest a possible corrected value for this result.
e) Add "error bars" to the points representing the first and last results.

 

© David Hoult 2008